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arXiv · 2507.08066

Kappa Plane Wave Modes and Continuous Squeezing in Quantum Field Theory

Arash Azizi
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Abstract

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

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Arash Azizi. 2025-07-10. Kappa Plane Wave Modes and Continuous Squeezing in Quantum Field Theory. https://arxiv.org/abs/2507.08066

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