Covariant effective action for an antisymmetric tensor field

Abstract

Covariant quantization of rank-2 antisymmetric fields is non-trivial due to additional symmetries of the gauge parameters. We present an intuitive way to deal with this additional symmetry of gauge parameters in terms of geometrical understanding of field space. We generalize the DeWitt-Vilkovisky covariant effective action formalism for quantization of such theories. As an application, we quantize a massive rank-2 antisymmetric field using the covariant effective action approach and reproduce previously obtained results.

Quantum aspects of antisymmetric tensor field with spontaneous Lorentz violation

“…[26,33] respectively, and to Ref. [34] for a more recent analysis in the context of covariant effective action.…”

“…(11). Such symmetries lead to a degeneracy in the ghost determinant appearing in the Faddeev-Popov procedure [33], and require special treatment for quantization [33][34][35]. We follow a general quantization procedure developed in Ref.…”

“…We follow a general quantization procedure developed in Ref. [34] based on DeWitt-Vilkovisky's approach [22,23] that yields covariant and background independent resutls, to deal with the additional symmetries of gauge parameters and derive the 1-loop effective action.…”

“…(11), andχ a be the corresponding fixing condition for gauge parameters ǫ α (can be read off of Eqs. (9) and (10) ), then [34]…”

Quantum effective action for degenerate vector field theories

“…The particular degeneracy structure of the fluctuation operator discussed in this article is generically present in softly broken gauge theories. The quantization of such theories has been discussed recently in the context of vector field and tensor field models [15,18,19]. The same type of degeneracy also arises in models of massive gravity [20][21][22], cosmological Galileon models [23][24][25][26], and generalized Proca models [15,27,28].…”