Fermionic one-particle states in curved spacetimes

Abstract

We show that a notion of one-particle state and the corresponding vacuum state exists in general curved backgrounds for spin $\frac{1}{2}$ fields. A curved spacetime can be equipped with a coordinate system in which the metric component $g_{--}=0$. We separate the component of the left-handed massless Dirac field which is annihilated by the null vector ${\partial }_{-}$ and compute the corresponding Feynman propagator. We find that the propagating modes are localized on two dimensional subspaces and the Feynman propagator is similar to the Feynman propagator of chiral fermions in two dimensional Minkowski spacetime. Therefore, it can be interpreted in terms of one-particle states and the corresponding vacuum state similarly to the second quantization in Minkowski spacetime.

36 pages, substantially revised, to appear in JHEP

References in corpus (5)

• Quantum gravity and Standard-Model-like fermions
• Chiral Gravitational Waves from Chiral Fermions
• Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
• Breakdown of Lorentz Invariance for Spin-1/2 Particle Motion in Curved Space-Time with Applications to Muon Decay
• Chiral fermions on 2D curved spacetimes

Cited by in corpus (2)

• Hadamard Renormalization of a 2-Dimensional Dirac Field
• Quantum of the bare cosmological constant