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Articles de revues sur le sujet « Weyl-invariance »

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Auteur : Grafiati
Publié le 14 mars 2023

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1

NIETO, J. A. « REMARKS ON WEYL INVARIANT p-BRANES AND Dp-BRANES ». Modern Physics Letters A 16, no 40 (28 décembre 2001) : 2567–78. http://dx.doi.org/10.1142/s0217732301005497.

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A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity–dilaton effective action in higher dimensions, we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the Weyl invariance of p-branes. Our considerations can be extended to the case of super-p-branes.
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2

Iorio, A., L. O'Raifeartaigh, I. Sachs et C. Wiesendanger. « Weyl gauging and conformal invariance ». Nuclear Physics B 495, no 1-2 (juin 1997) : 433–50. http://dx.doi.org/10.1016/s0550-3213(97)00190-9.

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3

Gover, A. R., A. Shaukat et A. Waldron. « Tractors, mass, and Weyl invariance ». Nuclear Physics B 812, no 3 (mai 2009) : 424–55. http://dx.doi.org/10.1016/j.nuclphysb.2008.11.026.

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4

Zaikov, R. P. « Conformal invariance in Weyl gravity ». International Journal of Theoretical Physics 26, no 6 (juin 1987) : 537–48. http://dx.doi.org/10.1007/bf00670092.

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5

Dabholkar, Atish. « Quantum Weyl invariance and cosmology ». Physics Letters B 760 (septembre 2016) : 31–35. http://dx.doi.org/10.1016/j.physletb.2016.06.034.

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6

Edery, Ariel, et Yu Nakayama. « Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance ». Modern Physics Letters A 30, no 30 (7 septembre 2015) : 1550152. http://dx.doi.org/10.1142/s0217732315501527.

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Recently, it has been pointed out that dimensionless actions in four-dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed restricted Weyl invariance. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein–Hilbert action with cosmological constant and a Higgs mass. The model also contains an extra massless scalar field which couples to the Higgs field (and gravity). If the coupling of this extra scalar field to the Higgs field is negligibly small, this fixes the coefficient of the nonminimal coupling [Formula: see text] between the Higgs field and gravity. Besides the Higgs sector, all the other fields of the Standard Model can be incorporated into the original restricted Weyl invariant action.
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7

BIZDADEA, C., E. M. CIOROIANU et A. C. LUNGU. « NO INTERACTIONS FOR A COLLECTION OF WEYL GRAVITONS INTERMEDIATED BY A SCALAR FIELD ». International Journal of Modern Physics A 21, no 19n20 (10 août 2006) : 4083–126. http://dx.doi.org/10.1142/s0217751x06031284.

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The cross-couplings among several Weyl gravitons (described in the free limit by a sum of linearized Weyl actions) in the presence of a scalar field are studied with the help of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincaré invariance, (background) Lorentz invariance, and the preservation of the number of derivatives on each field, together with the supplementary assumption that the internal metric defined by the sum of Weyl Lagrangians is positively defined, we prove that there are no consistent cross-interactions among different Weyl gravitons in the presence of a scalar field. The couplings of a single Weyl graviton to a scalar field are also discussed.
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8

FUJIWARA, TAKANORI, YUJI IGARASHI et JISUKE KUBO. « WEYL INVARIANCE AND SPURIOUS BLACK HOLES IN TWO-DIMENSIONAL DILATON GRAVITY ». International Journal of Modern Physics A 09, no 27 (30 octobre 1994) : 4811–35. http://dx.doi.org/10.1142/s0217751x94001953.

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In two-dimensional dilaton gravity theories, there may exist a global Weyl invariance which makes the black hole spurious. If the global invariance and the local Weyl invariance of the matter coupling are intact at the quantum level, there is no Hawking radiation. We explicitly verify the absence of anomalies in these symmetries for the model proposed by Callan, Giddings, Harvey and Strominger. The crucial observation is that the conformal anomaly can be cohomologically trivial and so not truly anomalous in such dilaton gravity models.
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9

Alvarez, Enrique, Sergio González-Martín et Mario Herrero-Valea. « Some cosmological consequences of Weyl invariance ». Journal of Cosmology and Astroparticle Physics 2015, no 03 (19 mars 2015) : 035. http://dx.doi.org/10.1088/1475-7516/2015/03/035.

