Kappa Plane Wave Modes and Continuous Squeezing in Quantum Field Theory

Abstract

We introduce a new family of field modes in flat spacetime -- termed $\hat{I}º$-plane wave modes -- constructed from $\hat{I}º$-dependent linear combinations of Minkowski plane waves. These modes define a one-parameter family of vacua, $|0_{\hat{I}}º⟩$, that smoothly interpolate between different quantizations, reducing to the Minkowski vacuum in the limit $\hat{I}º\to 0$. We show that $|0_{\hat{I}}º⟩$ is uniquely characterized as a continuous-mode squeezed vacuum, with frequency-dependent squeezing parameter $r(\hat{I}½)$ satisfying $\tanh r(\hat{I}½)=e^{-\ddot{I}€\hat{I}½/\hat{I}º}$. We also derive two Bogoliubov transformations between $\hat{I}º$-plane wave and $\hat{I}º$-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.

18 pages, PRD version