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Journal articles on the topic 'Superspace formalism'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Bonora, Loriano, and Rudra Prakash Malik. "BRST and Superfield Formalism—A Review." Universe 7, no. 8 (2021): 280. http://dx.doi.org/10.3390/universe7080280.

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This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for w

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2

Lasukov, V. V. "String formalism in superspace-time." Russian Physics Journal 54, no. 7 (2011): 801–13. http://dx.doi.org/10.1007/s11182-011-9687-z.

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3

FAIZAL, MIR. "HARMONIC SUPERSPACE GAUGEON FORMALISM FOR THE ABJM THEORY." Modern Physics Letters A 27, no. 26 (2012): 1250147. http://dx.doi.org/10.1142/s0217732312501477.

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In this paper, we will analyze the ABJM theory in harmonic superspace. The harmonic superspace variables will be parametrized by the coset SU(2)/U(1) and thus will have manifest [Formula: see text] supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical subspace from the total Hilbert space. We will also show that the evolution of the [Formula: see text]-matrix is unitary for this ABJM theory in harmonic superspace.

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4

Aratyn, H., C. Rasinariu, and A. Das. "Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace." Modern Physics Letters A 12, no. 34 (1997): 2623–30. http://dx.doi.org/10.1142/s0217732397002752.

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We generalize the Drinfeld–Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl (n+1,n), providing the Hermitian symmetric space structure.

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5

Madsen, Jens Ole, and Eric Ragoucy. "Quantum hamiltonian reduction in superspace formalism." Nuclear Physics B 429, no. 2 (1994): 277–90. http://dx.doi.org/10.1016/0550-3213(94)00258-4.

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6

Bereciartua, P. J., F. J. Zuñiga, J. M. Perez-Mato, et al. "Structure refinement and superspace description of the system Bi2(n + 2)Mo n O6(n + 1) (n = 3, 4, 5 and 6)." Acta Crystallographica Section B Structural Science 68, no. 4 (2012): 323–40. http://dx.doi.org/10.1107/s0108768112017478.

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The system Bi2(n + 2)Mo n O6(n + 1) is described within the superspace formalism. Two superspace models are proposed for the different members of this family, depending on the parity of the parameter n. The superspace model for the odd members is constructed through the embedding of the cationic distribution of the member with n = 3, and the modification of a superspace model previously proposed for the compound Bi2MoO6. However, this model cannot be applied to the even members of the family. Performing the appropriate transformations, a suitable superspace model for the even members is obtain

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7

Sofi, Ashaq Hussain, and Sajad Ul Majeed. "Chern-Simons-Matter Theory in Superspace Formalism." OALib 02, no. 04 (2015): 1–8. http://dx.doi.org/10.4236/oalib.1101421.

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8

McKeon, D. G. C. "Harmonic superspace with four-dimensional Euclidean space." Canadian Journal of Physics 78, no. 4 (2000): 261–66. http://dx.doi.org/10.1139/p00-048.

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The supersymmetry algebra in four-dimensional Euclidean space is formulated in such a way that an SU(2) invariance of the algebra is apparent. This leads to a superfield formalism for representations of the algebra that can be adapted to harmonic superspace. Models in this harmonic superspace are quite similar to N = 2 models in four-dimensional Minkowski space.PACS Nos.: 11.30Pb, 03.65Fd

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9

Ganai, Prince A., Mudasir Ahmad Mir, Ideed Rafiqi, and Nadeem Ul Islam. "Chern–Simons theory in aether superspace." Modern Physics Letters A 32, no. 39 (2017): 1750214. http://dx.doi.org/10.1142/s0217732317502145.

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In this paper, we will analyze the breaking of Lorentz symmetry using aether superspace. We will analyze the aether deformation of a Chern–Simons theory using this deformed superspace. As this theory, will have gauge symmetry, we will add gauge and ghost terms to the original action. We will analyze the nonlinear BRST symmetry for this theory. We also analyze the quantum BRST symmetry in BV formalism.

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10

MEZIANE, A., and M. TAHIRI. "GEOMETRICAL FORMULATION OF THE BRST TRANSFORMATIONS OF GAUGE-AFFINE GRAVITY." Modern Physics Letters A 11, no. 11 (1996): 885–90. http://dx.doi.org/10.1142/s0217732396000898.

