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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

Citations:

Zbl 0070.22102
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References:

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