Symmetries Shared by Particle Physics and Quantum Optics

TL;DR

This paper explores the shared symmetries between particle physics and quantum optics, focusing on the O(1,1) group, and shows how it underpins various models including the parton model and quantum states of light.

Contribution

It demonstrates that the O(1,1) symmetry group unifies concepts in quantum optics and particle physics, providing a common mathematical framework for diverse theories.

Findings

Squeeze states of light are representations of the O(1,1) group.

The O(1,1) group supports Feynman's ideas of the parton and quark models.

A covariant picture of the parton model with decoherence is developed.

Abstract

It is known that two coupled harmonic oscillators can support the symmetry group as rich as O(3,3) which corresponds to the Lorentz group applicable to three space-like and three time-like coordinates. This group contains many subgroups, including O(3), O(3,2), O(2,1) which are already familiar to us. In this report, we discuss the symmetry of O(1,1) which plays pivotal roles in quantum optics and particle physics. For this one-parameter group, a full-fledged group theory is not necessary, and we can start the discussion from the Hamiltonian of the coupled oscillator system. It is shown first that, from the group theoretical point of view, the squeeze state of light is a representation of this O(1,1) group. It is then shown that the same mathematical device supports three seemingly different ideas of Feynman, namely the parton model, the relativistic quark model for hadrons, and the ``rest of the universe'' in connection with the density matrix. If these three theories are combined, they produce a covariant picture of Feynman's parton model with a built-in decoherence mechanism.