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10

Kuzenko, Sergei M., et Gabriele Tartaglino-Mazzucchelli. « Super-Weyl invariance in 5D supergravity ». Journal of High Energy Physics 2008, no 04 (10 avril 2008) : 032. http://dx.doi.org/10.1088/1126-6708/2008/04/032.

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11

Zhao, Shu-Cheng, et Duan Yishi. « Conformal (Weyl) invariance and Higgs mechanism ». Il Nuovo Cimento A 105, no 12 (décembre 1992) : 1739–43. http://dx.doi.org/10.1007/bf02740923.

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12

Jain, Sanjay, et A. Jevicki. « String field theory from Weyl invariance ». Physics Letters B 220, no 3 (avril 1989) : 379–86. http://dx.doi.org/10.1016/0370-2693(89)90891-5.

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13

Navarro-Salas, J., M. Navarro et C. F. Talavera. « Weyl invariance and black hole evaporation ». Physics Letters B 356, no 2-3 (août 1995) : 217–22. http://dx.doi.org/10.1016/0370-2693(95)00848-f.

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14

Codello, A., G. D’Odorico, C. Pagani et R. Percacci. « The renormalization group and Weyl invariance ». Classical and Quantum Gravity 30, no 11 (13 mai 2013) : 115015. http://dx.doi.org/10.1088/0264-9381/30/11/115015.

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15

MIYATA, HIDEO, et NORIYASU OHTSUBO. « WEYL ORBIFOLD MODELS ». Modern Physics Letters A 11, no 28 (14 septembre 1996) : 2285–96. http://dx.doi.org/10.1142/s0217732396002277.

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Superstring models on Weyl orbifolds are investigated in [Formula: see text] heterotic string theories. Some of the Weyl orbifold models are shown to be consistent with worldsheet supersymmetry, N=1 spacetime supersymmetry and modular invariance. Two ways of embedding in [Formula: see text] are studied and residual gauge groups are classified.
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16

MOON, TAEYOON, JOOHAN LEE et PHILLIAL OH. « CONFORMAL INVARIANCE IN EINSTEIN–CARTAN–WEYL SPACE ». Modern Physics Letters A 25, no 37 (7 décembre 2010) : 3129–43. http://dx.doi.org/10.1142/s0217732310034201.

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We consider conformally invariant form of the actions in Einstein, Weyl, Einstein–Cartan and Einstein–Cartan–Weyl space in general dimensions (> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein–Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb–Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.
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17

Fernández Cristóbal, José Ma. « Weyl invariance in metric f(R) gravity ». Revista Mexicana de Física 64, no 2 (14 mars 2018) : 181. http://dx.doi.org/10.31349/revmexfis.64.181.

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We aim to derive the most general f(R) gravity theory, including thematter, so that it be Weyl invariant. Making use of the mathematicalequivalence of these theories with an type of scalar-tensor theory, and byimposing the Weyl invariance for the pure gravity as well as for the mattersector, we obtain the fundamental equation that restricts the form of V (phi) (and, accordingly, of f(R)) so that the resulting action to be Weylinvariant in the Jordan frame. We show that this action is not otherthan the so-called dilaton gravity action with one scalar eld,, whicheective mass is R and Phi dependent. In the Einstein frame, the actionbecomes the Einstein-Hilbert action with the Ricci scalar being constantdue to that the eective mass of scalar eld in this frame vanish. So,we can assume that the Ricci scalar, in the Einstein frame, is the trueCosmological Constant. Therefore, is not preposterous to guess that, atleast mathematically, all Weyl invariant metric f(R) theory in the Jordanframe is equivalent, at classical level, to the Einstein gravity, in theEinstein frame, with a constant Ricci scalar. At quantum level, as it isknown, both theories are not equivalent due to the presence of anomaliesin one of the frames.
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18

Álvarez, Enrique, et Sergio González-Martín. « Weyl invariance with a nontrivial mass scale ». Journal of Cosmology and Astroparticle Physics 2016, no 09 (7 septembre 2016) : 012. http://dx.doi.org/10.1088/1475-7516/2016/09/012.

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19

Gover, A. R., A. Shaukat et A. Waldron. « Weyl invariance and the origins of mass ». Physics Letters B 675, no 1 (mai 2009) : 93–97. http://dx.doi.org/10.1016/j.physletb.2009.03.072.

