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Multi-time formulation of pair creation. (English) Zbl 1286.81069

Summary: In a recent work [the authors, “Multi-time wave functions for quantum field theory”, Ann. Physics 345, 17–54 (2014; doi:10.1016/j.aop.2014.03.004)], we have described a formulation of a model quantum field theory in terms of a multi-time wave function and proposed a suitable system of multi-time Schrödinger equations governing the evolution of that wave function. Here, we provide further evidence that multi-time wave functions provide a viable formulation of relevant quantum field theories by describing a multi-time formulation, analogous to the one in [loc. cit.], of another model quantum field theory. This model involves three species of particles, say \(x\)-particles, anti-\(x\)-particles, and y-particles, and postulates that a \(y\)-particle can decay into a pair consisting of an \(x\) and an anti-\(x\) particle, and that an \(x\)-anti-\(x\) pair, when they meet, annihilate each other creating a \(y\)-particle. (Alternatively, the model can also be interpreted as representing beta decay.) The wave function is a multi-time version of a time-dependent state vector in Fock space (or rather, the appropriate product of Fock spaces) in the particle-position representation. We write down multi-time Schrödinger equations and verify that they are consistent, provided that an even number of the three particle species involved are fermionic.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R15 Operator algebra methods applied to problems in quantum theory
81T10 Model quantum field theories
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
81Q99 General mathematical topics and methods in quantum theory
81T99 Quantum field theory; related classical field theories
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