Quantum Inequalities and Particle Creation in the Presence of an External, Time-Dependent Mamaev-Trunov Potential

Quantum Inequalities and Particle Creation in the Presence of an External, Time-Dependent Mamaev-Trunov Potential

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Kalista Schauer,1,a) Dr. Michael Pfenning,1,b) and Jared Cochrane1,c)

1 United States Military Academy at West Point, West Point, New York 10996-1790, USA
a) Corresponding author: kalistaschauer [at] gmail.com
b) michael.pfenning [at] westpoint.edu
c) jared.cochrane.mil [at] mail.mil


In 2011, Mr. Dan Solomon proposed a model of a quantized scalar field interacting with a time-dependent Mamaev-Trunov potential in two-dimensional Minkowski spacetime. This model is g overned by the K lein-Gordon wave equation with a time-dependent potential. Mr. Solomon claims that this model violates both the classical energy conditions of special relativity and the quantum energy conditions of quantum field theory in curved spacetime. Every classical energy condition can be violated, and their natural replacements are known as quantum inequalities. Mr. Solomon attempted to prove violations of the spatial and temporal quantum inequalities, and he correctly assumed that the n egative energy splits into two fluxes at t he C auchy s urface, where the p otential is t urned off. Unfortunately, Solomon neglects the contribution to the energy density due to particle creation when the potential is turned off at time t = 0 . In this project, we calculate the contribution to the stress energy tensor due to particle creation. We show that while the classical energy conditions are violated, the quantum energy inequalities hold, contrary to Mr. Solomon’s statements.