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Journal articles on the topic 'Feynman technique'

Author: Grafiati

Published: 7 June 2025

Last updated: 16 July 2025

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1

Haldar, Ankur. "Modification of Feynman Technique of Differentiation." International Journal of Science and Research (IJSR) 11, no. 11 (2022): 456–57. http://dx.doi.org/10.21275/sr221103004432.

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2

Le, Khanh Linh, and Thi Kieu Oanh Pham. "Enhancing Grade 10 Students' Vocabulary Retention Using the Feynman Technique." International Journal of Social Science and Human Research 08, no. 03 (2025): 1647–58. https://doi.org/10.5281/zenodo.15082139.

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This study explored the effectiveness of the Feynman technique in improving vocabulary retention among Grade 10 students. The research involved a structured intervention using the Feynman technique, a cognitive approach aimed at fostering a deeper understanding and long-term retention of vocabulary through simplified explanations and active participation. A total of 20 Grade 10 students participated in a seven-week program, during which they applied the Feynman technique to learn and retain new vocabulary introduced during English lessons. To evaluate the impact, pre- and post-intervention assessments, including vocabulary quizzes and retention tests, were conducted to measure vocabulary acquisition and retention. Additionally, a survey was administered to gather students feedback on the technique and its perceived effectiveness. The findings showed a notable improvement in vocabulary retention, with students demonstrating greater understanding and more accurate recall of vocabulary items after employing the technique. The survey results also indicated that students found the approach engaging and effective, reporting a positive attitude toward its use in vocabulary learning. Based on these results, the researchers recommend the Feynman technique be integrated into vocabulary teaching strategies to enhance retention and comprehension among Grade 10 learners.

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3

Reyes, Englevert, Ron Mhel Francis Blanco, Defanee Rose Doroon, Jay Lord Limana, and Ana Marie Torcende. "Feynman Technique as a Heutagogical Learning Strategy for Independent and Remote Learning." Recoletos Multidisciplinary Research Journal 9, no. 2 (2021): 1–13. http://dx.doi.org/10.32871/rmrj2109.02.06.

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The Feynman Technique is a mental model and learning strategy used to simplify any complex information. This study endeavors to provide empirical evidence on the effectiveness of the Feynman Technique as a heutagogy-based learning strategy that fits the e-learning landscape. Utilizing true experimental research design, grades 4, 7, and 11 students from typical elementary and national high schools were randomly assigned to experimental and control groups and underwent pre- and posttests. Using two-sample and paired T-tests, results show that students under the experimental group, which applied the Feynman Technique, showed higher posttest scores and learning gains than those in the control group. Hence, this study proves that the Feynman Technique can be an effective tool to improve K-12 students’ learning, especially now given the new learning delivery modalities.

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4

Fitriah, Siti, Siti Zulfa Agustin, Yoga Mestika Putra, Ulil Amri, and Aprilia Kartika Putri. "Sosialisasi Teknik Feynman Untuk Meningkatkan Kualitas Belajar Siswi MTSS Al Fattah Kabupaten Sarolangun." Estungkara: Jurnal Pengabdian Pendidikan Sejarah 3, no. 1 (2024): 84–93. https://doi.org/10.22437/est.v3i1.32636.

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The aim of this activity is to socialize learning techniques to improve the quality of learning of MTSS Al Fattah students in Sarolangun district. This activity is carried out to increase students' comprehension ability in understanding the lesson material. Therefore, we need a fairly effective technique that can be easily applied. The Feynman technique is a learning technique that is quite effective in overcoming this problem. The implementation of this service activity is carried out in two stages, namely the planning stage and the implementation stage. At the planning stage, the material that needs to be used as a learning object is determined. At the implementation stage, the lecture and question and answer method was applied. The lecture method is used to introduce the Feynman technique and how to apply it, and the question and answer method is used to determine the extent to which students understand the presentation and application of the Feynman technique in the learning process. The results of the assessment rubric showed that the majority of students can easily understand the lesson material after using the Feynman technique. It is known from the researchers' assessment that almost 72% of MTSS Al Fattah students can deliver material in front of the class very well. Apart from that, this service activity also received a positive response from the majority of MTSS Al Fattah students.

