0000000000037023
AUTHOR
Silvia Pla
(F, G) -summed form of the QED effective action
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F}=\frac{1}{4}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}(x)$, $\mathcal{G}=\frac{1}{4}{\stackrel{\texttildelow{}}{F}}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}(x)$, including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrar…
Translational anomaly of chiral fermions in two dimensions
It is well known that a quantized two-dimensional Weyl fermion coupled to gravity spoils general covariance and breaks the covariant conservation of the energy-momentum tensor. In this brief article, we point out that the quantum conservation of the momentum can also fail in flat spacetime, provided the Weyl fermion is coupled to a time-varying homogeneous electric field. This signals a quantum anomaly of the space-translation symmetry, which has not been highlighted in the literature so far.
Adiabatic regularization with a Yukawa interaction
We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stress-energy tensor $\langle T_{\mu\nu} \rangle$ and the bilinear $\langle \bar\psi\psi\rangle$ in a spatially flat FLRW spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields…
Role of gravity in the pair creation induced by electric fields
We analyze the pair production induced by homogenous, time-dependent electric fields in an expanding space-time background. We point out that, in obtaining the semiclassical Maxwell equations, two distinct notions of adiabatic renormalization are possible. In Minkowski space the two recipes turn out to be equivalent. However, in the presence of gravity only the recipe requiring an adiabatic hierarchy between the gravitational and the gauge field is consistent with the conservation of the energy-momentum tensor.
R-summed form of adiabatic expansions in curved spacetime
The Feynman propagator in curved spacetime admits an asymptotic (Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably, all terms in the series containing the Ricci scalar R can be summed exactly. We show that this (non-perturbative) property of the Schwinger-DeWitt series has a natural and equivalent counterpart in the adiabatic (Parker-Fulling) series expansion of the scalar modes in an homogeneous cosmological spacetime. The equivalence between both R-summed adiabatic expansions can be further extended when a background scalar field is also present.
Pair production due to an electric field in 1+1 dimensions and the validity of the semiclassical approximation
Solutions to the backreaction equation in $1+1$-dimensional semiclassical electrodynamics are obtained and analyzed when considering a time-varying homogeneous electric field initially generated by a classical electric current, coupled to either a quantized scalar field or a quantized spin-$\frac{1}{2}$ field. Particle production by way of the Schwinger effect leads to backreaction effects that modulate the electric field strength. Details of the particle production process are investigated along with the transfer of energy between the electric field and the particles. The validity of the semiclassical approximation is also investigated using a criterion previously implemented for chaotic i…
Adiabatic regularization for Dirac fields in time-varying electric backgrounds
The adiabatic regularization method was originally proposed by Parker and Fulling to renormalize the energy-momentum tensor of scalar fields in expanding universes. It can be extended to renormalize the electric current induced by quantized scalar fields in a time-varying electric background. This can be done in a way consistent with gravity if the vector potential is considered as a variable of adiabatic order one. Assuming this, we further extend the method to deal with Dirac fields in four spacetime dimensions. This requires a self-consistent ansatz for the adiabatic expansion, in presence of a prescribed time-dependent electric field, which is different from the conventional expansion u…