Toward a QFT treatment of nonexponential decay

Francesco Giacosa

doi:10.1051/epjconf/201818202045

Abstract

We study the properties of the survival probability of an unstable quantum state described by a Lee Hamiltonian. This theoretical approach resembles closely Quantum Field Theory (QFT): one can introduce in a rather simple framework the concept of propagator and Feynman rules, Within this context, we re-derive (in a detailed and didactical way) the well-known result according to which the amplitude of the survival probability is the Fourier transform of the energy distribution (or spectral function) of the unstable state (in turn, the energy distribution is proportional to the imaginary part of the propagator of the unstable state). Typically, the survival probability amplitude is the starting point of many studies of non-exponential decays. This work represents a further step toward the evaluation of the survival probability amplitude in genuine relativistic QFT. However, although many similarities exist, QFT presents some differences w.r.t. the Lee Hamiltonian which should be studied in the future.

Highlights

Quantum decays are a common phenomenon in particle, nuclear, and atomic physics [1,2,3]
Similar Hamiltonians have been used in various areas of physics, which go from atomic physics and quantum optic [4, 22, 23] to QCD [24]
We have proven that Eq (1) holds in the Quantum Field Theory (QFT)-like approach of effective Lee Hamiltonians by showing all the main steps leading to it

Summary

Introduction

Quantum decays are a common phenomenon in particle, nuclear, and atomic physics [1,2,3]. Lee Hamiltonians [18] (LH) represent a useful theoretical framework for the study of decays, e.g. Refs. The issue of non-exponential decay in a pure QFT framework is still debated: while in Ref. While the final goal is the derivation of Eq (1), and of non-exponential decay, in a genuine QFT relativistic environment, in this work we take a more humble intent. The article is organized as follows: in Sec. 2 we present the Lee Hamiltonian, both in the discrete and in the continuous cases.

Discrete LH

Continuous LH

Time evolution operator

Spectral function and survival probability

Conclusions