Quantum "Twin Peaks" or Path Integrals in the Future Light Cone

TL;DR

This paper constructs a Lorentz-invariant path integral measure in Minkowski space, drawing analogies with Euclidean Wiener measures, and explores the correspondence between paths in the future cone and Euclidean coverings.

Contribution

It introduces a novel Lorentz-invariant path integral measure and establishes a correspondence between Minkowski future cone paths and Euclidean plane coverings.

Findings

Constructed a Lorentz-invariant path integral measure.

Established a correspondence between Minkowski and Euclidean paths.

Demonstrated invariance properties under relevant groups.

Abstract

By analogy with the Wiener measure on the Euclidean plane that is invariant under the group of rotations and quasi-invariant under the group of diffeomorphisms, we construct the path integrals measure that is invariant under the Lorentz group and quasi-invariant under the group of diffeomorphisms. The correspondence between the paths in the future cone of the Minkowskian plane and the paths in the coverings of the Euclidean plane is established.