Multi-time Quantum Field Theory

Sören Petrat, Roderich Tumulka

Wayne Nicholas Polyzou, Tracie Michlin, Fatih Bulut

Roderich Tumulka

In a recent work (Petrat and Tumulka 2013 arXiv:1309.0802), 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 Petrat and Tumulka (2013 arXiv:1309.0802), 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.

Sören Petrat, Roderich Tumulka

In a recent work (Petrat and Tumulka 2013 arXiv:1309.0802), 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 Petrat and Tumulka (2013 arXiv:1309.0802), 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.

R. Grobe

CHRISTOF WETTERICH