Relativistic Quantum Mechanics and Quantum Field Theory

TL;DR

This paper develops a relativistic framework for quantum mechanics and quantum field theory, incorporating superluminal velocities, nonlocal interactions, and Bohmian trajectories, with a focus on covariance and measurement processes.

Contribution

It introduces a manifestly covariant formulation of relativistic quantum mechanics and quantum field theory, including a Bohmian interpretation with particle trajectories.

Findings

Relativistic particle mechanics can include superluminal velocities and nonlocal interactions.

A covariant quantum mechanics formulation using many-time wave functions is proposed.

Bohmian trajectories are extended to quantum field theory with particle creation and destruction.

Abstract

A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant formulation of relativistic quantum mechanics (QM) of fixed number of particles (with or without spin) is presented, based on many-time wave functions and the spacetime probabilistic interpretation. These results are used to formulate the Bohmian interpretation of relativistic QM in a manifestly relativistic-covariant form. The results are also generalized to quantum field theory (QFT), where quantum states are represented by wave functions depending on an infinite number of spacetime coordinates. The corresponding Bohmian interpretation of QFT describes an infinite number of particle trajectories. Even though the particle trajectories are continuous, the appearance of creation and destruction of a finite number of particles results from quantum theory of measurements describing entanglement with particle detectors.