Adiabatic expansions for Dirac fields, renormalization, and anomalies

Abstract

We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to improve the adiabatic regularization/renormalization scheme. We provide details on the application of the method for Dirac fields living in a four-dimensional Friedmann-Lemaitre-Robertson-Walker spacetime with a Yukawa coupling to an external scalar field. We check the consistency of our proposal by working out the conformal anomaly. We also analyze a two-dimensional Dirac field in Minkowski space coupled to a homogeneous electric field and reproduce the known results on the axial anomaly. The adiabatic expansion of the modes given here can be used to properly characterize the allowed physical states of the Dirac fields in the above external backgrounds.

10 pages. Revised version, misprints corrected, some points clarified

References in corpus (7)

• Preferred instantaneous vacuum for linear scalar fields in cosmological space-times
• The Creation of Particles in an Expanding Universe
• Effects of Quantized Scalar Fields in Cosmological Spacetimes with Big Rip Singularities
• Equivalence of Adiabatic and DeWitt-Schwinger renormalization schemes
• Pair creation in electric fields, anomalies, and renormalization of the electric current
• Study of the preheating phase of chaotic inflation
• Creation of quantized particles, gravitons and scalar perturbations by the expanding universe

Cited by in corpus (26)

• Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem
• Running vacuum in quantum field theory in curved spacetime: renormalizing ${\rho }_{vac}$ without $\sim m^4$ terms
• Running vacuum in QFT in FLRW spacetime: The dynamics of ${\rho }_{\mathrm{vac}}(H)$ from the quantized matter fields
• Gravitational production of nearly thermal fermionic Dark Matter
• Role of gravity in the pair creation induced by electric fields
• Running couplings from adiabatic regularization
• An analytic evaluation of gravitational particle production of fermions via Stokes phenomenon
• On the origin of entropy of gravitationally produced dark matter: the entanglement entropy
• Adiabatic regularization for Dirac fields in time-varying electric backgrounds
• Pair production due to an electric field in 1+1 dimensions and the validity of the semiclassical approximation
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Curvature and thermal corrections in tree-level CPT-Violating Leptogenesis
• Breaking of adiabatic invariance in the creation of particles by electromagnetic fields
• Note on the pragmatic mode-sum regularization method: translational-splitting in a cosmological background
• Equivalence of the adiabatic expansion and Hadamard renormalization for a charged scalar field
• R-summed form of adiabatic expansions in curved spacetime
• Cosmological decay of Higgs-like scalars into a fermion channel
• Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes
• Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology
• Low Energy States and CPT invariance at the Big Bang
• Translational anomaly of chiral fermions in two dimensions
• Fock quantization of the Dirac field in hybrid quantum cosmology: Relation with adiabatic states
• Ultralight dark matter or dark radiation cosmologically produced from infrared dressing
• Induced energy-momentum tensor of Dirac field in 2D de Sitter QED
• Argument for the radiation-dominated behavior of matter fields in the preinflationary era
• Physical scale adiabatic regularization in cosmological spacetimes