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Fields and their BRST and anti-BRST transformations in gauge-affine gravity are determined by using a superspace formalism. The method is based on the introduction of a basis, instead of the natural one, for differential forms on a (4, 2)-dimensional superspace, whose body is a metric-affine spacetime. This basis is defined after having introduced the coordinate ghost and anti-ghost superfields from a [Formula: see text]-superconnection.

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11

Zhao, Dan, Rong-Hua Zhang, Fei-Fei Li, Juan Yang, Bing-Guo Liu, and Yun-Chang Fan. "(3 + 1)-Dimensional commensurately modulated structure and photoluminescence properties of diborate KSbOB2O5." Dalton Transactions 44, no. 13 (2015): 6277–87. http://dx.doi.org/10.1039/c5dt00267b.

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12

Peral, I., G. Madariaga, V. Petříček, and T. Breczewski. "Average structure of the composite crystal urea/octanedioic acid at room temperature within the superspace formalism." Acta Crystallographica Section B Structural Science 57, no. 3 (2001): 386–93. http://dx.doi.org/10.1107/s0108768101002166.

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The average structure of the composite urea/octanedioic acid has been refined using the superspace formalism [superspace group H′3121(00γ)00\bar{1}]. Modulation effects seem to be almost negligible. The guest substructure appears to be largely disordered and has been modelled using rigid units occupying 12 equiprobable different orientations inside the urea tunnels. Guest molecules are slightly tilted with respect to the tunnel axis favouring a stronger guest–guest intratunnel interaction.

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13

Guevarra, Jonathan, Andreas Schönleber, Sander van Smaalen, and Frank Lichtenberg. "Superspace description of the crystal structures of Ca n (Nb,Ti) n O3n + 2 (n = 5 and 6)." Acta Crystallographica Section B Structural Science 63, no. 2 (2007): 183–89. http://dx.doi.org/10.1107/s0108768107002340.

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The crystal structures of two members of the homologous series Ca n (Nb,Ti) n O3n + 2, with n = 5 and 6, are presented within the superspace formalism. A common (3 + 1)-dimensional superspace model is used to describe the crystal structures of both compositions within a particular homologous series, where the primary modulation wavevector and the width of the atomic domains vary systematically with composition. The two crystal structures are characterized as commensurately modulated structures consisting of discontinuous atomic domains described by occupational crenel functions. The displacive

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14

Zhao, Dan, Fa-Xue Ma, Rui-Juan Zhang, et al. "Structure modulation, band structure, density of states and luminescent properties of columbite-type ZnNb2O6." CrystEngComm 18, no. 16 (2016): 2929–36. http://dx.doi.org/10.1039/c5ce01828e.

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This study reports the four-dimensional commensurately modulated structure of ZnNb<sub>2</sub>O<sub>6</sub> using superspace formalism for aperiodic structures considering the modulation vector, q = 1/3 b*.

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15

Ganai, Prince A., Owais Ahmad, Javier Perez Tobia, Alexander Fennell, and Vedaant Vyas. "Lorentz symmetry breaking in supersymmetric quantum electrodynamics." International Journal of Geometric Methods in Modern Physics 17, no. 03 (2020): 2050038. http://dx.doi.org/10.1142/s0219887820500383.

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Lorentz symmetry is one of the fundamental symmetries of nature; however, it can be broken by several proposals such as quantum gravity effects, low energy approximations in string theory and dark matter. In this paper, Lorentz symmetry is broken in supersymmetric quantum electrodynamics using aether superspace formalism without breaking any supersymmetry. To break the Lorentz symmetry in three-dimensional quantum electrodynamics, we must use the [Formula: see text] aether superspace. A new constant vector field is introduced and used to deform the deformed generator of supersymmetry. This for

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16

TAHIRI, M. "UNCONSTRAINED SUPERSPACE FORMALISM OF TOPOLOGICAL 2-D GRAVITY." Modern Physics Letters A 10, no. 26 (1995): 1949–58. http://dx.doi.org/10.1142/s021773239500209x.

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An unconstrained superconnection formalism is used to derive in a natural way the fields and their BRST transformations in topological 2-D gravity. Anti-BRST transformations of the fields are also obtained. We also show how the usual BRST exact quantum action is anti-BRST exact.

