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Journal articles on the topic 'Foundations of quantum theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Barnum, Howard, Stephanie Wehner, and Alexander Wilce. "Introduction: Quantum Information Theory and Quantum Foundations." Foundations of Physics 48, no. 8 (2018): 853–56. http://dx.doi.org/10.1007/s10701-018-0188-6.

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2

Sudbery, Tony. "FOUNDATIONS OF QUANTUM GROUP THEORY." Bulletin of the London Mathematical Society 29, no. 6 (1997): 758–59. http://dx.doi.org/10.1112/s0024609397223283.

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3

Lee, Y. P. "Quantum $K$ -theory, I: Foundations." Duke Mathematical Journal 121, no. 3 (2004): 389–424. http://dx.doi.org/10.1215/s0012-7094-04-12131-1.

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4

D’Ariano, Giacomo Mauro, and Paolo Perinotti. "Quantum Information and Foundations." Entropy 22, no. 1 (2019): 22. http://dx.doi.org/10.3390/e22010022.

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5

Falkenburg, Brigitte, Harvey R. Brown, and Rom Harre. "Philosophical Foundations of Quantum Field Theory." Noûs 25, no. 4 (1991): 580. http://dx.doi.org/10.2307/2216085.

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6

Mittelstaedt, Peter. "Conceptual Foundations of Quantum Field Theory." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33, no. 1 (2002): 128–31. http://dx.doi.org/10.1016/s1355-2198(01)00042-9.

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7

Huggett, N. "Philosophical foundations of quantum field theory." British Journal for the Philosophy of Science 51, no. 4 (2000): 617–37. http://dx.doi.org/10.1093/bjps/51.4.617.

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8

Isaev, Petr S., and Elena A. Mamchur. "Conceptual Foundations of Quantum Field Theory." Physics-Uspekhi 43, no. 9 (2000): 953–58. http://dx.doi.org/10.1070/pu2000v043n09abeh000829.

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9

CHANG, L. N., Z. LEWIS, D. MINIC, and T. TAKEUCHI. "QUANTUM SYSTEMS BASED UPON GALOIS FIELDS — FROM SUB-QUANTUM TO SUPER-QUANTUM CORRELATIONS." International Journal of Modern Physics A 29, no. 03n04 (2014): 1430006. http://dx.doi.org/10.1142/s0217751x14300063.

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In this paper, we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.

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10

Felline, Laura. "Quantum Information Theory and the Foundations of Quantum Mechanics." International Studies in the Philosophy of Science 28, no. 3 (2014): 349–52. http://dx.doi.org/10.1080/02698595.2014.953348.

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11

Whitaker, M. "Theory and experiment in the foundations of quantum theory." Progress in Quantum Electronics 24, no. 1-2 (2000): 1–106. http://dx.doi.org/10.1016/s0079-6727(00)00002-1.

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12

Olavo, L. S. F. "Foundations of quantum mechanics: non-relativistic theory." Physica A: Statistical Mechanics and its Applications 262, no. 1-2 (1999): 197–214. http://dx.doi.org/10.1016/s0378-4371(98)00395-1.

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13

Gill, T. L., T. Morris, and S. K. Kurtz. "Foundations for Proper-time Relativistic Quantum Theory." Universal Journal of Physics and Application 9, no. 1 (2015): 24–40. http://dx.doi.org/10.13189/ujpa.2015.030104.

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14

Gill, Tepper L., Trey Morris, and Stewart K. Kurtz. "Foundations for proper-time relativistic quantum theory." Journal of Physics: Conference Series 615 (May 14, 2015): 012013. http://dx.doi.org/10.1088/1742-6596/615/1/012013.

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15

Rosen, Joe. "Symmetry at the foundations of quantum theory." Foundations of Physics 21, no. 11 (1991): 1297–304. http://dx.doi.org/10.1007/bf00732831.

