Supergeometric Approach to Quantum Field Theory

TL;DR

This paper reviews a SuperGeometric approach to Quantum Field Theories that incorporates fermionic fields with a covariant geometric framework, introducing non-trivial curvature in the field space.

Contribution

It introduces a supergeometric framework for QFTs that allows for covariant scalar-fermion transformations and incorporates non-trivial fermionic curvature.

Findings

Constructed a minimal SG-QFT model with non-zero fermionic curvature.

Demonstrated the approach in both two and four spacetime dimensions.

Discussed potential future developments in SG-QFTs.

Abstract

We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the field-space supermetric, we show how a non-trivial field-space Riemannian curvature can be introduced in the fermionic sector, beyond the usual one that may have its origin in the scalar part of the theory. We present a minimal SG-QFT model with proper non-zero fermionic curvature both in two and four spacetime dimensions. Possible future directions in further developing SG-QFTs are discussed.