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17

Kruglov, Sergey I., and Mir Faizal. "Wave function of the universe from a matrix-valued first-order formalism." International Journal of Geometric Methods in Modern Physics 12, no. 04 (2015): 1550050. http://dx.doi.org/10.1142/s0219887815500504.

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In this paper, the Wheeler–DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler–DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler–DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler–DeWitt equation in this matrix-valued first-or

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18

Gurzadyan, A. V., and A. A. Kocharyan. "Superspace and global stability in general relativity." International Journal of Modern Physics D 26, no. 05 (2017): 1741019. http://dx.doi.org/10.1142/s021827181741019x.

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A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalized Jacobi equation reformulated for pseudo-Riemannian manifolds. We give a direct formalism for dynamical analysis in the superspace, the requisite equation pertinent for stability analysis of the universe by means of generalized covariant and Fermi derivative is derived. Then, the relevant definitions and formulae are retrieved for cosmological models with a scalar field.

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19

Mikki, Said. "On the Topological Structure of Nonlocal Continuum Field Theories." Foundations 2, no. 1 (2021): 20–84. http://dx.doi.org/10.3390/foundations2010003.

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An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which phy

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20

KATO, JUNJI, and AKIKO MIYAKE. "TOPOLOGICAL HYPERMULTIPLET ON N = 2 TWISTED SUPERSPACE IN FOUR DIMENSIONS." Modern Physics Letters A 21, no. 34 (2006): 2569–89. http://dx.doi.org/10.1142/s021773230602161x.

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We propose an N = 2 twisted superspace formalism with a central charge in four dimensions by introducing a Dirac–Kähler twist. Using this formalism, we construct an off-shell twisted hypermultiplet action and find an explicit form of fermionic scalar, vector and tensor transformations. We construct an off-shell Donaldson–Witten theory coupled to the twisted hypermultiplet. We show that this action possesses N = 4 twisted supersymmetry at the on-shell level. It turns out that the four-dimensional Dirac–Kähler twist is equivalent to Marcus' twist.

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21

MATSUDA, SATOSHI, and TSUNEO UEMATSU. "SUPER SCHWARZIAN DERIVATIVES IN N = 4 SU(2)-EXTENDED SUPERCONFORMAL ALGEBRAS." Modern Physics Letters A 05, no. 11 (1990): 841–51. http://dx.doi.org/10.1142/s0217732390000937.

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We investigate anomalous terms in finite superconformal transformations in N = 4 SU(2)-extended superconformal algebras (SCA). Based on the superspace formalism we obtain super Schwarzian derivatives for the N = 4 SCA. Solutions for global superconformal transformations with the vanishing super-Schwarzian derivatives are given.

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22

Ribeiro, J. L. "Superspace symmetry and phenomenology of incommensurate type-II multiferroics." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C515. http://dx.doi.org/10.1107/s2053273314094844.

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The recent upsurge of research work on multiferroic materials has made clear the need for a comprehensive knowledge of the constraints imposed by symmetry on the magnetic structure and tensor properties of incommensurate magnetic phases. That knowledge can be provided by the magnetic superspace formalism in a simple and robust manner. In this communication I will briefly review some of the basic concepts of this formalism pertaining to magnetic systems. Several practical examples will be given in order to illustrate how the assignment of a magnetic superspace group to a given phase is, in gene

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23

Perez, O., and L. Elcoro. "Superspace formalism to crack complex codes in material chemistry." Acta Crystallographica Section A Foundations of Crystallography 64, a1 (2008): C120. http://dx.doi.org/10.1107/s010876730809613x.

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24

Pérez, Olivier. "Superspace formalism: the Swiss army knife of the crystallographer." Acta Crystallographica Section A Foundations of Crystallography 69, a1 (2013): s264. http://dx.doi.org/10.1107/s0108767313097730.

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25

KACHKACHI, M., and T. LHALLABI. "N = 2 SUPERCONFORMAL ANOMALIES AND CURVED HARMONIC SUPERSPACE." International Journal of Modern Physics A 07, no. 15 (1992): 3601–21. http://dx.doi.org/10.1142/s0217751x92001605.