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5

Schelstraete, Sigurd, and Henri Verschelde. "A technique for generating Feynman diagrams." Zeitschrift für Physik C Particles and Fields 67, no. 2 (1995): 343–49. http://dx.doi.org/10.1007/bf01571297.

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6

Şavkli, Çetin. "Feynman-Schwinger technique in field theories." Czechoslovak Journal of Physics 51, S2 (2001): B71—B102. http://dx.doi.org/10.1007/s10582-001-0049-x.

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7

Travero, Arnel S., Charlito M. Castrodes, and Paul John B. Panganiban. "Students’ Perceptions of Feynman Technique in Mathematics Learning: A Case of a State University in Claveria, Misamis Oriental." Research and Analysis Journal 8, no. 06 (2025): 01–05. https://doi.org/10.18535/raj.v8i06.535.

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Mathematics learning remains a significant challenge for many students due to its perceived complexity and the limitations of traditional teaching methods. The Feynman Technique, an active learning strategy that emphasizes self-explanation and simplification of concepts, has been proposed as an effective tool for enhancing comprehension and engagement in mathematics. This study explores students’ perceptions of the Feynman Technique in learning mathematics at a state university in Claveria, Misamis Oriental. Employing a phenomenological qualitative research design, data were collected through semi-structured interviews and reflective journals from purposively selected mathematics students who had experience using the technique. Thematic analysis revealed that students perceived the Feynman Technique as beneficial in fostering deeper conceptual understanding, increasing engagement, and enhancing confidence in learning mathematics. However, challenges such as difficulty in simplifying complex concepts and self-doubt in explanations were also identified. Despite these challenges, students generally preferred the technique over traditional methods and recommended its use for improving mathematics learning. The findings suggest that integrating the Feynman Technique into mathematics education can support active learning and self-directed knowledge construction. Educators should provide scaffolding and structured guidance to maximize its effectiveness. Future research may explore its long-term impact on academic performance and its applicability across different mathematical topics.

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8

Bsharat, Tahani R. K., Lasmi Febrianingrum, and Mosleh Habibullah. "Empowering Language Learners: Unleashing the Potential of The Feynman Technique in English Language Acquisition." PANYONARA: Journal of English Education 6, no. 2 (2024): 67–78. https://doi.org/10.19105/panyonara.v6i2.14936.

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Abstract: This study investigates the effectiveness of the Feynman Technique in enhancing English language learning (ELL) outcomes. As a relatively new approach compared to traditional language instruction methods, the Feynman Technique emphasizes deeper understanding, active learning, and metacognitive reflection. Using a mixed-methods quasi-experimental design with pre- and post-intervention assessments, alongside observations and interviews, this research explores its impact on language proficiency and learning experiences in L2 English learners. Results demonstrate a significant improvement in language proficiency, with scores increasing from an average of 65% in pre-intervention assessments to 82% post-intervention, indicating a 17% improvement. Additionally, students reported increased confidence and engagement. In conclusion, the Feynman Technique has the potential to revolutionize language education by enabling students to become more autonomous and capable in a global context.

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9

Nassar, Antônio B. "Feynman propagator and space-time transformation technique." Physica A: Statistical Mechanics and its Applications 141, no. 1 (1987): 24–32. http://dx.doi.org/10.1016/0378-4371(87)90259-7.

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10

Lam, C. S. "Spinor helicity technique and string reorganization for multiloop diagrams." Canadian Journal of Physics 72, no. 7-8 (1994): 415–38. http://dx.doi.org/10.1139/p94-058.

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11

Pang, Alex C. Y., and Chueng-Ryong Ji. "A Spinor Technique in Symbolic Feynman Diagram Calculation." Journal of Computational Physics 115, no. 2 (1994): 267–75. http://dx.doi.org/10.1006/jcph.1994.1194.