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16

Danielewski, Marek, and Lucjan Sapa. "Foundations of the Quaternion Quantum Mechanics." Entropy 22, no. 12 (2020): 1424. http://dx.doi.org/10.3390/e22121424.

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We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.

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17

Barnett, Stephen M., John Jeffers, and David T. Pegg. "Quantum Retrodiction: Foundations and Controversies." Symmetry 13, no. 4 (2021): 586. http://dx.doi.org/10.3390/sym13040586.

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Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum retrodiction and highlight its intimate connection with the Bayesian interpretation of probability. The close link with Bayesian methods enables us to explore controversies and misunderstandings about retrodiction that have appeared in the literature. To be clear, quantum retrodiction is universally applicable and draws its validity directly from conventional predictive quantum theory coupled with Bayes’ theorem.

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18

CLARK, SEAN, DAVID HILL, and WEIQIANG WANG. "QUANTUM SUPERGROUPS I. FOUNDATIONS." Transformation Groups 18, no. 4 (2013): 1019–53. http://dx.doi.org/10.1007/s00031-013-9247-4.

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19

ZAUNER, GERHARD. "QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY." International Journal of Quantum Information 09, no. 01 (2011): 445–507. http://dx.doi.org/10.1142/s0219749911006776.

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This is a one-to-one translation of a German-written Ph.D. thesis from 1999. Quantum designs are sets of orthogonal projection matrices in finite(b)-dimensional Hilbert spaces. A fundamental differentiation is whether all projections have the same rank r, and furthermore the special case r = 1, which contains two important subclasses: Mutually unbiased bases (MUBs) were introduced prior to this thesis and solutions of b + 1 MUBs whenever b is a power of a prime were already given. Unaware of those papers, this concept was generalized here under the notation of regular affine quantum designs. Maximal solutions are given for the general case r ≥ 1, consisting of r(b2 - 1)/(b - r) so-called complete orthogonal classes whenever b is a power of a prime. For b = 6, an infinite family of MUB triples was constructed and it was — as already done in the author's master's thesis (1991) — conjectured that four MUBs do not exist in this dimension. Symmetric informationally complete positive operator-valued measures (SIC POVMs) in this paper are called regular quantum 2-designs with degree 1. The assigned vectors span b2 equiangular lines. These objects had been investigated since the 1960s, but only a few solutions were known in complex vector spaces. In this thesis further maximal analytic and numerical solutions were given (today a lot more solutions are known) and it was (probably for the first time) conjectured that solutions exist in any dimension b (generated by the Weyl–Heisenberg group and with a certain additional symmetry of order 3).

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20

Mrugała, Ryszard. "Lectures on quantum theory. Mathematical and structural foundations." Reports on Mathematical Physics 39, no. 3 (1997): 448–49. http://dx.doi.org/10.1016/s0034-4877(97)89760-1.

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21

Davies, E. B. "Some Remarks on the Foundations of Quantum Theory." British Journal for the Philosophy of Science 56, no. 3 (2005): 521–39. http://dx.doi.org/10.1093/bjps/axi129.

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22

Isham, Chris J., and Meinhard Mayer. "Lectures on Quantum Theory: Mathematical and Structural Foundations." Physics Today 49, no. 8 (1996): 66. http://dx.doi.org/10.1063/1.2807731.

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23

Weinberg, Steven, and O. W. Greenberg. "The Quantum Theory of Fields, Vol. 1: Foundations." Physics Today 48, no. 11 (1995): 78. http://dx.doi.org/10.1063/1.2808256.

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24

Isaev, Petr S., and Elena A. Mamchur. "Conceptual Foundations of Quantum Field Theory." Uspekhi Fizicheskih Nauk 170, no. 9 (2000): 1025. http://dx.doi.org/10.3367/ufnr.0170.200009l.1025.

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25

LOMBARDI, OLIMPIA, JUAN SEBASTIAN ARDENGHI, SEBASTIAN FORTIN, and MARTIN NARVAJA. "FOUNDATIONS OF QUANTUM MECHANICS: DECOHERENCE AND INTERPRETATION." International Journal of Modern Physics D 20, no. 05 (2011): 861–75. http://dx.doi.org/10.1142/s0218271811019074.