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20

Lü, H., C. N. Pope et K. S. Stelle. « Weyl group invariance and p-brane multiplets ». Nuclear Physics B 476, no 1-2 (septembre 1996) : 89–117. http://dx.doi.org/10.1016/0550-3213(96)00264-7.

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21

Dewar, Neil, et James Read. « Conformal Invariance of the Newtonian Weyl Tensor ». Foundations of Physics 50, no 11 (6 octobre 2020) : 1418–25. http://dx.doi.org/10.1007/s10701-020-00386-w.

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AbstractIt is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.
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22

GRUMILLER, D., D. HOFMANN et W. KUMMER. « 2D GRAVITY WITHOUT TEST PARTICLES IS POINTLESS ». Modern Physics Letters A 16, no 24 (10 août 2001) : 1597–600. http://dx.doi.org/10.1142/s0217732301004935.

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23

Háková, Lenka, et Agnieszka Tereszkiewicz. « ON GENERALIZATION OF SPECIAL FUNCTIONS RELATED TO WEYL GROUPS ». Acta Polytechnica 56, no 6 (31 décembre 2016) : 440–47. http://dx.doi.org/10.14311/ap.2016.56.0440.

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Weyl group orbit functions are defined in the context of Weyl groups of simple Lie algebras. They are multivariable complex functions possessing remarkable properties such as (anti)invariance with respect to the corresponding Weyl group, continuous and discrete orthogonality. A crucial tool in their definition are so-called sign homomorphisms, which coincide with one-dimensional irreducible representations. In this work we generalize the definition of orbit functions using characters of irreducible representations of higher dimensions. We describe their properties and give examples for Weyl groups of rank 2 and 3.
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24

ABE, MITSUO, et NOBORU NAKANISHI. « UNITARY THEORY OF TWO-DIMENSIONAL QUANTUM GRAVITY AND ITS EXACT COVARIANT OPERATOR SOLUTION ». International Journal of Modern Physics A 06, no 22 (20 septembre 1991) : 3955–71. http://dx.doi.org/10.1142/s0217751x91001921.

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The manifestly covariant canonical operator formalism of two-dimensional quantum gravity is formulated on the basis of Sato’s gauge-fixing of the Weyl invariance. The unitarity problem, due to ghost-counting mismatch, is resolved by making the gravitational FP ghosts also play the role of the Weyl FP ghosts. All two-dimensional (anti)commutators between fundamental fields are explicitly obtained.
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25

SUZUKI, HIROSHI. « THERMAL PARTITION FUNCTION OF NON-CRITICAL BOSONIC STRINGS ». Modern Physics Letters A 04, no 21 (20 octobre 1989) : 2085–92. http://dx.doi.org/10.1142/s0217732389002343.

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The thermal free energy of free non-critical bosonic strings in a D-dimensional spacetime is examined. By integrating (or summing) over the Weyl freedom, the free energy and the one-loop vacuum amplitude are modular invariant for any D<26. Thus the (background) Weyl invariance is realized. In the case of L→∞, where L is the compactification radius of the Weyl mode, the physical spectrum circulating in the loop becomes continuous. A connection between this continuous spectrum and the unitarity of string perturbation theory is briefly mentioned.
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26

Maki, Takuya, Nahomi Kan et Kiyoshi Shiraishi. « Dirac-Born-Infeld-Einstein Theory with Weyl Invariance ». Journal of Modern Physics 03, no 09 (2012) : 1081–87. http://dx.doi.org/10.4236/jmp.2012.39142.

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27

Cellarosi, Francesco, et Jens Marklof. « Quadratic Weyl sums, automorphic functions and invariance principles ». Proceedings of the London Mathematical Society 113, no 6 (24 octobre 2016) : 775–828. http://dx.doi.org/10.1112/plms/pdw038.

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28

Faci, S. « Conformal invariance : From Weyl to SO(2,d) ». EPL (Europhysics Letters) 101, no 3 (1 février 2013) : 31002. http://dx.doi.org/10.1209/0295-5075/101/31002.

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29

Zhang, Nan, Gan Zhao, Lin Li, Pengdong Wang, Lin Xie, Bin Cheng, Hui Li et al. « Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium ». Proceedings of the National Academy of Sciences 117, no 21 (12 mai 2020) : 11337–43. http://dx.doi.org/10.1073/pnas.2002913117.

