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Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 21 лютого 2023

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1

Hasenfratz, A., and P. Hasenfratz. "Lattice Gauge Theories." Annual Review of Nuclear and Particle Science 35, no. 1 (December 1985): 559–604. http://dx.doi.org/10.1146/annurev.ns.35.120185.003015.

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2

Shuo-hong, Guo. "Lattice Gauge-Theories." Communications in Theoretical Physics 4, no. 5 (September 1985): 613–30. http://dx.doi.org/10.1088/0253-6102/4/5/613.

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3

Majumdar, Peter. "Lattice gauge theories." Scholarpedia 7, no. 4 (2012): 8615. http://dx.doi.org/10.4249/scholarpedia.8615.

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4

Golterman, Maarten. "Lattice chiral gauge theories." Nuclear Physics B - Proceedings Supplements 94, no. 1-3 (March 2001): 189–203. http://dx.doi.org/10.1016/s0920-5632(01)00953-7.

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5

Barbiero, Luca, Christian Schweizer, Monika Aidelsburger, Eugene Demler, Nathan Goldman та Fabian Grusdt. "Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ2 lattice gauge theories". Science Advances 5, № 10 (жовтень 2019): eaav7444. http://dx.doi.org/10.1126/sciadv.aav7444.

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From the standard model of particle physics to strongly correlated electrons, various physical settings are formulated in terms of matter coupled to gauge fields. Quantum simulations based on ultracold atoms in optical lattices provide a promising avenue to study these complex systems and unravel the underlying many-body physics. Here, we demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices, using a combination of coherent lattice modulation with strong interactions. Specifically, we propose implementation of ℤ2 lattice gauge theories coupled to matter, reminiscent of theories previously introduced in high-temperature superconductivity. We discuss a range of settings from zero-dimensional toy models to ladders featuring transitions in the gauge sector to extended two-dimensional systems. Mastering lattice gauge theories in optical lattices constitutes a new route toward the realization of strongly correlated systems, with properties dictated by an interplay of dynamical matter and gauge fields.

6

Fachin, Stefano, and Claudio Parrinello. "Global gauge fixing in lattice gauge theories." Physical Review D 44, no. 8 (October 15, 1991): 2558–64. http://dx.doi.org/10.1103/physrevd.44.2558.

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7

Ryang, S., T. Saito, F. Oki, and K. Shigemoto. "Lattice thermodynamics for gauge theories." Physical Review D 31, no. 6 (March 15, 1985): 1519–21. http://dx.doi.org/10.1103/physrevd.31.1519.

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8

PESANDO, IGOR. "VECTOR INDUCED LATTICE GAUGE THEORIES." Modern Physics Letters A 08, no. 29 (September 21, 1993): 2793–801. http://dx.doi.org/10.1142/s0217732393003184.

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We consider vector induced lattice gauge theories, in particular we consider the QED induced and we show that at negative temperature corresponds to the dimer problem while at positive temperature it describes a gas of branched polymers with loops. We show that the fermionic models have D c = 6 as upper critical dimension for N ≠ ∞ while the N = ∞ model has no upper critical dimension. We also show that the bosonic models without potential are not critical in the range of stability of the integral definition of the partition function but they behave as the fermionic models when we analytically continue the free energy.

9

Pendleton, Brian. "Acceleration of lattice gauge theories." Nuclear Physics B - Proceedings Supplements 4 (April 1988): 590–94. http://dx.doi.org/10.1016/0920-5632(88)90160-0.

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10

Maiani, L., G. C. Rossi, and M. Testa. "On lattice chiral gauge theories." Physics Letters B 261, no. 4 (June 1991): 479–85. http://dx.doi.org/10.1016/0370-2693(91)90459-4.

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11

Testa, Massimo. "On lattice chiral gauge theories." Nuclear Physics B - Proceedings Supplements 26 (January 1992): 228–33. http://dx.doi.org/10.1016/0920-5632(92)90241-j.

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12

Tagliacozzo, L., A. Celi, A. Zamora, and M. Lewenstein. "Optical Abelian lattice gauge theories." Annals of Physics 330 (March 2013): 160–91. http://dx.doi.org/10.1016/j.aop.2012.11.009.