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We present the differential geometry formalism of the N = 2 conformal supergravity in harmonic superspace, which allows one to derive the BRST symmetry corresponding to N = 2 super-diffeomorphisms, local Lorentz transformations and local super-Weyl transformations. The extended transgression formula is used and the N = 2 superconformal anomalies are shown.

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26

Howe, P. S., and U. Lindström. "Local supertwistors and conformal supergravity in six dimensions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (2020): 20200683. http://dx.doi.org/10.1098/rspa.2020.0683.

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The local supertwistor formalism, which involves a superconformal connection acting on the bundle of such objects over superspace, is used to investigate superconformal geometry in six dimensions. The geometry corresponding to (1, 0) and (2, 0) off-shell conformal supergravity multiplets, as well the associated finite super-Weyl transformations, are derived.

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27

BUCHBINDER, IOSEPH L., and SERGEI M. KUZENKO. "COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM." Modern Physics Letters A 13, no. 20 (1998): 1623–35. http://dx.doi.org/10.1142/s0217732398001704.

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We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

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28

Gallego, Samuel V., J. Manuel Perez-Mato, Luis Elcoro, et al. "MAGNDATA: towards a database of magnetic structures. II. The incommensurate case." Journal of Applied Crystallography 49, no. 6 (2016): 1941–56. http://dx.doi.org/10.1107/s1600576716015491.

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A free web page under the nameMAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016).J. Appl. Cryst.49, 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic st

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29

DAS, ASHOK, and JNANADEVA MAHARANA. "DUALITY OF THE SUPERSTRING IN SUPERSPACE." Modern Physics Letters A 09, no. 15 (1994): 1361–68. http://dx.doi.org/10.1142/s0217732394001180.

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The evolution of a closed NSR string is considered in the background of constant graviton and antisymmetric fields. The σ-model action is written in a manifestly supersymmetric form in terms of superfields. The first order formalism adopted for the closed bosonic string is generalized to implement duality transformations and the constant dual backgrounds are obtained for the dual theory. We recover the G→G−1 duality for the case when antisymmetric tensor field is set to zero. Next, the case when the backgrounds depend on one superfield, is also analyzed. This scenario is similar to the cosmolo

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30

AIDAOUI, A., and M. TAHIRI. "SUPERCONNECTION FORMALISM FOR QUANTIZED BF THEORIES ON BRST–VSUSY SUPERSPACE." International Journal of Geometric Methods in Modern Physics 07, no. 08 (2010): 1321–30. http://dx.doi.org/10.1142/s0219887810004828.

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The arbitrary dimensional BF theory is presented in a superconnection formalism. This makes the off-shell BRST-VSUSY superalgebra more obvious. We also discuss how to build the BRST–VSUSY exact quantum action.

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31

AIDAOUI, A., and M. TAHIRI. "BRST–VSUSY SUPERSPACE AND TWISTED SUPERFIELDS FOR D=4 BF SYSTEMS." Modern Physics Letters A 20, no. 33 (2005): 2567–73. http://dx.doi.org/10.1142/s021773230501769x.

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We propose to construct the off-shell supersymmetric structure present in quantized D=4 BF theories in terms of a BRST–VSUSY superspace formalism. The method is based on the introduction of constrained scalar superfields. We also discuss how to find the D=4 BF action from D=N=4 supersymmetric action by an appropriate twisting process.

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32

BARCELOS-NETO, J., and E. S. CHEB-TERRAB. "SYMPLECTIC QUANTIZATION OF SUPERFIELDS." International Journal of Modern Physics A 09, no. 31 (1994): 5563–81. http://dx.doi.org/10.1142/s0217751x94002272.

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We show how the extension of the Faddeev-Jackiw symplectic quantization (including true constraints) can be used in superspace. We first deal with supersymmetric free field theory in the component language. After that, we consider the method applied to superfields, taken as canonical variables. We also use the formalism, directly in superfield formulation, for the supersymmetric nonlinear sigma model.

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33

Urcelay-Olabarria, Irene, Juan Manuel Perez-Mato, José Luis García Muñoz, and Eric Ressouche. "Sheding light on the multiferroicity in Mn1-xCoxWO4using superspace formalism." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C519. http://dx.doi.org/10.1107/s2053273314094807.

