Canonical Quantization of the U(1) Gauge Field in the Rindler Coordinates

Abstract

This paper describes the canonical quantization of the U(1) gauge field across all four regions in the Rindler coordinates in the Lorentz-covariant gauge. Concretely, in the four regions (future, past, left and right Rindler-wedges) in the Rindler coordinates, the gauge-fixed Lagrangian in the Lorentz-covariant gauge is obtained, which is composed of the U(1) gauge field, the B-field and ghost fields. Since the U(1) gauge and B-fields are decoupled from the ghost fields by the property of the U(1) gauge theory, the U(1) gauge field and the B-field are examined in this study. Then, by solving the equations of motion obtained from the gauge-fixed Lagrangian, the solutions of each mode of the U(1) gauge field and the B-field can be obtained. Following this, with the Klein-Gordon inner-product defined in the Rindler coordinates, the normalization constants of each of those mode-solutions are determined. Subsequently, formulating the canonical commutation relations of the U(1) gauge field and its canonical conjugate momentum, the equal-time commutation relations of the coefficient of each mode-solution in each direction of the U(1) gauge field in each region of the Rindler coordinates are obtained. From these, it can be seen that those coefficients have physical meaning as creation/annihilation operators. The polarization vectors in each region of the Rindler coordinates are also given in this study.

36 pages; v2: accepted version

References in corpus (17)

• Thermal Hadronization and Hawking-Unruh Radiation in QCD
• Detection of acceleration radiation in a Bose-Einstein condensate
• The Gauge Fields and Ghosts in Rindler Space
• Thermalization of particle detectors: The Unruh effect and its reverse
• Entanglement of the Vacuum between Left, Right, Future, and Past: The Origin of Entanglement-Induced Quantum Radiation
• Unruh effect for fermions from the Zubarev density operator
• Restoration of Dynamically Broken Chiral and Color Symmetries for an Accelerated Observer
• Entanglement generation for uniformly accelerated atoms assisted by environment-induced interatomic interaction and the loss of the anti-Unruh effect
• Rindler/Contracted-CFT Correspondence
• Rindler Bulk Reconstruction and Subregion Duality in AdS/CFT
• Quantum radiation by electrons in lasers and the Unruh effect
• Entanglement of the Vacuum between Left, Right, Future, and Past: Dirac spinor in Rindler spaces and Kasner spaces
• Quantum radiation produced by the entanglement of quantum fields
• Canonical quantization of gauge fields in static space-times with applications to Rindler spaces
• Schwinger effect and a uniformly accelerated observer
• Calculation of acceleration effects using the Zubarev density operator
• Canonical Quantization of the U(1) Gauge Field in the right Rindler-wedge in the Rindler Coordinates