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13

DASS, N. D. HARI. "REGULARISATION OF CHIRAL GAUGE THEORIES." International Journal of Modern Physics B 14, no. 19n20 (August 10, 2000): 1989–2010. http://dx.doi.org/10.1142/s0217979200001138.

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Анотація:

This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity violation and the distinction between vector and chiral field theories. It then discusses the standard model of electroweak interactions from the perspective of chirality. It also reviews at length the phenomenon of anomalies in quantum field theories including the intuitive understanding of anomalies based on the Dirac sea picture as given by Nielsen and Ninomiya. It then raises the issue of a non-perturbative and constructive definition of the standard model as well as the importance of such formulations. The second Nielsen–Ninomiya theorem about the impossibility of regularising chiral gauge theories under some general assumptions is also discussed. After a brief review of lattice regularisation of field theories, it discusses the issue of fermions on the lattice with special emphasis on the problem of species doubling. The implications of these problems to introducing chiral fermions on the lattice as well as the interpretations of anomalies within the lattice formulations and the lattice Dirac sea picture are then discussed. Finally the difficulties of formulating the standard model on the lattice are illustrated through detailed discussions of the Wilson–Yukawa method, the domain wall fermions method and the recently popular Ginsparg–Wilson method.

14

Halimeh, Jad C., Haifeng Lang, and Philipp Hauke. "Gauge protection in non-abelian lattice gauge theories." New Journal of Physics 24, no. 3 (March 1, 2022): 033015. http://dx.doi.org/10.1088/1367-2630/ac5564.

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Abstract Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V, which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝ V / V 0 3 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp(V/V 0)/V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.

15

Golterman, Maarten F. L., and Yigal Shamir. "A gauge-fixing action for lattice gauge theories." Physics Letters B 399, no. 1-2 (April 1997): 148–55. http://dx.doi.org/10.1016/s0370-2693(97)00277-3.

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16

Bock, Wolfgang, Maarten Golterman, and Yigal Shamir. "Gauge-fixing approach to lattice chiral gauge theories." Nuclear Physics B - Proceedings Supplements 63, no. 1-3 (April 1998): 147–52. http://dx.doi.org/10.1016/s0920-5632(97)00706-8.

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17

Shamir, Yigal. "Lattice chiral gauge theories in a renormalizable gauge." Nuclear Physics B - Proceedings Supplements 53, no. 1-3 (February 1997): 664–67. http://dx.doi.org/10.1016/s0920-5632(96)00748-7.

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18

Mizutani, Masashi, and Atsushi Nakamura. "Stochastic gauge fixing for compact lattice gauge theories." Nuclear Physics B - Proceedings Supplements 34 (April 1994): 253–55. http://dx.doi.org/10.1016/0920-5632(94)90359-x.

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19

ALFORD, MARK G., and JOHN MARCH-RUSSELL. "DISCRETE GAUGE THEORIES." International Journal of Modern Physics B 05, no. 16n17 (October 1991): 2641–73. http://dx.doi.org/10.1142/s021797929100105x.

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In this review we discuss the formulation and distinguishing characteristics of discrete gauge theories, and describe several important applications of the concept. For the abelian (ℤN) discrete gauge theories, we consider the construction of the discrete charge operator F(Σ*) and the associated gauge-invariant order parameter that distinguishes different Higgs phases of a spontaneously broken U(1) gauge theory. We sketch some of the important thermodynamic consequences of the resultant discrete quantum hair on black holes. We further show that, as a consequence of unbroken discrete gauge symmetries, Grand Unified cosmic strings generically exhibit a Callan-Rubakov effect. For non-abelian discrete gauge theories we discuss in some detail the charge measurement process, and in the context of a lattice formulation we construct the non-abelian generalization of F(Σ*). This enables us to build the order parameter that distinguishes the different Higgs phases of a non-abelian discrete lattice gauge theory with matter. We also describe some of the fascinating phenomena associated with non-abelian gauge vortices. For example, we argue that a loop of Alice string, or any non-abelian string, is super-conducting by virtue of charged zero modes whose charge cannot be localized anywhere on or around the string (“Cheshire charge”). Finally, we discuss the relationship between discrete gauge theories and the existence of excitations possessing exotic spin and statistics (and more generally excitations whose interactions are purely “topological”).