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The use of the superspace symmetry formalism allows to rationalize the physical properties induced by an incommensurate magnetic ordering [1]. The incommensurate magnetic structures (ICMS) in Mn1-xCoxWO4 have been studied in the light of this formalism. MnWO4 is a multiferroic material in which the magnetic order of one of its magnetic phases induces ferroelectricity. Like most multiferroic materials MnWO4 is extremely sensitive to small perturbations such as chemical substitution. It turned out that doping with Co2+ is particularly interesting since it strongly stabilizes the multiferroic pha

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34

Onoda, Mitsuko, Ying Shi, A. Leithe-Jasper, and Takaho Tanaka. "Structure refinement of the layered composite crystal Sc2B1.1C3.2 in a five-dimensional formalism." Acta Crystallographica Section B Structural Science 57, no. 4 (2001): 449–57. http://dx.doi.org/10.1107/s0108768101006607.

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The crystal structure of a layered compound Sc2B1.1C3.2, scandium boride carbide (M r = 140.43), has been re-refined as a commensurate composite crystal using 1795 single-crystal X-ray diffraction intensities with I > 2\sigma(I) collected by Shi, Leithe-Jasper, Bourgeois, Bando & Tanaka [(1999), J. Solid State Chem. 148, 442–449]. The crystal is composed of two layered subsystem structures, i.e. Sc—C—Sc sandwiches and graphite-like layers of the composition B1/3C2/3. The structure refinement was performed in a five-dimensional formalism based on the trigonal superspace group P\bar{3}m1(

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35

Tahiri, M. "Super and anti-super BF systems in the superspace formalism." Classical and Quantum Gravity 13, no. 6 (1996): 1323–32. http://dx.doi.org/10.1088/0264-9381/13/6/007.

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36

Lourenço, J. A., J. A. Helayël Neto, and W. Spalenza. "Topological Gravity on (D,N)-Shift Superspace Formulation." Advances in High Energy Physics 2018 (August 1, 2018): 1–8. http://dx.doi.org/10.1155/2018/2786081.

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We reassess the subject of topological gravity by following the shift supersymmetry formalism. The gauge-fixing of the theory goes under the Batalin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and antighost superfields, associated with the supervielbein and the super-Lorentz connection. We extend the formulation of the topological gravity action to an arbitrary number of dimensions of the shift superspace by adopting a formulation based on the gauge-fixing for BF-type models.

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37

KHELASHVILI, G. A., and V. I. OGIEVETSKY. "NON-RENORMALIZABILITY OF THE MASSIVE N = 2 SUPER-YANG–MILLS THEORY." Modern Physics Letters A 06, no. 23 (1991): 2143–54. http://dx.doi.org/10.1142/s0217732391002335.

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The massive N = 2 supersymmetric Yang–Mills theory is investigated. Its non-renormalizability is revealed starting from the fourth order of the perturbation theory. The N = 2 harmonic superspace approach and the Stueckelberg-like formalism are used. The Stueckelberg fields form some nonlinear sigma model. Non-renormalizability of the latter produces non-renormalizability of the N = 2 supersymmetric Yang–Mills theory.

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38

Christensen, Jeppe, Sven Lidin, Bernard Malaman, and Gerard Venturini. "Vacancy-ordering effects in AlB2-type ErGe2 − x (0.4 < x ≤ 0.5)." Acta Crystallographica Section B Structural Science 64, no. 3 (2008): 272–80. http://dx.doi.org/10.1107/s0108768108005119.

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In the Er–Ge system, the compostion range ErGe2 to Er2Ge3 has been investigated. Eight samples were produced by arc melting of the elements, and analyzed using X-ray powder diffraction. Nine crystal structures were found to be present in the samples. The structures are described as a homologous series and presented within the superspace formalism using the superspace group X2/m(α0γ)0s, X representing the centring vector (½, ½, 0, ½). In this description the modulation vector q = (αa* + γc*) is shown to be a direct measure of the Ge content as ErGe2 − α (α falls in the range 1\over 3 to ½). The

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39

DELBOURGO, R., P. D. JARVIS, and G. THOMPSON. "Sp(2) INVARIANT BRST FORMALISM, SUPERSYMMETRY AND WESS-ZUMINO GAUGES." Modern Physics Letters A 01, no. 02 (1986): 95–101. http://dx.doi.org/10.1142/s0217732386000142.

