## Second order gauge theory.(English)Zbl 1109.70019

Summary: A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama’s program [R. Utiyama, Phys. Rev., II. Ser. 101, 1597–1607 (1956; Zbl 0070.22102)]. A novel field strength $$G = \partial F + fAF$$ arises besides the one of the first order treatment, $$F = \partial A - \partial A + fAA$$. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky generalized electrodynamics is derived as a particular case in which the Lagrangian of the gauge field is $$L_{P} \propto G^{2}$$. In this application the photon mass is estimated. The $$SU (N)$$ infrared regime is analysed by means of Alekseev-Arbuzov-Baikov’s Lagrangian.

### MSC:

 70S15 Yang-Mills and other gauge theories in mechanics of particles and systems

Zbl 0070.22102
Full Text:

### References:

 [1] Utiyama, R., Phys. rev., 101, 1597, (1956) [2] Ogievetski, V.I.; Polubarinov, I.V., Nuovo cim., 23, 173, (1962) [3] N. Nakanishi, I. Ojima, Covariant operator formalism of gauge theories and quantum gravity, in: Lecture Notes in Physics, vol. 27, World Scientific, 1991. [4] de Melo, C.A.M.; Pimentel, B.M.; Pompeia, P.J., Nuovo cim., B121, 193, (2006) [5] Poincaré, H., Science and hypothesis, (1952), Dover · Zbl 0049.29106 [6] Ostrogradsky, M.; Whitaker, E.T., Treatise on the analytical dynamics of particles and rigid bodies, Mem. acad. Saint |St. Petersburg, 6, 4, 385, (1959), Cambridge University Press Cambridge [7] Bopp, F., Ann. physik, 38, 345, (1940) [8] Podolsky, B.; Podolsky, B.; Kikuchi, C.; Podolsky, B.; Schwed, P., Phys. rev., Phys. rev., Rev. mod. phys., 20, 40, (1948) [9] Frenkel, J.; Frenkel, J.; Santos, R.B., Phys. rev. E, Int. J. mod. phys. B, 13, 315, (1999) [10] Green, A., Phys. rev., Phys. rev., 75, 1926, (1949) [11] Alekseev, A.I.; Arbuzov, B.A.; Baker, M.; Ball, J.S.; Zachariasen, F., Theor. math. phys., Nucl. phys. B, 229, 45, (1983) [12] Fock, V.A., Z. phys., 57, 261, (1929) [13] Felsager, B., Geometry, particles, and fields, (2000), Springer-Verlag New York [14] Moniz, E.J.; Sharp, D.H., Phys. rev. D, Phys. rev. D, 15, 2850, (1977) [15] Eidelman, S., Phys. lett. B, 592, 1, (2004) [16] Ryan, J.J.; Accetta, F.; Austin, R.H., Phys. rev. D, 32, 802, (1985) [17] Kubo, R.; Nagamiya, T., Solid state physics, (1968), McGraw-Hill New York [18] Alekseev, A.I.; Arbuzov, B.A.; Baikov, V.A., Theor. math. phys., 52, 739, (1982) [19] G. Dvali, R. Jackiw, So-Young Pi, Topological mass generation in four dimensions, Report-no: MIT-CTP-3704 [hep-th/0511175]. [20] Galvão, C.A.P.; Pimentel, B.M., Can. J. phys., 66, 460, (1988) [21] Güler, Y.; Pimentel, B.M.; Teixeira, R.G.; Tomazelli, J.L., Il nuovo cimento, Ann. phys., 267, 75, (1998)
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