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12

Zaidi, H. R. "Calculation of the squeezing spectrum using a Feynman-diagram technique." Canadian Journal of Physics 66, no. 2 (1988): 164–67. http://dx.doi.org/10.1139/p88-024.

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The squeezing spectrum of a parametric amplifier, with a quantized pump field, is calculated using the Feynman-diagram technique. The results of the existing theories are recovered. The connection with the theory of superconductivity becomes transparent in this approach.

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13

Chekhov, Leonid, and Bertrand Eynard. "Matrix eigenvalue model: Feynman graph technique for all genera." Journal of High Energy Physics 2006, no. 12 (2006): 026. http://dx.doi.org/10.1088/1126-6708/2006/12/026.

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14

Yamane, Yoshihiro, Tsuyoshi Misawa, Seiji Shiroya та Hironobu Unesaki. "Formulation of data synthesis technique for Feynman-α method". Annals of Nuclear Energy 25, № 1-3 (1998): 141–48. http://dx.doi.org/10.1016/s0306-4549(97)00034-0.

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15

FACHIN, STEFANO, and GEORGE LEIBBRANDT. "TECHNIQUE FOR DERIVING FEYNMAN INTEGRALS IN AXIAL-TYPE GAUGES." International Journal of Modern Physics A 10, no. 19 (1995): 2747–67. http://dx.doi.org/10.1142/s0217751x95001297.

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Employing the [Formula: see text] prescription for axial-type gauges, and working in the unified-gauge formalism defined by nμ and the null vector Fμ, we develop a simple technique for evaluating higher-rank integrals from known lower-rank integrals. Based on partial differentiation and implementation of an auxiliary constraint condition, the technique is applicable to a wide variety of integrals containing either single, double or triple spurious poles. We illustrate our procedure with several examples. There are strong indications that the new technique is also capable of generating the finite parts of axial-type integrals.

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16

Nikolov, Nikolay M., Raymond Stora, and Ivan Todorov. "Renormalization of massless Feynman amplitudes in configuration space." Reviews in Mathematical Physics 26, no. 04 (2014): 1430002. http://dx.doi.org/10.1142/s0129055x14300027.

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A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincaré covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.

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17

ARGERI, MARIO, and PIERPAOLO MASTROLIA. "FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS." International Journal of Modern Physics A 22, no. 24 (2007): 4375–436. http://dx.doi.org/10.1142/s0217751x07037147.

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We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D = 4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

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18

Groote, S., and A. A. Pivovarov. "Threshold expansion of Feynman diagrams within a configuration space technique." Nuclear Physics B 580, no. 1-2 (2000): 459–84. http://dx.doi.org/10.1016/s0550-3213(00)00260-1.

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19

Kotikov, A. V. "Differential equations method. New technique for massive Feynman diagram calculation." Physics Letters B 254, no. 1-2 (1991): 158–64. http://dx.doi.org/10.1016/0370-2693(91)90413-k.

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20

Okuda, Ryohei, Atsushi Sakon, Sin-ya Hohara, Wataru Sugiyama, Hiroshi Taninaka та Kengo Hashimoto. "An improved Feynman-α analysis with a moving–bunching technique". Journal of Nuclear Science and Technology 53, № 10 (2016): 1647–52. http://dx.doi.org/10.1080/00223131.2015.1125310.

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21

Egorov, Vadim, and Timofei Rusalev. "Quantum field-theoretical descriprion of neutrino oscillations in T2K experiment." EPJ Web of Conferences 222 (2019): 03002. http://dx.doi.org/10.1051/epjconf/201922203002.