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Covariant quantization of Fermi-Bose supersymmetric gauge theories is formulated within an enlarged superspace (xµ, θα, ξm) with manifest ξ-supertranslation (=extended BRST) and Sp(2) invariance. In Wess-Zumino gauges, the correct ghost and auxiliary field structure emerges by counting arguments for the (N=1) super-Yang-Mills, conformal and Einstein supergravity cases. The super-Yang-Mills case is analyzed in detail for both supercovariant and Wess-Zumino gauge-fixing, with particular emphasis on the Sp(2) assignments of the ghost superfields.

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40

Izaola, Zunbeltz, Santiago González, Luis Elcoro, J. M. Perez-Mato, Gotzon Madariaga, and Alberto García. "Revision of pyrrhotite structures within a common superspace model." Acta Crystallographica Section B Structural Science 63, no. 5 (2007): 693–702. http://dx.doi.org/10.1107/s0108768107037275.

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The structure of pyrrhotite (Fe1 − x S with 0.05 ≤ x ≤ 0.125) has been reinvestigated in the framework of the superspace formalism. A common model with a centrosymmetric superspace group is proposed for the whole family. The atomic domains in the internal space representing the Fe atoms are parametrized as crenel functions that fulfil the closeness condition. The proposed model explains the x-dependent space groups observed and the basic features of the structures reported up to now. Our model yields for any x value a well defined ordered distribution of Fe vacancies in contrast to some of the

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41

Ullah, Farman, Prince A. Ganai, Cheralan P. Haritha, and Barilang Mawlong. "Super-Yang–Mills theory on a Lorentz breaking background." International Journal of Geometric Methods in Modern Physics 15, no. 08 (2018): 1850127. http://dx.doi.org/10.1142/s021988781850127x.

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In this paper, we will analyze a super-Yang–Mills Theory on a Lorentz breaking background. This theory will be analyzed using aether superspace formalism. We will also study the quantum symmetries of this theory. Thus, we will analyze this theory both in linear and nonlinear gauges. We will also study the effects of adding a bare mass term in the Curci–Ferrari gauge.

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42

TANII, YOSHIAKI, and YOSHIYUKI WATABIKI. "VERTEX FUNCTIONS IN THE PATH INTEGRAL FORMALISM OF OPEN STRING THEORIES." International Journal of Modern Physics A 03, no. 11 (1988): 2601–20. http://dx.doi.org/10.1142/s0217751x88001089.

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We study a systematic method to obtain the general vertex functions (of Neveu-Schwarz sector), which are used in the covariant path integral approach to the open bosonic and superstring theories. For the superstring the superspace formulation in the Wess-Zumino gauge is used to construct the vertices at the boundaries of world sheets. For both theories the vertex functions are explicitly obtained for the first four mass levels and coincide with those in the operator formalism.

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43

Elcoro, L., J. M. Perez-Mato, and R. L. Withers. "Intergrowth polytypoids as modulated structures: a superspace description of the Sr n (Nb,Ti) n O3n + 2 compound series." Acta Crystallographica Section B Structural Science 57, no. 4 (2001): 471–84. http://dx.doi.org/10.1107/s0108768101005444.

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A new, unified superspace approach to the structural characterization of the perovskite-related Sr n (Nb,Ti) n O3n + 2 compound series, strontium niobium/titanium oxide, is presented. To a first approximation, the structure of any member of this compound series can be described in terms of the stacking of (110)-bounded perovskite slabs, the number of atomic layers in a single perovskite slab varying systematically with composition. The various composition-dependent layer-stacking sequences can be interpreted in terms of the structural modulation of a common underlying average structure. The av

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44

Bandos, Igor, Patrick Meessen, and Tomás Ortín. "Noether-Wald and Komar charges in supergravity, fermions, and Killing supervectors in superspace." Journal of Physics: Conference Series 2912, no. 1 (2024): 012007. https://doi.org/10.1088/1742-6596/2912/1/012007.

