Quantum field theory in flat spacetime with multiple time directions

TL;DR

This paper generalizes quantum field theory in spacetimes with multiple time directions, extending previous work to higher-dimensional spaces with multiple time axes, and demonstrates consistency with Minkowski spacetime results.

Contribution

It introduces a new formulation of quantum field theory in spacetimes with multiple time directions, including additional modes in canonical quantization and showing analytical continuation consistency.

Findings

Consistent formulation of QFT in multi-time spacetimes

Extension of previous Klein space results to higher dimensions

Introduction of additional modes in canonical quantization

Abstract

This letter serves as the generalization of the work 2505.16436, where we investigated the quantum field theory in Klein space which has two time directions. We extend studies to the general spacetime $\mathbb{R}^{n,d-n}\,(n,d-n\geq2)$ in a similar manner: the ``length of time'' $q$ is regarded as the evolution direction of the system; additional modes beyond the plane wave modes are introduced in the canonical quantization. We show that this novel formulation is consistent with the analytical continuation of the results in Minkowski spacetime.