Matter-enhanced transition probabilities in quantum field theory

TL;DR

This paper investigates how matter surrounding particles in detectors influences transition probabilities in quantum field theory, revealing finite-size corrections that can break Lorentz invariance, especially for light particles.

Contribution

It introduces a modified S-matrix framework that accounts for matter effects and finite-time corrections, highlighting their impact on transition probabilities and Lorentz symmetry.

Findings

Finite-size corrections of order 1/T are derived.

Matter effects can significantly alter transition probabilities.

Lorentz invariance can be broken by matter-induced corrections.

Abstract

The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincar\'e transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, $S[\text T]$, that satisfies the boundary condition at T. Using $S[\text T]$, the finite-size corrections of the form of ${1/\text T}$ are found. The corrections to the Fermi's golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths.