13 research outputs found
Systematization of Basic Divergent Integrals in Perturbation Theory and Renormalization Group Functions
We show that to n loop order the divergent content of a Feynman amplitude is
spanned by a set of basic (logarithmically divergent) integrals which need not
be evaluated. Only the coefficients of the basic divergent integrals are
necessary to determine renormalization group functions. Relations between these
coefficients of different loop orders are derived.Comment: 10 pages, 5 figure
Dual embedding of the Lorentz-violating electrodinamics and Batalin-Vilkovisky quantization
Modifications of the electromagnetic Maxwell Lagrangian in four dimensions
have been considered by some authors. One may include an explicit massive term
(Proca) and a topological but not Lorentz-invariant term within certain
observational limits.
We find the dual-corresponding gauge invariant version of this theory by
using the recently suggested gauge embedding method. We enforce this
dualisation procedure by showing that, in many cases, this is actually a
constructive method to find a sort of parent action, which manifestly
establishes duality. We also use the gauge invariant version of this theory to
formulate a Batalin-Vilkovisky quantization and present a detailed discussion
on the excitation spectrum.Comment: 8 page
Remarks on the Causality, Unitarity and Supersymmetric Extension of the Lorentz and CPT-Violating Maxwell-Chern-Simons Model
The gauge-invariant Chern-Simons-type Lorentz- and CPT-breaking term is here
re-assessed and issues like causality, unitarity, spontaneous gauge-symmetry
breaking are investigated. Moreover, we obtain a minimal extension of such a
system to a supersymmetric environment. We comment on resulting peculiar
self-couplings for the gauge sector, as well as on background contribution for
gaugino masses.Comment: 5 pages, NPB style, talk presented at "Renormalization Group and
Anomalies in Gravity and Cosmology", Ouro Preto, Brazil, March 200
Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
We present a both ultraviolet and infrared regularization independent
analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta
function to two loop order. We show explicitly that off-shell infrared
divergences as well as the overall two loop ultraviolet divergence cancel out
whilst the beta function receives contributions of infrared modes.Comment: 7 pages, 2 figures, typos correcte
Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation
We compare a momentum space implicit regularisation (IR) framework with other
renormalisation methods which may be applied to dimension specific theories,
namely Differential Renormalisation (DfR) and the BPHZ formalism. In
particular, we define what is meant by minimal subtraction in IR in connection
with DfR and dimensional renormalisation (DR) .We illustrate with the
calculation of the gluon self energy a procedure by which a constrained version
of IR automatically ensures gauge invariance at one loop level and handles
infrared divergences in a straightforward fashion. Moreover, using the
theory setting sun diagram as an example and comparing explicitly
with the BPHZ framework, we show that IR directly displays the finite part of
the amplitudes. We then construct a parametrization for the ambiguity in
separating the infinite and finite parts whose parameter serves as
renormalisation group scale for the Callan-Symanzik equation. Finally we argue
that constrained IR, constrained DfR and dimensional reduction are equivalent
within one loop order.Comment: 21 pages, 2 figures, late
On the equivalence between Implicit Regularization and Constrained Differential Renormalization
Constrained Differential Renormalization (CDR) and the constrained version of
Implicit Regularization (IR) are two regularization independent techniques that
do not rely on dimensional continuation of the space-time. These two methods
which have rather distinct basis have been successfully applied to several
calculations which show that they can be trusted as practical, symmetry
invariant frameworks (gauge and supersymmetry included) in perturbative
computations even beyond one-loop order.
In this paper, we show the equivalence between these two methods at one-loop
order. We show that the configuration space rules of CDR can be mapped into the
momentum space procedures of Implicit Regularization, the major principle
behind this equivalence being the extension of the properties of regular
distributions to the regularized ones.Comment: 16 page
Classical Solutions in a Lorentz-violating Maxwell-Chern-Simons Electrodynamics
We take as starting point the planar model arising from the dimensional
reduction of the Maxwell Electrodynamics with the (Lorentz-violating)
Carroll-Field-Jackiw term. We then write and study the extended Maxwell
equations and the corresponding wave equations for the potentials. The solution
to these equations show some interesting deviations from the usual MCS
Electrodynamics, with background-dependent correction terms. In the case of a
time-like background, the correction terms dominate over the MCS sector in the
region far from the origin, and establish the behaviour of a massless
Electrodynamics (in the electric sector). In the space-like case, the solutions
indicate the clear manifestation of spatial anisotropy, which is consistent
with the existence of a privileged direction is space.Comment: latex, 8 page
Gauge invariance and the CPT and Lorentz violating induced ChernâSimons-like term in extended QED
Abstract The radiative induction of the CPT and Lorentz violating ChernâSimons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector b ” when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by quantum corrections. As a complement we obtain the result that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term