QFT in Klein space

Abstract

In this paper, we investigate the quantum field theory in Klein space that has two time directions. To study the canonical quantization, we select the ``length of time" $q$ as the evolution direction of the system. In our novel construction, some additional modes beyond the plane wave modes are crucial in the canonical quantization and the later derivation of the LSZ reduction formula. We also derive the free two-point function by using Wick contraction in the canonical quantization formalism. Moreover, we introduce the path-integral formalism in which we can redefine the vacuum states and rederive the correlation functions. We show that all the results in the Klein space derived in our novel approach match those obtained via analytical continuation from the Minkowski spacetime.