A Truncated Majorana

Abstract

We investigate the quantum field dynamics of truncating a Majorana wave packet via a time-dependent channel shutter. Modeling truncation as a controlled modification of chiral propagation rather than a literal spatial cut, we analyze a $1+1$D massless Majorana field subjected to a time-dependent rotation between its chiral components. We demonstrate that this protocol manifests two complementary physical limits. Globally, a mismatch between early- and late-time channel identifications induces a fermionic Bogoliubov transformation. We prove this asymptotic change universally generates an infrared soft-mode memory, $\beta(\omega, \nu) \propto (\omega+\nu)^{-1}$, leading to a logarithmic divergence in the Hilbert--Schmidt norm. This orthogonality-catastrophe-like obstruction persists even under infinitely smooth switching in the massless limit. Conversely, in the number-conserving regime where pair production vanishes, the shutter acts as a purely causal filter. We establish exact local field identities showing that, restricted to the even local observable algebra, the retained sector is exactly equivalent to a single-particle state while the discarded sector reduces to the vacuum. Ultimately, we show that global infrared memory and local causal truncation are complementary diagnostics of the same dynamical operation. These results provide a rigorous field-theoretic foundation for time-dependent control in topological platforms, cleanly separating effective operational benchmarks from microscopic boundary dynamics.