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In this paper, we review Castagnino's contributions to the foundations of quantum mechanics. First, we recall his work on quantum decoherence in closed systems, and the proposal of a general framework for decoherence from which the phenomenon acquires a conceptually clear meaning. Then, we introduce his contribution to the hard field of the interpretation of quantum mechanics: the modal-Hamiltonian interpretation solves many of the interpretive problems of the theory, and manifests its physical relevance in its application to many traditional models of the practice of physics. In the third part of this work we describe the ontological picture of the quantum world that emerges from the modal-Hamiltonian interpretation, stressing the philosophical step toward a deep understanding of the reference of the theory.

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26

Freire, Olival. "Quantum dissidents: Research on the foundations of quantum theory circa 1970." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40, no. 4 (2009): 280–89. http://dx.doi.org/10.1016/j.shpsb.2009.09.002.

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27

Chiribella, Giulio, and Xiao Yuan. "Quantum theory from quantum information: the purification route." Canadian Journal of Physics 91, no. 6 (2013): 475–78. http://dx.doi.org/10.1139/cjp-2012-0472.

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Quantum information provided a new angle on the foundations of quantum mechanics, where the emphasis is placed on operational tasks pertaining to information-processing and computation. In this spirit, several authors have proposed that the mathematical structure of quantum theory could (and should) be rebuilt from purely information-theoretic principles. Here we review the particular route proposed by D'Ariano, Perinotti, and one of the authors (Chiribella et al. Phys. Rev. A, 84, 012311 (2011)), with the purpose of giving a synopsis of the informational principles therein, along with a translation of those principles into the mathematical language of standard quantum theory.

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28

NICOLAIDIS, A. "CATEGORICAL FOUNDATION OF QUANTUM MECHANICS AND STRING THEORY." International Journal of Modern Physics A 24, no. 06 (2009): 1175–83. http://dx.doi.org/10.1142/s0217751x09043079.

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The unification of quantum mechanics and general relativity remains the primary goal of theoretical physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late 19th century. The Peircean logic has the mathematical structure of a category with the relation Rij among two individual terms Si and Sj, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus indicating category theory as the foundation of quantum mechanics. The same relational algebra generates a number of group structures, among them W∞. The group W∞ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories.

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29

Pulmannová, S. "On the role of quantum structures in the foundations of quantum theory." Soft Computing 5, no. 2 (2001): 135–36. http://dx.doi.org/10.1007/s005000100094.

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30

Singh, Tejinder P. "From quantum foundations to spontaneous quantum gravity – An overview of the new theory." Zeitschrift für Naturforschung A 75, no. 10 (2020): 833–53. http://dx.doi.org/10.1515/zna-2020-0073.

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AbstractSpontaneous localisation is a falsifiable dynamical mechanism which modifies quantum mechanics and explains the absence of position superpositions in the macroscopic world. However, this is an ad hoc phenomenological proposal. Adler’s theory of trace dynamics, working on a flat Minkowski space-time, derives quantum (field) theory and spontaneous localisation, as a thermodynamic approximation to an underlying noncommutative matrix dynamics. We describe how to incorporate gravity into trace dynamics, by using ideas from Connes’ noncommutative geometry programme. This leads us to a new quantum theory of gravity, from which we can predict spontaneous localisation and give an estimate of the Bekenstein-Hawking entropy of a Schwarzschild black hole.

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31

Bilban, Tina. "Realism and Antirealism in Informational Foundations of Quantum Theory." Quanta 3, no. 1 (2014): 32. http://dx.doi.org/10.12743/quanta.v3i1.24.

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32

Adler, Stephen L. "Quantum Theory as an Emergent Phenomenon: Foundations and Phenomenology." Journal of Physics: Conference Series 361 (May 10, 2012): 012002. http://dx.doi.org/10.1088/1742-6596/361/1/012002.

