Remarks on relativistic scalar models with chemical potential

TL;DR

This paper reviews classical relativistic scalar field theories at nonzero chemical potential, discussing their descriptions, Hamiltonian choices, Lorentz invariance breaking, and deriving effective theories for Nambu-Goldstone modes.

Contribution

It provides a detailed analysis of finite-density scalar field theories, clarifies the equivalence of different descriptions, and explicitly derives low-energy effective theories for NG modes.

Findings

Equivalence of chemical potential and time-dependent field descriptions

Explicit derivation of NG mode effective field theory

Analysis of Lorentz invariance breaking effects

Abstract

We discuss selected aspects of classical relativistic scalar field theories with nonzero chemical potential. First, we offer a review of classical field theory at nonzero density within the Lagrangian formalism. The aspects covered include the question of equivalence of descriptions of finite-density states using a chemical potential or time-dependent field configurations, the choice of Hamiltonian whose minimization yields the finite-density equilibrium state, and the issue of breaking of Lorentz invariance. Second, we demonstrate how the low-energy effective field theory for Nambu-Goldstone (NG) modes arising from the spontaneous breakdown of global internal symmetries can be worked out explicitly by integrating out the heavy (Higgs) fields. This makes it possible to analyze the spectrum of NG modes and their interactions without having to deal with mixing of NG and Higgs fields, ubiquitous in the linear-sigma-model description of spontaneous symmetry breaking.