On the creation of spin 1/2 particles and renormalization in FLRW spacetime

Abstract

Within the framework of adiabatic regularisation, we present a simple algorithm to calculate number density and renormalised energy-momentum density of spin 1/2 particles in spatially flat FLRW spacetimes. The conformal and axial anomalies thus found are in exact agreement with those obtained from other renormalization methods. This formalism can be considered as an appropriate extension of standard mechanism originally introduced for scalar fields, applicable to fermions in curved space.

Fermionic Schwinger effect and induced current in de Sitter space

“…is inappropriate (Ω k is a function to be determined as a power series of ). Instead, the WKB ansatz for spinor should take the following form [28][29][30]33] (see Appendix B for the derivation),…”

“…It is known that the WKB (adiabatic) expansion for a fermionic field cannot satisfy the equation of motion while satisfying the normalization condition to all orders of the expanding parameter . Nevertheless, the equivalence of the adiabatic and the DeWitt-Schwinger renormalization schemes was shown in [28], and there are applications of the adiabatic regularization of fermionic fields recently [29,30].…”

Particle Production via Dirac Dipole Moments in the Magnetized and Nonmagnetized Exponentially Expanding Universe

“…After these important works of Parker, the solutions of the relativistic particle wave equations have extensively been studied in various 3+1 dimensional spacetime backgrounds [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Using the WKB approach, the number density and renormalized energy-momentum tensor of the created spin-1/2 particle in the spatially flat (3+1)-dimensional Friedmann-Robertson-Walker (FRW) spacetime have been calculated [20]. The effect of the scalar particle creation on the collapse of a spherically symmetric massive star was investigated and it was demonstrated that the collapsing process was not independent from the particle creation rate [21].…”