Lorentz and CPT Violating Chern-Simons Term in the Formulation of Functional Integral

TL;DR

This paper demonstrates that within the functional integral formalism, the coefficient of the Lorentz- and CPT-violating Chern-Simons term induced by fermions remains undetermined, highlighting ambiguities in the theoretical formulation.

Contribution

It reveals the indeterminacy of the Chern-Simons coefficient in the functional integral approach, emphasizing the need for further clarification in Lorentz- and CPT-violating theories.

Findings

The coefficient of the Chern-Simons term is undetermined in the formalism.

The result impacts the understanding of Lorentz and CPT violation in quantum field theory.

Highlights ambiguity in theoretical predictions of Lorentz-violating effects.

Abstract

We show that in the functional integral formalism the (finite) coefficient of the induced, Lorentz- and CPT-violating Chern-Simons term, arising from the Lorentz- and CPT-violating fermion sector, is undetermined.