Boundary Conditions that Remove Certain Ultraviolet Divergences

• URL: http://arxiv.org/abs/2406.16180v1
• Date: Sun, 23 Jun 2024 18:11:29 GMT
• Title: Boundary Conditions that Remove Certain Ultraviolet Divergences
• Authors: Roderich Tumulka,
• Abstract summary: Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and taking limits in which an UV cut-off tends to infinity. I review a novel way of removing UV divergences: by imposing a kind of boundary condition on the wave function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and taking limits in which an UV cut-off tends to infinity. Here, I review a novel way of removing UV divergences: by imposing a kind of boundary condition on the wave function. These conditions, called interior-boundary conditions (IBCs), relate the values of the wave function at two configurations linked by the creation or annihilation of a particle. They allow for a direct definition of the Hamiltonian without renormalization or limiting procedures. In the last section, I review another boundary condition that serves for determining the probability distribution of detection times and places on a timelike 3-surface.

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