Relativistic Particle in Complex Space Time

TL;DR

This paper introduces a modified bilocal particle model in complex spacetime, explores its unique constraints, proposes a new physical equivalence concept, and finds that quantum states with momentum eigenstates exist only in four-dimensional spacetime, supported by an example scattering amplitude.

Contribution

It presents a novel complex spacetime particle model with unusual constraints and a new physical equivalence concept, highlighting the special role of four-dimensional spacetime in quantum theory.

Findings

Quantum physical states with momentum eigenstates exist only in four dimensions.

A scattering amplitude example demonstrates the model's applicability.

Unusual constraint structures are characterized and analyzed.

Abstract

A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture. It is found that in the quantum theory the physical state conditions are compatible with existence of eigenstates of momentum only when the dimension of space time is four. An example of scattering amplitude is calculated.