The averaged null energy condition and difference inequalities in quantum field theory

Abstract

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.

20 pages

References in corpus (2)

• Motion of Inertial Observers Through Negative Energy
• A note on the averaged null energy condition in quantum field theory

Cited by in corpus (17)

• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Quantum inequalities in two dimensional Minkowski spacetime
• Bounds on negative energy densities in flat spacetime
• A holographic proof of the averaged null energy condition
• Averaged Energy Conditions and Evaporating Black Holes
• Averaged null energy condition in spacetimes with boundaries
• Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes
• Quantum Inequalities for the Electromagnetic Field
• The averaged null energy condition for general quantum field theories in two dimensions
• Focusing and the Holographic Hypothesis
• Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes
• On Quantum Spacetime and the horizon problem
• Quantum interest for scalar fields in Minkowski spacetime
• Achronal ANEC, Weak Cosmic Censorship, and AdS/CFT duality
• Restrictions on negative energy density in a curved spacetime
• Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level
• Classification of quantum states based on the null energy condition