Phase-Induced Particle Creation in the Kappa-Gamma Vacuum

Abstract The $\kappa$ 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 $\kappa$. Here we promote this real squeezing to complex squeezing by introducing a phase angle $\gamma$, obtaining a two-parameter family of $\kappa\gamma$ plane wave modes and vacua $|0_{\kappa\gamma}\rangle$ in which $\kappa$ fixes the squeezing magnitude and $\gamma$ fixes its orientation in phase space. Our central result is phase-induced particle creation: at fixed $\kappa$, a mismatch $\Delta\gamma$ 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 $\gamma$ in time. We derive the reciprocal Bogoliubov maps between the $\kappa\gamma$ plane wave and $\kappa_{\rm R}$-Rindler bases, and evaluate the Wightman function, which splits into a stationary thermal (KMS) part set by $\kappa$ and a phase-sensitive nonstationary part set by $\gamma$. The latter also contributes to point-split local observables, producing a generally $\gamma$-dependent nonstationary flux despite unchanged diagonal Planckian weights. With the stated infrared prescription the $\kappa\gamma$ vacuum is Hadamard, carrying the standard Minkowski short-distance singularity and no additional horizon singularity.