SCIENCE SPIN-OFFS

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Multi-Time Wave Functions for Quantum Field Theory
Authors: Sören Petrat, Roderich Tumulka

(Submitted on 3 Sep 2013 (v1), last revised 2 Oct 2013 (this version, v2))

Abstract: Multi-time wave functions such as $\phi(t_1,x_1,\ldots,t_N,x_N)$ have one time variable $t_j$ for each particle. This type of wave function arises as a relativistic generalization of the wave function $\psi(t,x_1,\ldots,x_N)$ of non-relativistic quantum mechanics. We explore here the possibility of formulating quantum field theories in terms of multi-time wave functions. We mainly consider a particular quantum field theory (that is not fully Lorentz invariant) in the particle-position representation (of state vectors that are vectors in Fock space); we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and discuss their consistency. 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.

http://arxiv.org/abs/1309.0802