Existence of relativistic dynamics for two directly interacting Dirac particles in 1+3 dimensions

Lienert, Matthias und Nöth, Markus (2021): Existence of relativistic dynamics for two directly interacting Dirac particles in 1+3 dimensions. In: Reviews in Mathematical Physics, Vol. 33, No. 7, 2150023

Abstract

Here we prove the existence and uniqueness of solutions of a class of integral equations describing two Dirac particles in 1+3 dimensions with direct interactions. This class of integral equations arises naturally as a relativistic generalization of the integral version of the two-particle Schrodinger equation. Crucial use of a multi-time wave function psi(x(1), x(2)) with x(1), x(2) is an element of R-2 is made. A central feature is the time delay of the interaction. Our main result is an existence and uniqueness theorem for a Minkowski half-space, meaning that the Minkowski spacetime is cut off before t = 0. We furthermore show that the solutions are determined by Cauchy data at the initial time;however, no Cauchy problem is admissible at other times. A second result is to extend the first one to particular FLRW spacetimes with a Big Bang singularity, using the conformal invariance of the Dirac equation in the massless case. This shows that the cutoff at t = 0 can arise naturally and be fully compatible with relativity. We thus obtain a class of interacting, manifestly covariant and rigorous models in 1 + 3 dimensions.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0129-055X
• Language: English