A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1+1 dimensions

作者：Lienert Matthias^*

来源：Journal of Mathematical Physics, 2015, 56(4): 042301.

DOI：10.1063/1.4915952

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i. e., a map from (space-time) N to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to a relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a newmethod to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.

• 出版日期2015-4