Boundary Conditions That Remove Certain Ultraviolet Divergences

• Main Author: Roderich Tumulka
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Symmetry
• Subjects: interior-boundary condition; particle creation; renormalization
• Online Access: https://www.mdpi.com/2073-8994/13/4/577

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 by taking limits in which a UV cutoff tends toward infinity. Here, I review a novel way of removing UV divergences: by imposing a type 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 to determine the probability distribution of detection times and places on a time-like 3-surface.