The Quantum Vacuum of Spacetime with a Fundamental Length

Abstract

A quantum theory of gravity implies a fine-grained structure of spacetime, which can be conveniently modeled as some form of pixelation at the Planck scale, with potentially observable consequences. In this work, we build upon previous results to investigate the effect of pixelation on the quantum vacuum, making use of the framework of Doubly Special Relativity (DSR). At the center of the DSR approach is an observer dependent length scale, defining the pixelation of spacetime. A key feature of quantum field theory in DSR is the dispersive nature of the vacuum state and the associated appearance of curvature in momentum space. As a result, the standard treatment of the renormalized stress-energy-momentum tensor acquires correction terms. As an illustration, we present here a calculation of the thermal vacuum and modified Casimir effect, using both modified propagators and momentum measures. We choose a consistent choice of momentum space metric that both generates the modified dispersion relations we use and preserves the Lorentz invariant character of the results obtained. Put together this constitutes a consistent calculation framework we can apply to other more complex scenarios.

arXiv commentAccepted in Physical Review D, pending final version

References in corpus (12)

• Quantum Gravity at a Lifshitz Point
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Foundations of Black Hole Accretion Disk Theory
• The principle of relative locality
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Relative-locality distant observers and the phenomenology of momentum-space geometry
• Quantum Gravity as an Information Network: Self-Organization of a 4D Universe
• A Note on analytic formulas of Feynman propagators in position space
• Accelerated Particle Detectors with Modified Dispersion Relations
• Fundamental length scale and the bending of light in a gravitational field
• Dynamics and the Emergence of Geometry in an Information Mesh

Cited by in corpus (2)

• Discrete Spacetime Theories Can Explain the Muon Magnetic Moment Discrepancy
• Thermal Casimir effect in $\kappa$-Minkowski space-time