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We consider neutrino oscillations in the T2K experiment using a new quantum field-theoretical approach to the description of processes passing at finite space-time intervals. It is based on the Feynman diagram technique in the coordinate representation, supplemented by modified rules of passing to the momentum representation. Effectively this leads to the Feynman propagators in the momentum representation being modified, while the rest of the Feynman rules remain unchanged. The approach does not make use ofwave packets, the initial and final particle states are described by plane waves, which essentially simplifies the calculations. The oscillation fading out due to momentum distribution of the initial particles is taken into account. The obtained results reproduce the predictions of the standard description and confirm that the far detector position corresponds to the first minimum for muon production probability and the first maximum for electron production probability.

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22

Pukach, Petro, Yurii Chernukha, Olha Chernukha, Yurii Bilushchak, and Myroslava Vovk. "Mathematical Modeling of Impurity Diffusion Processes in a Multiphase Randomly Inhomogeneous Body Using Feynman Diagrams." Symmetry 17, no. 6 (2025): 920. https://doi.org/10.3390/sym17060920.

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Modeling of impurity diffusion processes in a multiphase randomly inhomogeneous body is performed using the Feynman diagram technique. The impurity diffusion equations are formulated for each of the phases separately. Their random boundaries are subject to non-ideal contact conditions for concentration. The contact mass transfer problem is reduced to a partial differential equation describing diffusion in the body as a whole, which accounts for jump discontinuities in the searched function as well as in its derivative at the stochastic interfaces. The obtained problem is transformed into an integro-differential equation involving a random kernel, whose solution is constructed as a Neumann series. Averaging over the ensemble of phase configurations is performed. The Feynman diagram technique is developed to investigate the processes described by parabolic partial differential equations. The mass operator kernel is constructed as a sum of strongly connected diagrams. An integro-differential Dyson equation is obtained for the concentration field. In the Bourret approximation, the Dyson equation is specified for a multiphase randomly inhomogeneous medium with uniform phase distribution. The problem solution, obtained using Feynman diagrams, is compared with the solutions of diffusion problems for a homogeneous layer, one having the coefficients of the base phase and the other having the characteristics averaged over the body volume.

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23

Kalinovsky, Yuriy L., Alexandra V. Friesen, Elizaveta D. Rogozhina, and Lyubov’ I. Golyatkina. "Application of a computer algebra systems to the calculation of the \(\pi\pi\)-scattering amplitude." Discrete and Continuous Models and Applied Computational Science 28, no. 3 (2020): 216–29. http://dx.doi.org/10.22363/2658-4670-2020-28-3-216-229.

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The aim of this work is to develop a set of programs for calculation the scattering amplitudes of the elementary particles, as well as automating the calculation of amplitudes using the appropriate computer algebra systems (Mathematica, Form, Cadabra). The paper considers the process of pion-pion scattering in the framework of the effective Nambu-Iona-Lasinio model with two quark flavours. The Package-X for Mathematica is used to calculate the scattering amplitude (starting with the calculation of Feynman diagrams and ending with the calculation of Feynman integrals in the one-loop approximation). The loop integrals are calculated in general kinematics in Package-X using the Feynman parametrization technique. A simple check of the program is made: for the case with zero temperature, the scattering lengths \(a_0 = 0.147\) and \(a_2 = -0.0475\) are calculated and the total cross section is constructed. The results are compared with other models as well as with experimental data.

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24

Li, Jiaqi. "Feynman Integral Problem Solving Techniques: Application on Parametric Integrals." Highlights in Business, Economics and Management 45 (December 24, 2024): 348–53. https://doi.org/10.54097/sb6k3s37.

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This paper focuses on parametric integration in Feynman integral solving technique. This paper mainly introduces the theory of integration and the method of solving the problem. This paper mainly introduces the methods and techniques of indefinite integral method and definite integral method, and introduces the methods under these two categories in detail. Different methods and techniques are adopted in this paper, and many application examples are listed. Parametric integrals have many advantages, such as rich expressions. Parametric integrals can represent a wide range of functions, including important functions in theory and practice, and have important applications in many fields. Secondly, complex integrals can be solved. For some complex integral problems, especially when the original function is not an elementary function, it may be very difficult to solve them directly. However, parametric integrals provide a new way to solve such problems by introducing parameters and exchanging operation order. Moreover, it can effectively solve practical application problems and promote the development of mathematics. The study of parametric integral not only enricheth the content of mathematical theory, but also enables mathematicians to have a deeper understanding of the properties of functions, the nature of integrals and the internal relations between them through the study of parametric integral.