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The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5and HfTe5. The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop “Weyl semiconductors” provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.
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30

NAKAZAWA, NAOHITO. « COMMENT ON THE TRACE ANOMALY IN STOCHASTIC QUANTIZATION ». Modern Physics Letters A 07, no 10 (28 mars 1992) : 841–47. http://dx.doi.org/10.1142/s0217732392003475.

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We investigate the origin of the trace (conformal) anomaly in the context of stochastic quantization. Based on the Langevin equation, we study the local Ward-Takahashi identities corresponding to the Weyl invariance and the general coordinate invariance. It is shown that the Ito's stochastic calculus essentially picks up the non-trivial Jacobian factor which appears in the path-integral measure. We also provide how to construct the Langevin equation which maintains the general coordinate invariance in consistent with the Ito's calculus.
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31

Fan, Hong-Yi, et Yue Fan. « Derivation of Squeezed States Via Weyl Ordering Approach ». Modern Physics Letters A 12, no 31 (10 octobre 1997) : 2325–29. http://dx.doi.org/10.1142/s0217732397002405.

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By virtue of the invariance of Weyl ordering under similar transformations we find a new approach to derive explicit forms of squeezed states. The technique of integration within an ordered product of operators is fully used in our discussions.
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32

DESER, S. « FIRST ORDER, 2D, EINSTEIN GRAVITIES ». International Journal of Modern Physics D 05, no 06 (décembre 1996) : 579–82. http://dx.doi.org/10.1142/s0218271896000369.

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The Palatini variational method breaks down in 2D: First order forms of the Einstein action do not fix the affinity completely, as they possess an additional, Weyl, invariance absent in the second order versions.
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33

Oda, Ichiro. « Higgs potential from Weyl conformal gravity ». Modern Physics Letters A 35, no 37 (5 octobre 2020) : 2050304. http://dx.doi.org/10.1142/s0217732320503046.

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We consider Weyl’s conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a [Formula: see text] term in moving from the Jordan frame to the Einstein frame. A massless Nambu–Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.
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34

Berezin, V. A., V. I. Dokuchaev, Yu N. Eroshenko et A. L. Smirnov. « On the cosmological solutions in Weyl geometry ». Journal of Cosmology and Astroparticle Physics 2021, no 11 (1 novembre 2021) : 053. http://dx.doi.org/10.1088/1475-7516/2021/11/053.

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Abstract We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.
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35

Adler, Stephen L. « A frame-dependent gravitational effective action mimics a cosmological constant, but modifies the black hole horizon ». International Journal of Modern Physics D 25, no 12 (octobre 2016) : 1643001. http://dx.doi.org/10.1142/s021827181643001x.

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A frame-dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson–Walker spacetimes. However, in a static spherically symmetric Schwarzschild-like geometry it modifies the black hole horizon structure within microscopic distances of the nominal horizon, in such a way that [Formula: see text] never vanishes. This could have important implications for the black hole “information paradox”.
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36

Arvanitakis, Alex S. « Chiral strings, topological branes, and a generalised Weyl-invariance ». International Journal of Modern Physics A 34, no 06n07 (10 mars 2019) : 1950031. http://dx.doi.org/10.1142/s0217751x19500313.

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We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.
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37

Bellucci, Stefano, et Robert N. Oerter. « Weyl invariance of the Green-Schwarz heterotic sigma model ». Nuclear Physics B 363, no 2-3 (octobre 1991) : 573–92. http://dx.doi.org/10.1016/0550-3213(91)80034-j.

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38

Hayashi, Nobuharu. « String field equation in curved spacetime from Weyl invariance ». Physics Letters B 238, no 1 (mars 1990) : 50–56. http://dx.doi.org/10.1016/0370-2693(90)92099-5.

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39

Wood, W. R., et G. Papini. « Breaking Weyl invariance in the interior of a bubble ». Physical Review D 45, no 10 (15 mai 1992) : 3617–27. http://dx.doi.org/10.1103/physrevd.45.3617.

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40

Prester, Predrag Dominis. « Field redefinitions, Weyl invariance and the nature of mavericks ». Classical and Quantum Gravity 31, no 15 (18 juillet 2014) : 155006. http://dx.doi.org/10.1088/0264-9381/31/15/155006.