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33

Lewenstein, Maciej, Li You, J. Cooper, and K. Burnett. "Quantum field theory of atoms interacting with photons: Foundations." Physical Review A 50, no. 3 (1994): 2207–31. http://dx.doi.org/10.1103/physreva.50.2207.

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34

Oeckl, Robert. "General boundary quantum field theory: Foundations and probability interpretation." Advances in Theoretical and Mathematical Physics 12, no. 2 (2008): 319–52. http://dx.doi.org/10.4310/atmp.2008.v12.n2.a3.

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35

D'Ariano, Giacomo Mauro, and Andrei Khrennikov. "Preface of the special issue quantum foundations: information approach." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2068 (2016): 20150244. http://dx.doi.org/10.1098/rsta.2015.0244.

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This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory.

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36

Briggs, G. A. D., J. N. Butterfield, and A. Zeilinger. "The Oxford Questions on the foundations of quantum physics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2157 (2013): 20130299. http://dx.doi.org/10.1098/rspa.2013.0299.

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The twentieth century saw two fundamental revolutions in physics—relativity and quantum. Daily use of these theories can numb the sense of wonder at their immense empirical success. Does their instrumental effectiveness stand on the rock of secure concepts or the sand of unresolved fundamentals? Does measuring a quantum system probe, or even create, reality or merely change belief? Must relativity and quantum theory just coexist or might we find a new theory which unifies the two? To bring such questions into sharper focus, we convened a conference on Quantum Physics and the Nature of Reality. Some issues remain as controversial as ever, but some are being nudged by theory's secret weapon of experiment.

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37

Amaral, Barbara. "Resource theory of contextuality." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2157 (2019): 20190010. http://dx.doi.org/10.1098/rsta.2019.0010.

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In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental importance to study contextuality from the point of view of resource theories, which provide a powerful framework for the formal treatment of a property as an operational resource. In this contribution, we review recent developments towards a resource theory of contextuality and connections with operational applications of this property. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

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38

Khrennikov, Andrei. "Randomness: Quantum versus classical." International Journal of Quantum Information 14, no. 04 (2016): 1640009. http://dx.doi.org/10.1142/s0219749916400098.

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Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).

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39

RESCONI, GERMANO, GEORGE J. KLIR, and ELIANO PESSA. "CONCEPTUAL FOUNDATIONS OF QUANTUM MECHANICS: THE ROLE OF EVIDENCE THEORY, QUANTUM SETS, AND MODAL LOGIC." International Journal of Modern Physics C 10, no. 01 (1999): 29–62. http://dx.doi.org/10.1142/s0129183199000048.

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Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

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40

Asorey, M. "A concise introduction to quantum field theory." International Journal of Geometric Methods in Modern Physics 16, supp01 (2019): 1940005. http://dx.doi.org/10.1142/s021988781940005x.

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We review the basic principles of Quantum Field Theory (QFT) in a brief but comprehensive introduction to the foundations of QFT. The principles of QFT are introduced in canonical and covariant formalisms. The problem of ultraviolet (UV) divergences and its renormalization is analyzed in the canonical formalism. As an application, we review the roots of Casimir effect. For simplicity, we focus on the scalar field theory but the generalization for fermion fields is straightforward. However, the quantization of gauge fields require extra techniques which are beyond the scope of this paper. The special cases of free field theories and conformal invariant theories in lower space-time dimensions illustrate the relevance of the foundations of the theory. Finally, a short introduction to functional integrals and perturbation theory in the Euclidean formalism is included in the last section.

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41

Khrennikov, Andrei, and Karl Svozil. "Quantum Probability and Randomness." Entropy 21, no. 1 (2019): 35. http://dx.doi.org/10.3390/e21010035.

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42

Maudlin, Tim. "Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory." American Journal of Physics 86, no. 12 (2018): 953–55. http://dx.doi.org/10.1119/1.5050194.

