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Article Dans Une Revue Mathematical Physics, Analysis and Geometry Année : 2018

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

Résumé

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 cutoff (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cutoff 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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Dates et versions

hal-01514155 , version 1 (25-04-2017)
hal-01514155 , version 2 (28-03-2019)

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Jonas Lampart, Julian Schmidt, Stefan Teufel, Roderich Tumulka. Particle Creation at a Point Source by Means of Interior-Boundary Conditions. Mathematical Physics, Analysis and Geometry, 2018, 21 (2), ⟨10.1007/s11040-018-9270-8⟩. ⟨hal-01514155v2⟩
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