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25

L’Yi*, Won Sik. "Feynman Diagrammatic Calculation Technique in Non-relativistic Quantum Mechanical Perturbation Theory." New Physics: Sae Mulli 72, no. 7 (2022): 537–43. http://dx.doi.org/10.3938/npsm.72.537.

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26

Chekhov, Leonid, and Bertrand Eynard. "Hermitian matrix model free energy: Feynman graph technique for all genera." Journal of High Energy Physics 2006, no. 03 (2006): 014. http://dx.doi.org/10.1088/1126-6708/2006/03/014.

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27

Kitamura, Yasunori, Tsuyoshi Misawa, Hironobu Unesaki та Seiji Shiroya. "General formulae for the Feynman-α method with the bunching technique". Annals of Nuclear Energy 27, № 13 (2000): 1199–216. http://dx.doi.org/10.1016/s0306-4549(99)00113-9.

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28

Preti, Michelangelo. "STR: A Mathematica package for the method of uniqueness." International Journal of Modern Physics C 31, no. 10 (2020): 2050146. http://dx.doi.org/10.1142/s0129183120501466.

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We present Star–Triangle Relations (STRs), a Mathematica® package designed to solve Feynman diagrams by means of the method of uniqueness in any Euclidean space-time dimension. The method of uniqueness is a powerful technique to solve multi-loop Feynman integrals in theories with conformal symmetry imposing some relations between the powers of propagators and the space-time dimension. In our algorithm, we include both identities for scalar and Yukawa type integrals. The package provides a graphical environment in which it is possible to draw the desired diagram with the mouse input and a set of tools to modify and compute it. Throughout the use of a graphic interface, the package should be easily accessible to users with little or no previous experience on diagrams computation. This manual includes some pedagogical examples of computation of Feynman graphs as the scalar two-loop kite master integral and a fermionic diagram appearing in the computation of the spectrum of the [Formula: see text]-deformed [Formula: see text] SYM in the double scaling limit.

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29

Su, Z. B. "Path Integral Study of Polaron Transport under High Electric Field." International Journal of Modern Physics B 06, no. 07 (1992): 1059–78. http://dx.doi.org/10.1142/s0217979292000554.

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With help of the nonequilibrium Green’s function technique and the Feynman path integral theory, we present a self-consistent approach to the Thornber-Feynman model of a polaron under high electric field. The applied field and the electron-phonon interaction both are treated non-perturbatively so that the high-field effect as well as the quantum interference effect have been taken into account. A set of coupled equations are derived to consistently describe the drift motion and the fluctuation of the electron. By solving these equations numerically we obtain (1) the nonlinear relation between the drift velocity and the applied electric field; (2) the effective electron temperature, the nonequilibrium noise, and the distribution functions.

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30

Zdyb, Tatiana. "The Audacity Health Method: Enhancing Therapeutic Understanding and Client Empowerment." Journal of Educational & Psychological Research 6, no. 2 (2024): 01–04. http://dx.doi.org/10.33140/jepr.06.02.03.

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The Audacity Health method utilizes the Feynman Technique, a learning method developed by Nobel Prize-winning physicist Richard Feynman. It emphasizes deep understanding and simplification of complex concepts through teaching. This paper explores the application of the technique within the context of psychotherapy to enhance both therapist and client comprehensions of psychological processes. Implementing a step-by-step approach, therapists can break down and demystify intricate behavioural and emotional patterns, facilitating a more profound grasp of factors that cause and maintain the mental illness the individual is seeking therapy to treat. Through a case study example, this paper demonstrates how the method can be employed to clarify the client’s issues, empowering them to gain insight into their mental health and generate solutions for symptoms. The outcomes suggest that the Audacity Health method fosters more effective communication, reinforces therapeutic alliance, and promotes active client participation in treatment. Ultimately, this integration aims to optimize therapeutic efficacy by merging educational simplification with evidence-based psychotherapeutic interventions to advance mental health.

