The Dirac equation in general relativity, a guide for calculations

Abstract

In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by including several examples from textbooks and the existing literature. In addition some basic material has been included in the appendices. It is our hope that graduate students and other re- searchers will find these notes useful.

59 pages

References in corpus (3)

• Hermiticity of the Dirac Hamiltonian in Curved Spacetime
• Frenet-Serret formalism for null world lines
• Fermi coordinates in Schwarzschild spacetime: closed form expressions

Cited by in corpus (19)

• Running vacuum in QFT in FLRW spacetime: The dynamics of ${\rho }_{\mathrm{vac}}(H)$ from the quantized matter fields
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Thermalization by a synthetic horizon
• Investigation of the Aharonov-Bohm and Aharonov-Casher Topological Phases for Quantum Entangled States in 2+1 Dimensions
• Non-relativistic limit of scalar and Dirac fields in curved spacetime
• Dynamical behavior of black-hole spacetimes
• Baryogenesis in $R^2$-Higgs Inflation: the Gravitational Connection
• Geometric post-Newtonian description of massive spin-half particles in curved spacetime
• Pseudo-Hermitian Dirac operator on the torus for massless fermions under the action of external fields
• Spin-1/2 particles under the influence of a uniform magnetic field in the interior Schwarzschild solution
• Particle Creation in some LRS Bianchi I models
• Atom-field dynamics in curved spacetime
• Quantum theory, thermal gradients and the curved Euclidean space
• Thermodynamic Flux-Force Closure Relations for Systems out of the Onsager Region
• One-Dimensional Relativistic Self-Gravitating Systems
• Simulating superluminal propagation of Dirac particles using trapped ions
• Hydrodynamic representation and Energy Balance for Dirac and Weyl fermions in curved space-times
• Phase diagrams of quasinormal frequencies for Schwarzschild, Kerr, and Taub-NUT black holes
• Selective Thermalization, Chiral Excitations, and a Case of Quantum Hair in the Presence of Event Horizons