20

Kovács, Tamás G., and Zsolt Schram. "Homology and abelian lattice gauge theories." Acta Physica Hungarica A) Heavy Ion Physics 1, no. 3-4 (June 1995): 273–83. http://dx.doi.org/10.1007/bf03053747.

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21

Kijowski, Jerzy, and Gerd Rudolph. "New lattice approximation of gauge theories." Physical Review D 31, no. 4 (February 15, 1985): 856–64. http://dx.doi.org/10.1103/physrevd.31.856.

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22

Davis, Anne C., Tom W. B. Kibble, Arttu Rajantie, and Hugh P. Shanahan. "Topological defects in lattice gauge theories." Journal of High Energy Physics 2000, no. 11 (November 6, 2000): 010. http://dx.doi.org/10.1088/1126-6708/2000/11/010.

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23

Bodwin, Geoffrey T. "Lattice formulation of chiral gauge theories." Physical Review D 54, no. 10 (November 15, 1996): 6497–520. http://dx.doi.org/10.1103/physrevd.54.6497.

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24

Buividovich, P. V., and M. I. Polikarpov. "Entanglement entropy in lattice gauge theories." Journal of Physics A: Mathematical and Theoretical 42, no. 30 (July 14, 2009): 304005. http://dx.doi.org/10.1088/1751-8113/42/30/304005.

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25

Friedberg, R., T. D. Lee, Y. Pang, and H. C. Ren. "Noncompact lattice formulation of gauge theories." Physical Review D 52, no. 7 (October 1, 1995): 4053–81. http://dx.doi.org/10.1103/physrevd.52.4053.

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26

Aoki, Sinya. "Chiral Gauge Theories on a Lattice." Physical Review Letters 60, no. 21 (May 23, 1988): 2109–12. http://dx.doi.org/10.1103/physrevlett.60.2109.

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27

Funakubo, Koichi, and Taro Kashiwa. "Chiral Gauge Theories on a Lattice." Physical Review Letters 60, no. 21 (May 23, 1988): 2113–16. http://dx.doi.org/10.1103/physrevlett.60.2113.

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28

Mitrjushkin, V. K. "Classical solutions in lattice gauge theories." Physics Letters B 389, no. 4 (December 1996): 713–19. http://dx.doi.org/10.1016/s0370-2693(96)80014-1.

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29

Mathur, Manu. "Loop approach to lattice gauge theories." Nuclear Physics B 779, no. 1-2 (September 2007): 32–62. http://dx.doi.org/10.1016/j.nuclphysb.2007.04.031.

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30

Lüscher, M., and P. Weisz. "On-shell improved lattice gauge theories." Communications in Mathematical Physics 98, no. 3 (September 1985): 433. http://dx.doi.org/10.1007/bf01205792.

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31

Lüscher, M., and P. Weisz. "On-shell improved lattice gauge theories." Communications in Mathematical Physics 97, no. 1-2 (March 1985): 59–77. http://dx.doi.org/10.1007/bf01206178.

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32

Bałaban, T. "Averaging operations for lattice gauge theories." Communications in Mathematical Physics 98, no. 1 (March 1985): 17–51. http://dx.doi.org/10.1007/bf01211042.

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33

Gavai, R. V. "Recent advances in lattice gauge theories." Pramana 54, no. 4 (April 2000): 487–97. http://dx.doi.org/10.1007/s12043-000-0145-7.

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34

Schoenmaker, Wim, and Roger Horsley. "Transport coefficients and lattice gauge theories." Nuclear Physics B - Proceedings Supplements 4 (April 1988): 318–21. http://dx.doi.org/10.1016/0920-5632(88)90121-1.

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35

Kronfeld, Andreas S. "Topological aspects of lattice gauge theories." Nuclear Physics B - Proceedings Supplements 4 (April 1988): 329–51. http://dx.doi.org/10.1016/0920-5632(88)90123-5.

