Nilpotent Symmetries in Super-Group Field Cosmology

TL;DR

This paper explores gauge invariance in super-group field cosmology, introducing finite superfield-dependent BRST transformations that connect different gauges and preserve the theory's invariance at quantum and classical levels.

Contribution

It proposes and analyzes finite superfield-dependent BRST transformations in super-group field cosmology, extending gauge invariance understanding in multiverse models.

Findings

Finite superfield-dependent BRST transformations switch the void functional between gauges.

The invariance holds for all gauge choices at classical and quantum levels.

Explicit calculations confirm the general gauge invariance of the theory.

Abstract

In this paper we study the gauge invariance of the third quantized super-group field cosmology which is a model for multiverse. Further, we propose both the nfinitesimal (usual) as well as the finite superfield-dependent BRST symmetry transformations which leave the effective theory invariant. The effects of finite superfield-dependent BRST transformations on the path integral (so-called void functional in the case of third quantization) are implemented. Within the finite superfield-dependent BRST formulation, the finite superfield-dependent BRST transformations with specific parameter switch the void functional from one gauge to another. We establish this result for the most general gauge with the help of explicit calculations which holds for all possible sets of gauge choices at both the classical and the quantum levels.