Gauge theories and quantum gravity in a finite interval of time, on a compact space manifold

Abstract

We study gauge theories and quantum gravity in a finite interval of time $\tau$, on a compact space manifold $\Omega$. The initial, final and boundary conditions are formulated in gauge invariant and general covariant ways by means of purely virtual extensions of the theories, which allow us to "trivialize" the local symmetries and switch to invariant fields (the invariant metric tensor, invariant quark and gluon fields, etc.). The evolution operator $U(t_{\text{f}},t_{\text{i}})$ is worked out diagrammatically for arbitrary initial and final states, as well as boundary conditions on $\partial \Omega$, and shown to be well defined and unitary for arbitrary $\tau =t_{\text{f}}-t_{\text{i}}<\infty$. We illustrate the basic properties in Yang-Mills theory on the cylinder.

arXiv comment52 pages; PRD

References in corpus (23)

• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• Package-X: A Mathematica package for the analytic calculation of one-loop integrals
• Superrenormalizable quantum gravity with complex ghosts
• Lecture notes on interacting quantum fields in de Sitter space
• Unitarity, stability and loops of unstable ghosts
• The boundary S-matrix and the AdS to CFT dictionary
• Super-renormalizable or Finite Lee-Wick Quantum Gravity
• On the quantum field theory of the gravitational interactions
• Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model
• What Do CFTs Tell Us About Anti-de Sitter Spacetimes?
• A new formulation of Lee-Wick quantum field theory
• Quantum Gravity, Fakeons And Microcausality
• Perturbative S-matrix for massive scalar fields in global de Sitter space
• Interacting Field Theories in de Sitter Space are Non-Unitary
• Triangular invariants, three-point functions and particle stability on the de Sitter universe
• Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term
• Aspects of perturbative unitarity
• A new quantization principle from a minimally non time-ordered product
• Fakeons, unitarity, massive gravitons and the cosmological constant
• Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity
• Purely virtual extension of quantum field theory for gauge invariant fields: Yang-Mills theory
• Purely virtual extension of quantum field theory for gauge invariant fields: quantum gravity

Cited by in corpus (1)

• Quantum gravity with purely virtual particles from asymptotically local quantum field theory