Feynman and Squeezed States

TL;DR

This paper explores the connection between Lorentz-covariant solutions of a differential equation in particle physics and the mathematical framework of squeezed states in quantum optics, revealing a novel link between these fields.

Contribution

It demonstrates that Lorentz-covariant solutions for hadronic systems can serve as a basis for two-photon squeezed states, bridging quantum optics and relativistic particle models.

Findings

Lorentz-covariant solutions form a Poincaré group representation.

These solutions can model two-photon squeezed states in quantum optics.

Time-like separation relates to entropy increase in squeezed states.

Abstract

In 1971, Feynman et al. published a paper on hadronic mass spectra and transition rates based on the quark model. Their starting point was a Lorentz-invariant differential equation. This equation can be separated into a Klein-Gordon equation for the free-moving hadron and a harmonic oscillator equation for the quarks inside the hadron. However, their solution of the oscillator equation is not consistent with the existing rules of quantum mechanics and special relativity. On the other hand, their partial differential equation has many other solutions depending on boundary conditions. It is noted that there is a Lorentz-covariant set of solutions totally consistent with quantum mechanics and special relativity. This set constitutes a representation of the Poincar\'e group which dictates the fundamental space-time symmetry of particles in the Lorentz-covariant world. It is then shown that the same set of solutions can be used as the mathematical basis for two-photon coherent states or squeezed states in quantum optics. It is thus possible to transmit the physics of squeezed states into the hadronic world. While the time-like separation is the most puzzling problem in the covariant oscillator regime, this variable can be interpreted like the unobserved photon in the two-mode squeezed state which leads to an entropy increase.