Non-Abelian tensor gauge fields
Informatics and Automation, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 212-226.

Voir la notice de l'article provenant de la source Math-Net.Ru

A recently proposed extension of Yang–Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing nonlinear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze the particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spinor-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern–Simons density. The Lagrangian augmented by this Chern–Simons-like invariant describes the massive Yang–Mills boson, providing a gauge invariant mass gap for a four-dimensional gauge field theory.
@article{TRSPY_2011_272_a18,
     author = {George Savvidy},
     title = {Non-Abelian tensor gauge fields},
     journal = {Informatics and Automation},
     pages = {212--226},
     publisher = {mathdoc},
     volume = {272},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_272_a18/}
}
TY  - JOUR
AU  - George Savvidy
TI  - Non-Abelian tensor gauge fields
JO  - Informatics and Automation
PY  - 2011
SP  - 212
EP  - 226
VL  - 272
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2011_272_a18/
LA  - en
ID  - TRSPY_2011_272_a18
ER  - 
%0 Journal Article
%A George Savvidy
%T Non-Abelian tensor gauge fields
%J Informatics and Automation
%D 2011
%P 212-226
%V 272
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2011_272_a18/
%G en
%F TRSPY_2011_272_a18
George Savvidy. Non-Abelian tensor gauge fields. Informatics and Automation, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 212-226. http://geodesic.mathdoc.fr/item/TRSPY_2011_272_a18/

[1] Yang C.N., Mills R.L., “Conservation of isotopic spin and isotopic gauge invariance”, Phys. Rev., 96 (1954), 191 | DOI | MR

[2] Chern S.S., Topics in differential geometry, Ch. III: Theory of connections, Inst. Adv. Study, Princeton, NJ, 1951 | MR | Zbl

[3] Savvidy G., “Non-Abelian tensor gauge fields: Generalization of Yang–Mills theory”, Phys. Lett. B, 625 (2005), 341 | DOI | MR | Zbl

[4] Savvidy G., “Non-Abelian tensor gauge fields. I”, Intern. J. Mod. Phys. A, 21 (2006), 4931 | DOI | MR | Zbl

[5] Savvidy G., “Non-Abelian tensor gauge fields. II”, Intern. J. Mod. Phys. A, 21 (2006), 4959 | DOI | MR | Zbl

[6] Coleman S., Mandula J., “All possible symmetries of the $S$ matrix”, Phys. Rev., 159 (1967), 1251 | DOI | Zbl

[7] Haag R., Łopuszański J.T., Sohnius M., “All possible generators of supersymmetries of the $S$-matrix”, Nucl. Phys. B, 88 (1975), 257 | DOI | MR

[8] Barrett J.K., Savvidy G., “A dual Lagrangian for non-Abelian tensor gauge fields”, Phys. Lett. B, 652 (2007), 141 | DOI | MR | Zbl

[9] Savvidy G., “Interaction of non-Abelian tensor gauge fields”, Arm. J. Math., 1 (2008), 1, arXiv: 0804.2003 [hep-th] | MR | Zbl

[10] Rarita W., Schwinger J., “On a theory of particles with half-integral spin”, Phys. Rev., 60 (1941), 61 | DOI | Zbl

[11] Singh L.P.S., Hagen C.R., “Lagrangian formulation for arbitrary spin. II: The fermion case”, Phys. Rev. D, 9 (1974), 910 | DOI

[12] Fang J., Fronsdal C., “Massless fields with half-integral spin”, Phys. Rev. D, 18 (1978), 3630 | DOI

[13] Savvidy G., “Solution of free field equations in non-Abelian tensor gauge field theory”, Phys. Lett. B, 682 (2009), 143 | DOI | MR

[14] Cornwall J.M., Levin D.N., Tiktopoulos G., “Uniqueness of spontaneously broken gauge theories”, Phys. Rev. Lett., 30 (1973), 1268 | DOI

[15] Llewellyn Smith C.H., “High-energy behaviour and gauge symmetry”, Phys. Lett. B, 46 (1973), 233 | DOI

[16] Schwinger J., “Gauge invariance and mass”, Phys. Rev., 125 (1962), 397 | DOI | MR | Zbl

[17] Schwinger J., “Gauge invariance and mass. II”, Phys. Rev., 128 (1962), 2425 | DOI | MR | Zbl

