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arXiv · 1703.04476

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

Julian Schmidt·Jonas Lampart·Stefan Teufel·Roderich Tumulka
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Abstract

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.

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Julian Schmidt, Jonas Lampart, Stefan Teufel, Roderich Tumulka. 2017-04-25. Particle Creation at a Point Source by Means of Interior-Boundary Conditions. https://doi.org/10.1007/s11040-018-9270-8

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