Quantum field theory on a growing lattice

TL;DR

This paper develops a quantum field theory framework on a dynamically growing lattice, analyzing particle creation and energy implications, with potential cosmological applications and limitations.

Contribution

It introduces a quantized scalar field theory on a growing lattice, addressing the challenges and implications of mode creation in such a setting.

Findings

Growth-induced particle creation injects excessive energy into the vacuum.

Restrictions are necessary on the lattice to define a consistent theory.

Local mode birth may not be a viable cosmological model due to energy concerns.

Abstract

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth.