Spontaneous Symmetry Breaking & Entanglement in QFT

Abstract

This thesis explores two main themes: Amplitudes in Spontaneously Broken Lorentz Invariance and Entanglement Generation in the S Matrix. In the first part, we investigate how non-trivial classical solutions lead to theories where Lorentz generators, such as boosts, are spontaneously broken. Working in a non-diagonal basis due to non-localities arising from standard diagonalization procedures, we encountered technical challenges in the LSZ formalism. We analyzed the implications of non-relativistic dispersion relations, which introduce non-analyticities in the LSZ procedure. This was demonstrated through a detailed calculation of a 2-2 scattering amplitude involving 56 Feynman diagrams, revealing the analytic structure of poles and branch cuts. The low-energy behavior of these amplitudes exhibited intriguing patterns, though the contour prescription proved challenging to generalize due to the nature of Lorentz symmetry breaking. In the second part, we shifted focus to entanglement generation in the S-Matrix, exploring how quantum information concepts can shed light on the UV structure of EFTs. Using tools like FeynCalc and FeynArts, we calculated 2-2 photon scattering amplitudes in Euler-Heisenberg theory and resolved their helicity structure using custom Mathematica codes. We investigated how entanglement emerges in scattering processes for different product states, identifying universal patterns analogous to those in QED. By applying maximization and minimization principles of entanglement, we constrained EFT parameters and connected our findings to existing literature. Interestingly, different UV completions of Euler-Heisenberg theory (scalar, spinor, or vector exchange) led to distinct entanglement structures as a function of the scattering angle. This work bridges theoretical insights from the Positivity Program and quantum information theory, offering new perspectives on techniques used in theories with Lorentz symmetry breaking and a fresh perspective in studying entanglement generation in Effective Field Theories