Quantum Inhomogeneous Field Theory: Unruh-Like Effects and Bubble Wall Friction

TL;DR

This work extends quantum field theory techniques to a (1+1)-dimensional inhomogeneous setting by mapping a supersymmetric curved background to a quantum inhomogeneous field theory (QIFT) with a position-dependent mass. It builds a locally Hadamard state and implements Hadamard renormalization to obtain a covariantly conserved energy–momentum tensor, enabling a precise interpretation of quantum effects. The main findings are an Unruh-like thermal-like response for an observer just outside the right asymptotic region and a leading-order vanishing of quantum friction on a Higgs bubble wall during the electroweak phase transition. The approach provides a coherent algebraic framework for QIFT and offers avenues to extend the analysis to left regions, fermions, finite temperature, and higher dimensions, with implications for early-ununiverse dynamics.

Abstract

In this paper, we study a free scalar field in a specific (1+1)-dimensional curved spacetime. By introducing an algebraic state that is locally Hadamard, we derive the renormalized Wightman function and explicitly calculate the covariantly conserved quantum energy-momentum tensor up to a relevant order. From this result, we show that the Hadamard renormalization scheme, which has been effective in traditional quantum field theory in curved spacetime, is also applicable in the quantum inhomogeneous field theory. As applications of this framework, we show the existence of an Unruh-like effect for an observer slightly out of the right asymptotic region, as well as the vanishing of quantum frictional effect in the leading order ($e^{- bx}$) on the bubble wall expansion during the electroweak phase transition in the early universe.

Figures (1)

• Figure 1: We depict the monotonically increasing, S-shaped graph of $m_{\text{eff}}^2(x)$ as a function of $x$. Here, $x_\epsilon$ denotes the position of an observer located slightly out of the right asymptotic infinity. When we compute the positive frequency Wightman function $G^+$, we disregard the modes $\Phi_\epsilon$ within the energy range between $b \beta - \epsilon$ and $b \beta$, where $\frac{\epsilon}{b \beta} \ll 1$.