Toward Quantization of Inhomogeneous Field Theory

TL;DR

This paper investigates the quantization of inhomogeneous scalar field theories in 1+1 dimensions with broken Poincaré symmetry, revealing classical equivalences and proposing methods to realize phenomena like the Unruh effect, with potential experimental tests.

Contribution

It introduces a novel approach to quantize inhomogeneous field theories inspired by curved spacetime methods, highlighting classical equivalences and potential experimental implications.

Findings

Classical equivalence between inhomogeneous and curved spacetime scalar theories.

Proposal to realize the Unruh effect in inhomogeneous field theory.

Advocates algebraic approach for quantization of generic inhomogeneous theories.

Abstract

We explore the quantization of a $(1+1)$-dimensional inhomogeneous scalar field theory in which Poincar\'{e} symmetry is explicitly broken. We show the `classical equivalence' between a scalar field theory on curved spacetime background and its corresponding inhomogeneous scalar field theory. This implies that a hidden connection may exist among some inhomogeneous field theories, which corresponds to general covariance in field theory on curved spacetime. Based on the classical equivalence, we propose how to quantize a specific field theory with broken Poincar\'{e} symmetry inspired by standard field theoretic approaches, canonical and algebraic methods, on curved spacetime. Consequently, we show that the Unruh effect can be realized in inhomogeneous field theory and propose that it may be tested by a condensed matter experiment. We suggest that an algebraic approach is appropriate for the quantization of a generic inhomogeneous field theory.