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31

Kitamura, Yasunori, and Tsuyoshi Misawa. "Theory of Feynman-alpha technique with masking window for accelerator-driven systems." Annals of Nuclear Energy 103 (May 2017): 470–79. http://dx.doi.org/10.1016/j.anucene.2017.01.038.

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32

Kotikov, A. V. "The Gegenbauer Polynomial technique: the evaluation of a class of Feynman diagrams." Physics Letters B 375, no. 1-4 (1996): 240–48. http://dx.doi.org/10.1016/0370-2693(96)00226-2.

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33

LEI, X. L., and M. W. WU. "FEYNMAN DIAGRAM EXPANSION IN THE BALANCE-EQUATION TRANSPORT THEORY." Modern Physics Letters B 06, no. 30 (1992): 1935–41. http://dx.doi.org/10.1142/s0217984992001642.

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In the balance-equation theory for hot-electron transport, the fact that electrons and phonons have different temperatures in the initial density matrix prevents one from directly invoking the conventional statistical Wick theorem to carry out a high-order perturbation analysis. Nevertheless, the well-known Feynman rules and diagram technique are demonstrated to be applicable to any order of the electron—impurity and electron—phonon interactions within the Keldysh Green’s function formalism of this theory.

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34

Egorov, Vadim, and Igor Volobuev. "Description of processes passing at finite space and time intervals in the framework of QFT." EPJ Web of Conferences 222 (2019): 01009. http://dx.doi.org/10.1051/epjconf/201922201009.

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We consider a new approach to the description in the framework of QFT of processes passing at finite space and time intervals. The formalism is based on the Feynman diagram technique in the coordinate representation, in which the rules of passing to the momentum representation are modified in accordance with the experimental setup of neutrino oscillation experiments. In effect, only the propagators of particles in the momentum representation are modified, while all the other standard Feynman rules in the momentum representation remain the same. Since the initial and final particle states are described by plane waves, the approach does not need the use of wave packets, which greatly simplifies the calculations of amplitudes. Taking as examples the processes of displaced pion decay, neutral kaon and neutrino oscillations we show that the approach under consideration correctly reproduces the known standard results.

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35

CORCORAN, J. N., U. SCHNEIDER, and H. B. SCHÜTTLER. "PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS." International Journal of Modern Physics C 17, no. 11 (2006): 1527–49. http://dx.doi.org/10.1142/s0129183106009989.

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We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

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36

Aguilera-Verdugo, José de Jesús, Félix Driencourt-Mangin, Roger José Hernández-Pinto, et al. "A Stroll through the Loop-Tree Duality." Symmetry 13, no. 6 (2021): 1029. http://dx.doi.org/10.3390/sym13061029.

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The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.

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37

Hanh, Dinh Thi. "All-order calculations of the energy levels of heavy elements Indium (In) and Tin (Sn)." Tạp chí Khoa học 14, no. 9 (2019): 34. http://dx.doi.org/10.54607/hcmue.js.14.9.286(2017).

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The energy levels of the heavy elements In, Sn+ and Sn are presented in this article. Dominating corrections beyond the relativistic Hartree-Fock method are included to all orders in the Coulomb interaction using the Feynman diagram technique and the correlation potential method. The configuration interaction technique is combined with the many-body perturbation theory to construct the many-electron wave function for valence electrons and to include core-valence correlations. The good agreement of the results of our calculation with experiment data illustrates the power of the method.

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38

Pismensky, A. L. "Calculation of critical index η of the φ3-theory in four-loop approximation by the conformal bootstrap technique". International Journal of Modern Physics A 30, № 24 (2015): 1550138. http://dx.doi.org/10.1142/s0217751x15501389.

