Quantum Energy Inequalities for the Non-Minimally Coupled Scalar Field
arXiv:0708.2450 · doi:10.1088/1751-8113/41/2/025402
Abstract
In this paper we discuss local averages of the energy density for the non-minimally coupled scalar quantum field, extending a previous investigation of the classical field. By an explicit example, we show that such averages are unbounded from below on the class of Hadamard states. This contrasts with the minimally coupled field, which obeys a state-independent lower bound known as a Quantum Energy Inequality (QEI). Nonetheless, we derive a generalised QEI for the non-minimally coupled scalar field, in which the lower bound is permitted to be state-dependent. This result applies to general globally hyperbolic curved spacetimes for coupling constants in the range . We analyse the state-dependence of our QEI in four-dimensional Minkowski space and show that it is a nontrivial restriction on the averaged energy density in the sense that the lower bound is of lower order, in energetic terms, than the averaged energy density itself.
23pp. Minor corrections and clarifications added
References in corpus (3)
Cited by in corpus (13)
- Absolute quantum energy inequalities in curved spacetime
- Quantum energy inequalities and local covariance II: Categorical formulation
- Local Thermal Equilibrium States and Quantum Energy Inequalities
- Traversable Wormholes and Classical Scalar Fields
- Averaged null energy condition in a classical curved background
- Quantum Inequalities from Operator Product Expansions
- Quantum Interest in (3+1) dimensional Minkowski space
- Quantum Energy Inequalities in Pre-Metric Electrodynamics
- How Much NEC Breaking Can the Universe Endure?
- Wormhole restrictions from quantum energy inequalities
- Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level
- Positivity Conditions for Generalised Schwarzschild Space-Times
- A Quantum Energy Inequality for a Non-commutative QFT