Kappa Plane Wave Modes and Continuous Squeezing in Quantum Field Theory

TL;DR

This paper introduces $$-plane wave modes in quantum field theory, defining a family of vacua that interpolate between known quantizations and exhibit continuous squeezing, unifying various mode decompositions.

Contribution

It presents a new family of modes and vacua in flat spacetime, connecting Minkowski, Rindler, and Unruh quantizations through a continuous parameter.

Findings

Defined $$-plane wave modes from Minkowski plane waves.

Characterized the vacua as continuous-mode squeezed states.

Derived Bogoliubov transformations linking different mode decompositions.

Abstract

We introduce a new family of field modes in flat spacetime -- termed $\kappa$-plane wave modes -- constructed from $\kappa$-dependent linear combinations of Minkowski plane waves. These modes define a one-parameter family of vacua, $|0_\kappa\rangle$, that smoothly interpolate between different quantizations, reducing to the Minkowski vacuum in the limit $\kappa \to 0$. We show that $|0_\kappa\rangle$ is uniquely characterized as a continuous-mode squeezed vacuum, with frequency-dependent squeezing parameter $r(\nu)$ satisfying $\tanh r(\nu) = e^{-\pi \nu/\kappa}$. We also derive two Bogoliubov transformations between $\kappa$-plane wave and $\kappa$-Rindler operators, which exhibit a universal form and smoothly interpolate between all known mode decompositions, including those of Minkowski, Rindler, and Unruh quantizations as limiting cases.