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The method of calculation of [Formula: see text]-expansion in model of scalar field with [Formula: see text]-interaction based on conformal bootstrap equations is proposed. This technique is based on self-consistent skeleton equations involving full propagator and full triple vertex. Analytical computations of the Fisher’s index [Formula: see text] are performed in four-loop approximation. The three-loop result coincides with one obtained previously by the renormalization group equations technique based on calculation of a larger number of Feynman diagrams. The four-loop result agrees with its numerical value obtained by other authors.

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39

Wen, Hao, Yantao Luo, Jianhua Huang, and Yuhong Li. "Stochastic travelling wave solution of the $ N $-species cooperative systems with multiplicative noise." Electronic Research Archive 31, no. 8 (2023): 4406–26. http://dx.doi.org/10.3934/era.2023225.

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<abstract><p>The current paper is devoted to the stochastic $ N $-species cooperative system with a moderately strong noise. By the theory of monotone random systems and the technique of suitable marker of wavefront, the existence of the travelling wave solution is established. By applying the Feynman-Kac formula and sup-sub solution technique, the upper and lower bounded of the asymptotic wave speed are also obtained. Finally, we give an example for stochastic 3-species cooperative systems.</p></abstract>

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40

Wallerbos, E. J. M., та J. E. Hoogenboom. "Experimental demonstration of the finite measurement time effect on the Feynman-α technique". Annals of Nuclear Energy 25, № 15 (1998): 1247–52. http://dx.doi.org/10.1016/s0306-4549(98)00024-3.

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41

Altshuler, Boris L. "“Old” conformal bootstrap on AdS: O(N) symmetric scalar model." International Journal of Modern Physics A 35, no. 01 (2020): 2050001. http://dx.doi.org/10.1142/s0217751x20500013.

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Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger–Keldysh formalism is used in AdS/CFT instead of conventional Feynman–Witten diagrams technique, permits to calculate values of conformal dimensions in the [Formula: see text] symmetric model with conformal or composite Habbard–Stratonovich field.

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Obrezkov, Oleg O. "The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold." Infinite Dimensional Analysis, Quantum Probability and Related Topics 06, no. 02 (2003): 311–20. http://dx.doi.org/10.1142/s0219025703001109.

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A full proof of the Feynman–Kac-type formula for heat equation on a compact Riemannian manifold is obtained using some ideas originating from the papers of Smolyanov, Truman, Weizsaecker and Wittich.1-3 In particular, the technique exploited in the paper has some common lines with Chernoff theorem, which is one of the basic points of the approach to the topics undertaken in the above-mentioned papers.

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TAKAHASHI, YASUSHI, and HIROOMI UMEZAWA. "THERMO FIELD DYNAMICS." International Journal of Modern Physics B 10, no. 13n14 (1996): 1755–805. http://dx.doi.org/10.1142/s0217979296000817.

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A quantum field theory at finite temperature is presented. The temperature dependent vacuum is defined such that the vacuum expectation value agrees with the statistical average. The vacuum states with different temperature are connected by a Bogoliubov transformation. Our formalism allows the use of the Feynman diagrams for the causal Green’s function and the Bethe-Salpeter technique for bound states at finite temperature, The entropy operator is introduced.

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Xu, He, Xueting Li, and Wendi Cai. "Enhanced Feynman-Kac Formula for Nonlinear Uncertainty Quantification Problems." Highlights in Science, Engineering and Technology 107 (August 15, 2024): 259–67. http://dx.doi.org/10.54097/ej17cr76.

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Uncertainty qualification (UQ) issues and partial differential equations (PDEs) are becoming hot topics in the fields of physic and engineering. There are a various number of strategies for handling unknown linear PDEs, including Monte Carlo and the polynomial regression approach. Nevertheless, nonlinear issues could not be effectively solved using existing approach. This paper focuses primarily on a novel method, an enhanced Feynman-Kac formula with a Least Squares Monte Carlo approach. Numerical experiments were conducted in our research to verify its efficacy and convergence. This paper discovers that the enhanced approach exhibits strong performance regarding nonlinear PDE and UQ scenarios with high accuracy and strong performance of convergence. In the future, this technique might be efficiently applied in the fields of engineering and finance in real-world scenarios.