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43

Marnham, Lachlan. "Quantum Information Theory and the Foundations of Quantum Mechanics, by Christopher G. Timpson." Contemporary Physics 55, no. 2 (2014): 149. http://dx.doi.org/10.1080/00107514.2014.885576.

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44

Agnesi, Costantino, Francesco Vedovato, Matteo Schiavon, et al. "Exploring the boundaries of quantum mechanics: advances in satellite quantum communications." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2123 (2018): 20170461. http://dx.doi.org/10.1098/rsta.2017.0461.

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Recent interest in quantum communications has stimulated great technological progress in satellite quantum technologies. These advances have rendered the aforesaid technologies mature enough to support the realization of experiments that test the foundations of quantum theory at unprecedented scales and in the unexplored space environment. Such experiments, in fact, could explore the boundaries of quantum theory and may provide new insights to investigate phenomena where gravity affects quantum objects. Here, we review recent results in satellite quantum communications and discuss possible phenomena that could be observable with current technologies. Furthermore, stressing the fact that space represents an incredible resource to realize new experiments aimed at highlighting some physical effects, we challenge the community to propose new experiments that unveil the interplay between quantum mechanics and gravity that could be realizable in the near future. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

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45

Swanson, Noel. "A philosopher's guide to the foundations of quantum field theory." Philosophy Compass 12, no. 5 (2017): e12414. http://dx.doi.org/10.1111/phc3.12414.

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46

Khrennikov, Andrei, and Gregor Weihs. "Preface of the Special Issue Quantum Foundations: Theory and Experiment." Foundations of Physics 42, no. 6 (2012): 721–24. http://dx.doi.org/10.1007/s10701-012-9644-x.

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47

Frank, Michael P., and Karpur Shukla. "Quantum Foundations of Classical Reversible Computing." Entropy 23, no. 6 (2021): 701. http://dx.doi.org/10.3390/e23060701.

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The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer’s Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.

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48

Syros, C. "On the Foundations of Statistical Nuclear Physics." HNPS Proceedings 1 (February 18, 2020): 179. http://dx.doi.org/10.12681/hnps.2836.

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The density matric for the nucleus, the canonical ensemble in second quantized mechanical definition of the temperature have from Quantum Field Theory. The evolution conservative or dissipalive form and is ergodic.

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49

Shojaei-Fard, Ali. "Formal aspects of non-perturbative Quantum Field Theory via an operator theoretic setting." International Journal of Geometric Methods in Modern Physics 16, no. 12 (2019): 1950192. http://dx.doi.org/10.1142/s0219887819501925.

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The paper builds the original foundations of a new operator theoretic setting for the study of quantum dynamics of non-perturbative aspects originated from Green’s functions in Quantum Field Theory with strong couplings.

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50

Zhang, Heng, Chao Su, Jiawei Bai, Rongyao Yuan, Yujun Ma, and Wenjun Wang. "The Rheological Analytical Solution and Parameter Inversion of Soft Soil Foundation." Symmetry 13, no. 7 (2021): 1228. http://dx.doi.org/10.3390/sym13071228.

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In soft soil engineering projects, the building loads are always required to be symmetrically distributed on the surface of the foundation to prevent uneven settlement. Even if the buildings and soft clay are controlled by engineers, it can still lead to the rheology of the foundation. The analytical solution based on the Laplace integral transformation method has positive significance for providing a simple and highly efficient way to solve engineering problems, especially in the long-term uneven settlement deformation prediction of buildings on soft soil foundations. This paper proposes an analytical solution to analyze the deformation of soft soil foundations. The methodology is based on calculus theory, Laplace integral transformation, and viscoelastic theory. It combines an analytical solution with finite theory to solve the construction sequences and loading processes. In addition, an improved quantum genetic algorithm is put forward to inverse the parameters of soft soil foundations. The analytical solution based on Laplace integral transformation is validated through an engineering case. The results clearly illustrate the accuracy of the method.

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