On a quantization of deformed reducible gauge theories
A. A. Averianov, A. O. Barvinsky, I. L. Buchbinder, V. A. Krykhtin, D. V. Nesterov
TLDR
This paper quantizes deformed reducible gauge theories by restoring gauge invariance via a Stueckelberg procedure, deriving partition functions and effective actions.
Key contributions
- Converts deformed reducible gauge theories with broken symmetry into exactly gauge-invariant ones using a Stueckelberg procedure.
- Quantizes theories with first and second stages of reducibility, deriving partition functions with corresponding ghost fields.
- Applies the method to massive fermionic antisymmetric tensor field models in AdS space, calculating one-loop effective action.
Why it matters
This work provides a systematic method for quantizing complex gauge theories where symmetry is initially broken, a common challenge in theoretical physics. By restoring gauge invariance, it enables robust calculations of quantum effects, crucial for understanding fundamental interactions and field theories in curved spacetimes.
Original Abstract
We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be converted into exactly gauge-invariant theory which under a suitable choice of gauge conditions can be treated within the formalism of minimal wave operators manageable by the covariant Schwinger-DeWitt technique. We carry out quantization of such a theory in general terms when the initial generators of gauge transformations are of the first and second stages of reducibility and derive its partition function in terms of the functional integral with all corresponding ghost fields. This method is applied to quantization of massive fermionic totally antisymmetric tensor field models in $AdS$ space. One-loop quantum effective action for these models is derived in the form of the functional determinants of special Dirac-type differential operators in various dimensions.
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