Phase-induced particle creation in the Kappa-Gamma vacuum

Abstract The κ plane wave construction describes a one-parameter family of vacua as continuous-mode squeezed states of the Minkowski vacuum, with a real, frequency-dependent squeezing magnitude set by a single scale κ . Here we promote this real squeezing to complex squeezing by introducing a phase angle γ , obtaining a two-parameter family of κ γ plane wave modes and vacua | 0 κ γ ⟩ in which κ fixes the squeezing magnitude and γ fixes its orientation in phase space. Our central result is phase-induced particle creation: at fixed κ , a mismatch Δ γ between the phase that prepares the state and the phase that defines particles yields a nonzero Bogoliubov population, which vanishes when the two phases coincide and is enhanced in the infrared. This is an algebraic separation of squeezed-state particle notions that becomes a genuine dynamical creation process when a physical control—such as a modulated accelerating mirror—rotates γ in time. We derive the reciprocal Bogoliubov maps between the κ γ plane wave and κ R -Rindler bases, and evaluate the Wightman function, which splits into a stationary thermal (KMS) part set by κ and a phase-sensitive nonstationary part set by γ . The latter also contributes to point-split local observables, producing a generally γ -dependent nonstationary flux despite unchanged diagonal Planckian weights. With the stated infrared prescription the κ γ vacuum is Hadamard, carrying the standard Minkowski short-distance singularity and no additional horizon singularity.