Quantized Dissipation from the Inverse-Square Anomaly in a Non-Hermitian Klein-Gordon Field

• URL: http://arxiv.org/abs/2603.28525v1
• Date: Mon, 30 Mar 2026 14:52:45 GMT
• Title: Quantized Dissipation from the Inverse-Square Anomaly in a Non-Hermitian Klein-Gordon Field
• Abstract summary: We construct an exactly solvable relativistic model that embeds the anomalous inverse-square interaction into a non-Hermitian Klein-Gordon field theory.<n>Imposing a strictly outgoing boundary condition at the singularity-interpreted as irreversible absorption-selects a unique physical realization.<n>The resulting decay rates exhibit universal geometric spacing, determined solely by the anomalous scaling exponent.
• Score: 0.42970700836450487
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We construct an exactly solvable relativistic model that embeds the anomalous inverse-square interaction into a non-Hermitian Klein-Gordon field theory through a purely imaginary, scale-invariant scalar potential. The stationary field equation reduces to an inverse-square Schrodinger-type problem with a quadratic spectral parameter. Imposing a strictly outgoing boundary condition at the singularity-interpreted as irreversible absorption-selects a unique physical realization and converts the fall-to-the-center instability into a discrete, log-periodic spectrum of complex energies. The resulting decay rates exhibit universal geometric spacing, determined solely by the anomalous scaling exponent and insensitive to microscopic short-distance regularization. This structure defines an emergent kinematic energy scale that controls dissipative dynamics and provides a minimal analytic framework for studying scale anomaly, boundary-condition-induced non-Hermiticity, and quantized dissipation in relativistic open quantum systems.

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