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Abstract The supersymmetry properties of Killing vectors and spinors in supergravity theory can be clarified by relating them to Killing supervectors in the supergravity superspace. In the superspace approach it is manifest that supersymmetry ‘mixes’ a Killing vector with its fermionic spinor ‘superpartner’ and the Killing equations with the generalization of the Killing spinor equations. The latter reduces to the standard Killing spinor equation, albeit with a fermionic spinor, when the fermionic fields are set to zero. Using these supersymmetry transformations in the spacetime component appr

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45

Zhang, Rui-Juan, Dan Zhao, Qiu Zhong, Ya-Li Xue, and Guang-Xu Huang. "Na3Sm(PO4)2: (3+1)-dimensional commensurately modulated structure model and photoluminescence properties." Zeitschrift für Kristallographie - Crystalline Materials 234, no. 5 (2019): 281–89. http://dx.doi.org/10.1515/zkri-2018-2095.

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Abstract For the first time, we determined the detailed crystal structure of Na3Sm(PO4)2 using single crystal X-ray diffraction and established the commensurately modulated structure model using the superspace formalism. The structure adopts a (3+1)-dimensional superspace group Pca21(0β0)000 with the modulation vector q=1/3b*. At the same time, the photoluminescent properties of Na3Sm(PO4)2 sintered at different temperatures between 800 and 1200°C were studied. Under near-UV excitation (402 nm), Na3Sm(PO4)2 shows intense characteristic emission bands of Sm3+ (561, 596, 642 nm) with the CIE coo

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THÜMMEL, O. "EXTENDED CONFORMAL SUPERGRAVITY AND BELTRAMI VARIABLES." International Journal of Modern Physics A 09, no. 10 (1994): 1631–75. http://dx.doi.org/10.1142/s0217751x94000716.

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By using a geometric BRST formalism we investigate the two-dimensional N = 2 and N = 4 superspace geometry. The BRST algebra allows one to generalize the notion of Beltrami variables to the extended supergeometries. Furthermore, this geometric treatment yields a systematic way to derive different off-shell supergravities. Finally we construct the Chern–Simons form and calculate from this the superconformal anomaly for the N = 2 and N = 4 theories.

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47

Braga, Nelson R. F., and Sergio M. de Souza. "Superspace formulation for the Batalin-Vilkovisky formalism with extended BRST invariance." Physical Review D 53, no. 2 (1996): 916–22. http://dx.doi.org/10.1103/physrevd.53.916.

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48

Schoenleber, A., P. Pattison, and G. Chapuis. "Structure and phase transition ofp-chlorobenzamide described in the superspace formalism." Acta Crystallographica Section A Foundations of Crystallography 58, s1 (2002): c183. http://dx.doi.org/10.1107/s0108767302092358.

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49

Schönleber, Andreas, and Gervais Chapuis. "Quininium (R)-mandelate, a structure with large Z′ described as an incommensurately modulated structure in (3+1)-dimensional superspace." Acta Crystallographica Section B Structural Science 60, no. 1 (2004): 108–20. http://dx.doi.org/10.1107/s0108768103027605.

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Quininium (R)-mandelate, C20H25N2O_2^+·C8H7O_3^-, is an organic salt with an incommensurately modulated structure. The superspace approach is required for a precise description of the structure at room temperature. In addition to the main reflections, the diffraction pattern also exhibits higher-order satellite reflections. The large number of first- and second-order satellite reflections with relatively strong intensities indicates a significant modulation. No average structure solution could be obtained on the basis of the main reflections only and hence the structure solution was performed

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50

NISSIMOV, E., S. PACHEVA, and S. SOLOMON. "ACTION PRINCIPLE FOR OVERDETERMINED SYSTEMS OF NONLINEAR FIELD EQUATIONS." International Journal of Modern Physics A 04, no. 03 (1989): 737–52. http://dx.doi.org/10.1142/s0217751x89000352.

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We propose a general scheme for constructing an action principle for arbitrary consistent overdetermined systems of nonlinear field equations. The principal tool is the BFV-BRST formalism. There is no need for star-product nor Chern-Simons forms. The main application of this general construction is the derivation of a superspace action in terms of unconstrained superfields for the D = 10N = 1 Super-Yang-Mills theory. The latter contains cubic as well as quartic interactions.

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