[Paper Review] Secularly growing loop corrections to the dynamical Casimir effect

Sergey Alexeev|arXiv (Cornell University)|Jul 10, 2017

Quantum Electrodynamics and Casimir Effect8 references6 citations

TL;DR

This paper investigates quantum loop corrections to the dynamical Casimir effect in (1+1)-dimensional massless scalar field theory with Dirichlet boundary conditions on a time-like mirror world-line. Using perturbative QFT techniques, it demonstrates that two-loop and four-point correlation function corrections grow secularly with time—scaling as T² or T⁴ depending on the mirror trajectory—indicating a breakdown of perturbation theory even at weak coupling, which challenges the validity of semi-classical approximations in non-stationary quantum field theories with self-interactions.

ABSTRACT

The paper is based on the Bachelor Thesis defended this year in ITEP, Moscow. This is the extended version of [arXiv:1707.02242] and contains a lot more technical details of the calculations. We consider (1+1)-dimensional massless scalar field theory with Dirichlet boundary conditions on arbitrary time-like curve. It is well known that in this situation there is a non-zero energy flux at the tree-level, if the latter curve corresponds to a non--stationary motion of the boundary. Such a problem is usually referred to as the radiation due to moving mirrors. We calculate quantum loop corrections to the energy flux from moving mirrors and find that they grow with time. Hence, they are not suppressed in comparison with the semi--classical contributions. Thus, we observe the break down of the perturbation theory, discuss its physical origin and ways to deal with such a situation.

Motivation & Objective

• . To analyze loop corrections to the energy flux in the dynamical Casimir effect beyond tree-level.
• . To investigate whether quantum corrections grow with time in non-stationary mirror configurations.
• . To assess the breakdown of perturbation theory due to secular growth in self-interacting QFT.
• . To explore the physical origin and implications of time-growing loop corrections in moving mirror systems.
• . To lay the groundwork for resummation techniques in strongly non-stationary, interacting QFT systems.

Proposed method

• . Solves the Klein-Gordon equation with Dirichlet boundary conditions on arbitrary time-like world-lines.
• . Derives mode functions and verifies canonical commutation relations for the field operators.
• . Computes the tree-level energy-momentum tensor and Wightman function for various mirror trajectories.
• . Applies perturbative quantum field theory to compute one-, two-, and four-point loop corrections.
• . Uses Keldysh formalism to compute corrections to the Keldysh propagator and occupation numbers.
• . Performs time-ordered integrals with theta functions to extract secular growth in T, especially in the T→∞ limit.

Experimental results

Research questions

• RQ1 . Do loop corrections to the energy flux in the dynamical Casimir effect grow secularly with time in a self-interacting scalar field theory?
• RQ2 . What is the time dependence of two-loop corrections to the Keldysh propagator for different mirror trajectories (rest, constant velocity, broken world-line, relativistic limit)?
• RQ3 . How do four-point correlation function corrections scale with time in the presence of a moving mirror?
• RQ4 . Why does perturbation theory break down in this system despite a small coupling constant?
• RQ5 . What are the physical implications of growing quantum corrections for the semi-classical approximation in non-stationary QFT?

Key findings

• . Two-loop corrections to the Keldysh propagator's anomalous average ⟨akak′⟩ grow as T² for a broken world-line with β < 1.
• . For a mirror approaching the speed of light, two-loop corrections grow as T⁴, indicating stronger secular enhancement.
• . Four-point correlation function corrections also exhibit secular growth, scaling as λ²T² or λ²T⁴ depending on the mirror trajectory.
• . The one-loop correction to the Keldysh propagator vanishes for a mirror at rest, but becomes non-zero and time-dependent for non-stationary motion.
• . The secular growth of loop corrections implies a breakdown of perturbation theory, even for weak coupling, due to the absence of time-translation invariance.
• . The results suggest that resummation of leading secular terms is necessary to describe the true dynamics, similar to phenomena in de Sitter space and strong electric fields.