Understanding the chiral and parity anomalies without Feynman diagrams

TL;DR

This paper reviews a method using adiabatic expansion to study chiral and parity anomalies in Dirac fermions, avoiding traditional Feynman diagram calculations.

Contribution

It introduces a diagram-free approach to analyze anomalies via adiabatic expansion in Bose and Fermi systems.

Findings

Demonstrates the effectiveness of adiabatic expansion in anomaly analysis

Provides a new perspective on chiral and parity anomalies

Simplifies calculations by avoiding Feynman diagrams

Abstract

We review the construction of the adiabatic expansion for Bose and Fermi systems and show how it may be used to explore the chiral and parity anomalies for Dirac fermions without the need to compute Feynman diagrams.