Negative energy densities in integrable quantum field theories at one-particle level

Abstract

We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.

Minor changes, as to appear in Phys. Rev. D; 20 pages, 9 figures

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• Lectures on quantum energy inequalities
• The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz
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Cited by in corpus (7)

• Energy conditions in general relativity and quantum field theory
• Quantum backflow and scattering
• Local photons
• Relative entropy of coherent states on general CCR algebras
• Quantum energy inequalities in integrable models with several particle species and bound states
• Towards an explicit construction of local observables in integrable quantum field theories
• Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level