Quantization of charged fields in the presence of intense electromagnetic fields

TL;DR

This work develops a quantum-field-theoretic framework for quantizing charged fields in nontrivial backgrounds, with a focus on the Schwinger effect in intense electromagnetic fields. By extending states of low energy from cosmology to anisotropic electric backgrounds and by enforcing unitary time evolution, the author isolates physically meaningful vacua and derives a generalized quantum Vlasov equation that accounts for vacuum ambiguity. The operational perspective connects different vacuum choices to measurable detector outcomes, showing that transitions on and off the external field crucially shape observables in both Schwinger-like experiments and cosmological analogues. The thesis further explores the implications for black-hole physics, proving that Schwinger dissipation prevents kugelblitz formation from light and revealing quantum fermion superradiance and black-hole discharge in charged RN spacetimes. Overall, the work bridges general relativity and quantum field theory in curved backgrounds, offering a coherent toolkit for quantum vacua, particle creation, and spacetime dynamics with potential experimental relevance in analogue systems and high-field regimes.

Abstract

This thesis applies techniques from quantum field theory in curved spacetimes to study particle creation in external fields, focusing on the Schwinger effect (i.e., the production of particle-antiparticle pairs by intense electric fields). Although experimental verification remains out of reach, theoretical analysis advances our understanding of this phenomenon and its broader implications. The work develops the theoretical framework for quantizing charged fields in nontrivial backgrounds, addressing the ambiguities in defining the quantum vacuum and extending the concept of states of low energy from cosmology to the Schwinger setting. It examines how different quantizations allow for unitary time evolution, and generalizes the quantum Vlasov equation to encompass a wider range of schemes. An operational perspective reveals that quantum ambiguities have genuine physical meaning, being linked to different modes of interaction and measurement. The study also analyzes dynamical transitions between static regimes and their impact on observables, with applications to analog cosmological expansion in Bose-Einstein condensates and the Schwinger effect itself. In the context of black holes, the thesis shows that the Schwinger effect prevents the formation of black holes from light under current conditions and investigates fermionic charge superradiance, demonstrating how quantum effects lead to black-hole discharge (a process without classical analogue). Overall, the thesis underscores the fundamental role of external electromagnetic and gravitational fields in defining particles and vacua, revealing the limits of flat-spacetime intuition and identifying purely quantum phenomena with implications for black-hole physics. It contributes to bridging the conceptual gap between general relativity and quantum field theory and offers new tools toward a consistent quantum description of spacetime.

Figures (22)

• Figure 1: Sauter-type electric field of time width $\sigma$ and maximum amplitude $E_0$, corresponding to the vector potential given in \ref{['eq:Sauter']}.
• Figure 2: Smearing function \ref{['eq:SmearingFunction']} of compact support $[-T,T]$ and slope of length $\delta$.
• Figure 3: Dependence of (a) $W_{\textbf{k}}(t_0=0)$ and (b) $Y_{\textbf{k}}(t_0=0)$ defining the SLEs on the support $[-T,T]$ of the smearing functions \ref{['eq:SmearingFunction']}. We show the infrared mode whose wavevector $\textbf{k}$ is parallel to the electric field and $k=10^{-5}\sigma^{-1}$. We use units $\sigma=1$.
• Figure 4: Power spectrum divided by $k^3/(2\pi^2)$ at $t= 0$ for a mode parallel (solid) and antiparallel (dashed) to the electric field and for SLEs with different supports. The power spectra for ILES coincide with those for the SLE of smallest support.
• Figure 5: Absolute value of the contributions $g_{\ell}$ of the multipoles $\ell$ with respect to the monopole at $t = 0$ for a SLE with support $T=10^2\sigma$. Note that $g_{\ell}$ are negative for odd values of $\ell$ and positive for even $\ell$. We use units $\sigma=1$.