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36

Testa, Massimo. "Chiral gauge theories on the lattice." Nuclear Physics B - Proceedings Supplements 17 (September 1990): 467–69. http://dx.doi.org/10.1016/0920-5632(90)90294-5.

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37

Petronzio, Roberto, and Ettore Vicari. "Overrelaxed operators in lattice gauge theories." Physics Letters B 245, no. 3-4 (August 1990): 581–84. http://dx.doi.org/10.1016/0370-2693(90)90694-2.

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38

Montvay, I. "Supersymmetric gauge theories on the lattice." Nuclear Physics B - Proceedings Supplements 53, no. 1-3 (February 1997): 853–55. http://dx.doi.org/10.1016/s0920-5632(96)00801-8.

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39

Eleutério, S. M., and R. Vilela Mendes. "Stochastic models for lattice gauge theories." Zeitschrift für Physik C Particles and Fields 34, no. 4 (December 1987): 451–63. http://dx.doi.org/10.1007/bf01679864.

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40

Colangelo, P., and E. Scrimieri. "Gauge theories on a pseudorandom lattice." Physical Review D 35, no. 10 (May 15, 1987): 3193–97. http://dx.doi.org/10.1103/physrevd.35.3193.

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41

Gambini, Rodolfo, Lorenzo Leal, and Antoni Trias. "Loop calculus for lattice gauge theories." Physical Review D 39, no. 10 (May 15, 1989): 3127–35. http://dx.doi.org/10.1103/physrevd.39.3127.

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42

Eichten, Estia, and John Preskill. "Chiral gauge theories on the lattice." Nuclear Physics B 268, no. 1 (April 1986): 179–208. http://dx.doi.org/10.1016/0550-3213(86)90207-5.

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43

Witten, Edward. "Gauge theories and integrable lattice models." Nuclear Physics B 322, no. 3 (August 1989): 629–97. http://dx.doi.org/10.1016/0550-3213(89)90232-0.

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44

Narayanan, R., and H. Neuberger. "Progress in lattice chiral gauge theories." Nuclear Physics B - Proceedings Supplements 47, no. 1-3 (March 1996): 591–95. http://dx.doi.org/10.1016/0920-5632(96)00128-4.

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45

Martin, Olivier, K. J. M. Moriarty, and Stuart Samuel. "Computer techniques for lattice gauge theories." Computer Physics Communications 40, no. 2-3 (June 1986): 173–79. http://dx.doi.org/10.1016/0010-4655(86)90106-2.

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46

MCKELLAR, BRUCE H. J., CONRAD R. LEONARD, and LLOYD C. L. HOLLENBERG. "COUPLED CLUSTER METHODS FOR LATTICE GAUGE THEORIES." International Journal of Modern Physics B 14, no. 19n20 (August 10, 2000): 2023–37. http://dx.doi.org/10.1142/s0217979200001151.

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47

BOCK, WOLFGANG. "CHIRAL GAUGE THEORIES ON THE LATTICE WITHOUT GAUGE FIXING?" International Journal of Modern Physics C 05, no. 02 (April 1994): 327–29. http://dx.doi.org/10.1142/s0129183194000416.

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Анотація:

We discuss two proposals for a non-perturbative formulation of chiral gauge theories on the lattice. In both cases gauge symmetry is broken by the regularization. We aim at a dynamical restoration of symmetry. If the gauge symmetry breaking is not too severe this procedure could lead in the continuum limit to the desired chiral gauge theory.

48

Oliveira, O., and P. J. Silva. "Gribov copies and gauge fixing in lattice gauge theories." Nuclear Physics B - Proceedings Supplements 106-107 (March 2002): 1088–90. http://dx.doi.org/10.1016/s0920-5632(01)01937-5.

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49

Petronzio, Roberto. "Gauge spins for the renormalisation of lattice gauge theories." Physics Letters B 224, no. 3 (June 1989): 329–32. http://dx.doi.org/10.1016/0370-2693(89)91240-9.

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50

Lautrup, B., M. J. Lavelle, M. P. Tuite, and A. Vladikas. "Stochastic quantisation and gauge fixing in lattice gauge theories." Nuclear Physics B 290 (January 1987): 188–204. http://dx.doi.org/10.1016/0550-3213(87)90184-2.

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