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41

Zhao, Shu-Cheng. « Massive Yang-Mills Field Theory with Conformal (Weyl) Invariance ». Communications in Theoretical Physics 17, no 2 (mars 1992) : 205–10. http://dx.doi.org/10.1088/0253-6102/17/2/205.

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42

Del Aguila, F., et G. D. Coughlan. « The cosmological constant, non-compact symmetries and Weyl invariance ». Physics Letters B 180, no 1-2 (novembre 1986) : 25–28. http://dx.doi.org/10.1016/0370-2693(86)90127-9.

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43

Baulieu, Laurent, et Adel Bilal. « Weyl invariance and covariant gauge fixing for string fields ». Physics Letters B 192, no 3-4 (juillet 1987) : 339–45. http://dx.doi.org/10.1016/0370-2693(87)90118-3.

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44

FAN, HONG-YI. « INVARIANCE OF WEYL ORDERING OF FERMI OPERATORS UNDER SIMILAR TRANSFORMATIONS ». Modern Physics Letters A 21, no 10 (28 mars 2006) : 809–20. http://dx.doi.org/10.1142/s0217732306019025.

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A Weyl–Wigner quantization scheme for Fermi system which is parallel to the bosonic case is established. We prove a new theorem: Weyl ordering of Fermi operators is invariant under fermionic similar transformations. Comparing with the preceding paper,1 we see the Bose–Fermi supersymmetry in this aspect. As an application of the theorem, we construct a generalized fermionic squeezed state.
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45

TSUKIOKA, TAKUYA, et YOSHIYUKI WATABIKI. « QUANTIZATION OF BOSONIC STRING MODEL IN (26+2)-DIMENSIONAL SPACE–TIME ». International Journal of Modern Physics A 19, no 12 (10 mai 2004) : 1923–59. http://dx.doi.org/10.1142/s0217751x04017641.

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We investigate the quantization of the bosonic string model which has a local U (1) V × U (1) A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations á la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in (26+2)-dimensional background space–time involving two time-like coordinates.
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46

FAN, HONG-YI, et JI-SUO WANG. « ON THE WEYL ORDERING INVARIANCE UNDER GENERAL n-MODE SIMILAR TRANSFORMATIONS ». Modern Physics Letters A 20, no 20 (28 juin 2005) : 1525–32. http://dx.doi.org/10.1142/s0217732305017512.

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We reveal that Weyl ordering of operators is invariant under general n-mode similar transformations. The technique of integration within a Weyl ordered product of operators is employed to prove our statement. Application of this property in obtaining generalized squeezed state via similar transformation is discussed.
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47

SOO, CHOPIN, et LAY NAM CHANG. « A WEYL DESCRIPTION OF GRAVITY INTERACTIONS ». International Journal of Modern Physics A 24, no 18n19 (30 juillet 2009) : 3372–81. http://dx.doi.org/10.1142/s0217751x09046977.

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We compare the conventional description of the interaction of matter with the four known forces in the standard model with an alternative Weyl description in which the chiral coupling is extended to include gravity. The two are indistinguishable at the low energy classical level of equations of motion, but there are subtle differences at the quantum level when nonvanishing torsion and the Adler-Bell-Jackiw anomaly are taken into account. The spin current and energy-momentum of the chiral theory then contain non-Hermitian terms which are not present in the conventional theory. In the chiral alternative, CPT invariance is not automatic because chirality supersedes Hermiticity but full Lorentz invariance holds. New fermion loop processes associated with the theory are discussed together with a perturbative regularization which explicitly maintains the chiral nature and local symmetries of the theory.
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Oda, Ichiro. « Planck scale from broken local conformal invariance in Weyl geometry ». Advanced Studies in Theoretical Physics 14, no 1 (2020) : 9–28. http://dx.doi.org/10.12988/astp.2020.91245.

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49

Ellwanger, U., et M. G. Schmidt. « Loop-corrected string field equations from world-sheet Weyl invariance ». Zeitschrift f�r Physik C Particles and Fields 43, no 3 (septembre 1989) : 485–96. http://dx.doi.org/10.1007/bf01506545.

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Hassan, S. F., Angnis Schmidt-May et Mikael von Strauss. « Extended Weyl invariance in a bimetric model and partial masslessness ». Classical and Quantum Gravity 33, no 1 (11 décembre 2015) : 015011. http://dx.doi.org/10.1088/0264-9381/33/1/015011.

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