Kappa plane wave modes and continuous squeezing in quantum field theory
Arash Azizi · Physical review. D/Physical review. D. · 2025
We introduce a new family of field modes in flat spacetime—termed κ -—constructed from κ -dependent linear combinations of Minkowski plane waves. These modes define a one-parameter family of vacua | 0 κ ⟩ that smoothly interpolate between different quantizations, reducing to the Minkowski vacuum in the limit κ → 0 . We show that | 0 κ ⟩ is uniquely characterized as a continuous-mode squeezed vacuum, with frequency-dependent squeezing parameter r ( ν ) satisfying tanh r ( ν ) = e − π ν / 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.