Vacuum Polarization Tensor for QED in the Light Front Gauge

The use of light front coordinates in quantum field theories (QFT) always brought some problems and controversies. In this work we explore some aspects of its formalism with respect to the employment of dimensional regularization in the computation of the photon's self-energy at the one-loop level and how the fermion propagator has an important role in the outcoming results.

The CMS experiment at the CERN LHC

The Compact Muon Solenoid (CMS) detector is described. The detector operates at the Large Hadron Collider (LHC) at CERN. It was conceived to study proton-proton (and lead-lead) collisions at a centre-of-mass energy of 14 TeV (5.5 TeV nucleon-nucleon) and at luminosities up to 10(34)cm(-2)s(-1) (10(27)cm(-2)s(-1)). At the core of the CMS detector sits a high-magnetic-field and large-bore superconducting solenoid surrounding an all-silicon pixel and strip tracker, a lead-tungstate scintillating-crystals electromagnetic calorimeter, and a brass-scintillator sampling hadron calorimeter. The iron yoke of the flux-return is instrumented with four stations of muon detectors covering most of the 4 pi solid angle. Forward sampling calorimeters extend the pseudo-rapidity coverage to high values (vertical bar eta vertical bar <= 5) assuring very good hermeticity. The overall dimensions of the CMS detector are a length of 21.6 m, a diameter of 14.6 m and a total weight of 12500 t.

Do tadpoles vanish in the light-front?

In covariant gauges (CG) regularized with dimensional regularization (DR) it is a standard procedure to set all tadpole Feynman integrals to zero, though; explicitly, they diverge quadratically as the space-time volume. on the other hand, in the notoriously subtle light-front gauge (LTG) some divergent tadpole integrals are said to be nonvanishing, i.e., cannot be set to zero as in the CC case. In this article we analyse the reasons behind this seemingly ambiguous results.

Effective potential in curved space and cut-off regularizations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Predictive formulation of the Nambu-Jona-Lasinio model

A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu-Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely, the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated from the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects, which are independent of the ( arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model becomes predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.

Nucleon-nucleon scattering within a multiple subtractive renormalization approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

QED(3) RADIATIVE-CORRECTIONS IN THE HEISENBERG PICTURE

We evaluate the vacuum polarization tensor for three-dimensional quantum electrodynamics (QED3) via Heisenberg equations of motion in order to clarify the problem arising from the use of different regularization prescriptions in the interaction picture. We conclude that the photon does acquire physical mass of topological origin when such contribution is taken into account for the photon propagator.

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

A singular approach to discontinuous vector fields on the plane

In this paper we deal with discontinuous vector fields on R-2 and we prove that the analysis of their local behavior around a typical singularity can be treated via singular perturbation. The regularization process developed by Sotomayor and Teixeira is crucial for the development of this work. (c) 2006 Elsevier B.V. All rights reserved.

THE GREEN-FUNCTION IN THE BLOCH-NORDSIECK MODEL FOR QED(3)

The electron Green's function is obtained in the Bloch-Nordsieck approximation of three-dimensional QED. Dimensional regularization is used in the intermediate stages of calculation.

HEAT-KERNEL EXPANSION AT FINITE TEMPERATURE

We show how the zero-temperature result for the heat-kernel asymptotic expansion can be generalized to the finite-temperature one. We observe that this general result depends on the interesting ratio square-root tau/beta, where tau is the regularization parameter and beta = 1/T, so that the zero-temperature limit beta --> infinity corresponds to the cutoff limit tau --> 0. As an example, we discuss some aspects of the axial model at finite temperature.

VACUUM POLARIZATION TENSOR IN 3-DIMENSIONAL QUANTUM ELECTRODYNAMICS

We evaluate the one-loop vacuum polarization tensor for three-dimensional quantum electrodynamics (QED), using an analytic regularization technique, implemented in a gauge-invariant way. We show thus that a gauge boson mass is generated at this level of radiative correction to the photon propagator. We also point out in our conclusions that the generalization for the non Abelian case is straightforward.

The SU(2) Skyrme model and anomaly

The SU(2) Shyrme model, expanding in the collective coordinates variables, gives rise to second-class constraints. Recently this system was embedded in a more general Abelian gauge theory using the BFFT Hamiltonian method. in this work we quantize this gauge theory computing the Noether current anomaly using for this two different methods: an operatorial Dirac first class formalism and the non-local BV quantization coupled with the Fujikawa regularization procedure. (C) 2000 Elsevier B.V. B.V. All rights reserved.

CHIRAL SCHWINGER MODEL WITH A PODOLSKY TERM AT FINITE-TEMPERATURE

We study an exactly solvable two-dimensional model which mimics the basic features of the standard model. This model combines chiral coupling with an infrared behavior which resembles low energy QCD. This is done by adding a Podolsky higher-order derivative term in the gauge field to the Lagrangian of the usual chiral Schwinger model. We adopt a finite temperature regularization procedure in order to calculate the non-trivial fermionic Jacobian and obtain the photon and fermion propagators, first at zero temperature and then at finite temperature in the imaginary and real time formalisms. Both singular and non-singular cases, corresponding to the choice of the regularization parameter, are treated. In the nonsingular case there is a tachyonic mode as usual in a higher order derivative theory, however in the singular case there is no tachyonic excitation in the spectrum.