Multi-time wave functions for quantum field theory

2013/09/03 by Sören Petrat, Roderich Tumulka · 1 voice
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #hep-th #quant-ph

paper · pdf · doi:10.1016/j.aop.2014.03.004

arxiv published 2013/09/03 · arxiv updated 2014/01/24 · openalex publication_date 2014/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Multi-time wave functions such as φ(t₁,x₁,…,t_N,x_N) have one time variable t_j for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x₁,…,x_N) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle-position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga-Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space-time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages.

Citations

• Fermionic Wave Functions on Unordered Configurations

Discussions

• Multi-time wave functions There exists an active research on so-called multi-time wave functions. They are a relativistic version of multi-particle wave functions. In non-relativistic quantum mechanic [stackexchange, 3 points]