Phase-Induced Particle Creation in the Kappa-Gamma Vacuum

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 κγ plane wave modes and vacua |0κγ 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 Δγ 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 κγ plane wave and κR-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 κγ vacuum is Hadamard, carrying the standard Minkowski short-distance singularity and no additional horizon singularity.