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Adzhemyan, Loran Ts, Michal Hnatič, Mikhail V. Kompaniets, Tomáš Lučivjanský, and Lukáš Mižišin. "Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation." EPJ Web of Conferences 173 (2018): 02001. http://dx.doi.org/10.1051/epjconf/201817302001.

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The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ε = 4 − d.

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Franco, D. H. T., H. C. G. Caldas, A. L. Mota, and M. C. Nemes. "On the Renormalization of the Chiral Fermion Meson Model: An Algebraic Approach." Modern Physics Letters A 12, no. 14 (1997): 1041–49. http://dx.doi.org/10.1142/s0217732397001060.

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We re-investigate the problem of the renormalizability of the chiral fermion meson model on the light of the regularization-independent algebraic method. The present letter is intended as a useful application of a modern technique in theory of current interest for the description of low energy hadron phenomenology. We show that the model is stable under radiative corrections and anomaly free in a regularization-free way without having to resort to the explicit calculation of Feynman diagrams.

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SAKODA, SEJII. "EXACTNESS IN THE PATH INTEGRAL OF THE COULOMB POTENTIAL IN ONE SPACE DIMENSION." Modern Physics Letters A 23, no. 36 (2008): 3057–76. http://dx.doi.org/10.1142/s0217732308028491.

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We solve time-sliced path integrals of one-dimensional Coulomb system in an exact manner. In formulating path integrals, we make use of the Duru–Kleinert transformation with Fujikawa's gauge theoretical technique. Feynman kernels in the momentum representation both for bound states and scattering states will be obtained with clear pole structure that explains the exactness of the path integral. The path integrals presented here can be, therefore, evaluated exactly by making use of Cauchy's integral theorem.

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McKeon, D. G. C. "The effective Lagrangian and the scale anomaly in the nonlinear σ model". Canadian Journal of Physics 70, № 6 (1992): 455–57. http://dx.doi.org/10.1139/p92-076.

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We compute the one-loop effective Lagrangian for the generally covariant nonlinear σ model in two dimensions, using a technique of Bukbinder et al. This circumvents the need to evaluate Feynman diagrams and eliminates having to introduce a mass to serve as an infrared regulator. The two-dimensional space is assumed to have Weyl geometry. In the limit that the Weyl geometry becomes Riemannian, the standard result for the anomaly in the trace of the stress tensor is recovered.

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Menon, Madhu, and Roland E. Allen. "New technique for molecular-dynamics computer simulations: Hellmann-Feynman theorem and subspace Hamiltonian approach." Physical Review B 33, no. 10 (1986): 7099–101. http://dx.doi.org/10.1103/physrevb.33.7099.

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Pierotti, Marco A., Claudio Lombardo, and Camillo Rosano. "Nanotechnology: Going Small for a Giant Leap in Cancer Diagnostics and Therapeutics." Tumori Journal 94, no. 2 (2008): 191–96. http://dx.doi.org/10.1177/030089160809400210.

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“There is Plenty of Room at the Bottom” - not just “There is Room at the Bottom.” What I have demonstrated is that there is room - that you can decrease the size of things in a practical way. I now want to show that there is plenty of room. Richard Feynman, December 29, 1959 More than 30 years ago Richard Feynman pointed out that physicists knew no limits to prevent us from doing engineering at the level of atoms. Until recently, though, while the lack of physical limits was accepted as commonplace, molecular engineering was thought of as impractical, unnecessary, or requiring breakthroughs in knowledge and technique that placed it somewhere in the distant future. Many visionaries intimately familiar with the development of silicon technology still forecast it would take between 20 and 50 years before molecular engineering became a reality. This is well beyond the planning horizon of most companies. But recently, everything has begun to change. After the industrial revolution and the “computer age”, are we really facing a new era?

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