Search results for "Regular"
showing 10 items of 855 documents
Adiabatic regularization for spin-1/2 fields
2013
We extend the adiabatic regularization method to spin-1/2 fields. The ansatz for the adiabatic expansion for fermionic modes differs significantly from the WKB-type template that works for scalar modes. We give explicit expressions for the first adiabatic orders and analyze particle creation in de Sitter spacetime. As for scalar fields, the adiabatic method can be distinguished by its capability to overcome the UV divergences of the particle number operator. We also test the consistency of the extended method by working out the conformal and axial anomalies for a Dirac field in a Friedmann-Lemaitre-Robertson-Walker spacetime, in exact agreement with those obtained from other renormalization…
Coordinate-free quantization of first-class constrained systems
1996
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.
Equivalence of Adiabatic and DeWitt-Schwinger renormalization schemes
2014
We prove that adiabatic regularization and DeWitt-Schwinger point-splitting provide the same result for the renormalized expectation values of the stress-energy tensor for spin-$1/2$ fields. This generalizes the equivalence found for scalar fields, which is here recovered in a different way. We also argue that the coincidence limit of the DeWitt-Schwinger proper time expansion of the two-point function exactly agrees with the analogous expansion defined by the adiabatic regularization method at any order (for both scalar and spin-$1/2$ fields). We also illustrate the power of the adiabatic method to compute higher order DeWitt coefficients in FLRW universes.
Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
2018
Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external mome…
Running gravitational couplings, decoupling, and curved spacetime renormalization
2020
We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale $\mu$. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.
En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
2014
The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the…
Baryon chiral perturbation theory
2009
We provide a short introduction to the one-nucleon sector of chiral perturbation theory and address the issue of power counting and renormalization. We discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order ${\cal O}(q^6)$ and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors. Finally, we address the complex-mass scheme for describing unstable particles in effective field theory.
Inflation, renormalization, and CMB anisotropies
2010
5 páginas.-- Trabajo presentado al Spanish Relativity Meeting (ERE 2009).-- El PDF es la versión pre-print (arXiv:1002.3914v1).
Modelling uncertainties in phase-space boundary integral models of ray propagation
2020
Abstract A recently proposed phase-space boundary integral model for the stochastic propagation of ray densities is presented and, for the first time, explicit connections between this model and parametric uncertainties arising in the underlying physical model are derived. In particular, an asymptotic analysis for a weak noise perturbation of the propagation speed is used to derive expressions for the probability distribution of the phase-space boundary coordinates after transport along uncertain, and in general curved, ray trajectories. Furthermore, models are presented for incorporating geometric uncertainties in terms of both the location of an edge within a polygonal domain, as well as …
Relaxation of periodic and nonstandard growth integrals by means of two-scale convergence
2019
An integral representation result is obtained for the variational limit of the family functionals $\int_{\Omega}f\left(\frac{x}{\varepsilon}, Du\right)dx$, as $\varepsilon \to 0$, when the integrand $f = f (x,v)$ is a Carath\'eodory function, periodic in $x$, convex in $v$ and with nonstandard growth.