[18] Kunimasa T., Gotō T., “Generalization of the Stueckelberg formalism to the massive Yang–Mills field”, Prog. Theor. Phys., 37 (1967), 452 | DOI

[19] Veltman M., “Perturbation theory of massive Yang–Mills fields”, Nucl. Phys. B, 7 (1968), 637 | DOI

[20] Slavnov A.A., Faddeev L.D., “Bezmassovoe i massivnoe pole Yanga–Millsa”, TMF, 3:1 (1970), 18 | MR

[21] van Dam H., Veltman M., “Massive and mass-less Yang–Mills and gravitational fields”, Nucl. Phys. B, 22 (1970), 397 | DOI

[22] Slavnov A.A., “Massivnye kalibrovochnye polya”, TMF, 10:3 (1972), 305

[23] Veltman M.J.G., “Nobel lecture: From weak interactions to gravitation”, Rev. Mod. Phys., 72 (2000), 341 | DOI | MR | Zbl

[24] Sikivie P., An introduction to technicolor, Preprint CERN-TH-2951, 1980

[25] Farhi E., Susskind L., “Technicolour”, Phys. Rep., 74 (1981), 277 | DOI

[26] Dimopoulos S., Ellis J., “Challenges for extended technicolour theories”, Nucl. Phys. B, 182 (1981), 505 | DOI

[27] Slavnov A.A., “Mekhanizm Khiggsa kak kollektivnyi effekt, obuslovlennyi dopolnitelnym izmereniem”, TMF, 148:3 (2006), 339 | DOI | MR | Zbl

[28] Deser S., Jackiw R., Templeton S., “Three-dimensional massive gauge theories”, Phys. Rev. Lett., 48 (1982), 975 | DOI

[29] Deser S., Jackiw R., Templeton S., “Topologically massive gauge theories”, Ann. Phys., 140 (1982), 372 | DOI | MR

[30] Schonfeld J.F., “A mass term for three-dimensional gauge fields”, Nucl. Phys. B, 185 (1981), 157 | DOI

[31] Cremmer E., Scherk J., “Spontaneous dynamical breaking of gauge symmetry in dual models”, Nucl. Phys. B, 72 (1974), 117 | DOI

[32] Hagen C.R., “Action-principle quantization of the antisymmetric tensor field”, Phys. Rev. D, 19 (1979), 2367 | DOI | MR

[33] Kalb M., Ramond P., “Classical direct interstring action”, Phys. Rev. D, 9 (1974), 2273 | DOI

[34] Nambu Y., “Magnetic and electric confinement of quarks”, Phys. Rep., 23 (1976), 250 | DOI

[35] Ogievetskii V.I., Polubarinov I.V., “Notof i ego vozmozhnye vzaimodeistviya”, Yad. fiz., 4:1 (1966), 216

[36] Aurilia A., Takahashi Y., “Generalized Maxwell equations and the gauge mixing mechanism of mass generation”, Prog. Theor. Phys., 66 (1981), 693 | DOI

[37] Freedman D.Z., P.K.Townsend, “Antisymmetric tensor gauge theories and non-linear $\sigma $-models”, Nucl. Phys. B, 177 (1981), 282 | DOI | MR

[38] Slavnov A.A., Frolov S.A., “Kvantovanie neabeleva antisimmetrichnogo tenzornogo polya”, TMF, 75:2 (1988), 201 | MR

[39] Allen T.J., Bowick M.J., Lahiri A., “Topological mass generation in $(3+1)$-dimensions”, Mod. Phys. Lett. A, 6 (1991), 559 | DOI | MR | Zbl

[40] Henneaux M., Lemes V.E.R., Sasaki C.A.G., Sorella S.P., Ventura O.S., Vilar L.C.Q., “A no-go theorem for the nonabelian topological mass mechanism in four dimensions”, Phys. Lett. B, 410 (1997), 195, arXiv: hep-th/9707129 | DOI

[41] Lahiri A., “Dynamical non-Abelian two-form: BRST quantization”, Phys. Rev. D, 55 (1997), 5045, arXiv: hep-ph/9609510 | DOI | MR

[42] Botta Cantcheff M., “Doublet groups, extended Lie algebras, and well defined gauge theories for the two-form field”, Intern. J. Mod. Phys. A, 20 (2005), 2673, arXiv: hep-th/0310156 | DOI | MR | Zbl

[43] Savvidy G., Topological mass generation in four-dimensional gauge theory, E-print, 2010, arXiv: 1001.2808 [hep-th] | MR