368 research outputs found
Higher-derivative non-Abelian gauge fields via the Faddeev-Jackiw formalism
In this paper we analyze two higher-derivative theories, the generalized
electrodynamics and the Alekseev-Arbuzov-Baikov's effective Lagrangian from the
point of view of Faddeev-Jackiw sympletic approach. It is shown that the full
set of constraint is obtained directly from the zero-mode eigenvectors, and
that they are in accordance with known results from Dirac's theory, a remnant
and recurrent issue in the literature. The method shows to be rather economical
in relation to the Dirac's one, obviating thus unnecessary classification and
calculations. Afterwards, to conclude we construct the transition-amplitude of
the non-Abelian theory following a constrained BRST-method.Comment: 17 page
Nonperturbative Aspects of the two-dimensional Massive Gauged Thirring Model
In this paper we present a study based on the use of functional techniques on
the issue of insertions of massive fermionic fields in the two-dimensional
massless Gauged Thirring Model. As it will be shown, the fermionic mass
contributes to the Green's functions in a surprisingly simple way, leaving
therefore the original nonperturbative nature of the massless results still
intact in the massive theory. Also, by means of complementarity, we present a
second discussion of the massive model, now at its bosonic representation.Comment: 18 pages, to appear at Int. J. Mod. Phys.
The Epstein-Glaser causal approach to the Light-Front QED. I: Free theory
In this work we present the study of light-front field theories in the realm
of axiomatic theory. It is known that when one uses the light-cone gauge
pathological poles arises, demanding a prescription to be
employed in order to tame these ill-defined poles and to have correct Feynman
integrals due to the lack of Wick rotation in such theories. In order to shed a
new light on this long standing problem we present here a discussion based on
the use rigorous mathematical machinery of distributions combined with physical
concepts, such as causality, to show how to deal with these singular
propagators in a general fashion without making use of any prescription. The
first step of our development will consist in showing how analytic
representation for propagators arises by requiring general physical properties
in the framework of Wightman's formalism. From that we shall determine the
equal-time (anti)commutation relations in the light-front form for the scalar,
fermionic fields and for the dynamical components of the electromagnetic field.
In conclusion, we introduce the Epstein-Glaser causal method in order to have a
mathematical rigorous treatment of the free propagators of the theory, allowing
us to discuss the general treatment for propagators of the type . Moreover, we show that at given conditions our results reproduce known
prescriptions in the literature.Comment: 34 pages, v2 matching the published versio
K\"all\'en-Lehmann representation of noncommutative quantum electrodynamics
Noncommutative (NC) quantum field theory is the subject of many analyses on
formal and general aspects looking for deviations and, therefore, potential
noncommutative spacetime effects. Within of this large class, we may now pay
some attention to the quantization of NC field theory on lower dimensions and
look closely at the issue of dynamical mass generation to the gauge field. This
work encompasses the quantization of the two-dimensional massive quantum
electrodynamics and three-dimensional topologically massive quantum
electrodynamics. We begin by addressing the problem on a general dimensionality
making use of the perturbative Seiberg-Witten map to, thus, construct a general
action, to only then specify the problem to two and three dimensions. The
quantization takes place through the K\"all\'en-Lehmann spectral representation
and Yang-Feldman-K\"all\'en formulation, where we calculate the respective
spectral density function to the gauge field. Furthermore, regarding the photon
two-point function, we discuss how its infrared behavior is related to the term
generated by quantum corrections in two dimensions, and, moreover, in three
dimensions, we study the issue of nontrivial {\theta}-dependent corrections to
the dynamical mass generation
Causal approach for the electron-positron scattering in Generalized Quantum Electrodynamics
In this paper we study the generalized electrodynamics contribution for the
electron-positron scattering process, , the
Bhabha scattering. Within the framework of the standard model, for energies
larger when compared to the electron mass, we calculate the cross section
expression for the scattering process. This quantity is usually calculated in
the framework of the Maxwell electrodynamics and, by phenomenological reasons,
corrected by a cut-off parameter. On the other hand, by considering the
generalized electrodynamics instead of Maxwell's, we can show that the effects
played by the Podolsky mass is actually a natural cut-off parameter for this
scattering process. Furthermore, by means of experimental data of Bhabha
scattering we will estimate its lower bound value. Nevertheless, in order to
have a mathematically well defined description of our study we shall present
our discussion in the framework of the Epstein-Glaser causal theory.Comment: 24 pages, V2 to match published versio
Renormalizability of generalized quantum electrodynamics
In this work we present the study of the renormalizability of the Generalized
Quantum Electrodynamics (). We begin the article by reviewing the
on-shell renormalization scheme applied to . Thereafter, we calculate
the explicit expressions for all the counter-terms at one-loop approximation
and discuss the infrared behavior of the theory as well. Next, we explore some
properties of the effective coupling of the theory which would give an
indictment of the validity regime of theory: .
Afterwards, we make use of experimental data from the electron anomalous
magnetic moment to set possible values for the theory free parameter through
the one-loop contribution of Podolsky mass-dependent term to Pauli's form
factor .Comment: 9 page
Option pricing formulas under a change of numeraire
We present some formulations of the Cox-Ross-Rubinstein and Black-Scholes formulas for European options obtained through a suitable change of measure, which corresponds to a change of numèraire for the underlying price process. Among other consequences, a closed formula for the price of an European call option at each node of the multi-period binomial tree is achieved, too. Some of the results contained herein, though comparable with analogous ones appearing elsewhere in the financial literature, provide however a supplementary widening and deepening in view of useful applications in the more challenging framework of incomplete markets. This last issue, having the present paper as a preparatory material, will be treated extensively in a forthcoming paper
Higher derivative Chern-Simons extension in the noncommutative QED
The noncommutative (NC) massive quantum electrodynamics in dimensions
is considered. We show explicitly that the one-loop effective action arising
from the integrating out the fermionic fields leads to the ordinary NC
Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion
mass). In the next to leading order, the higher-derivative contributions to NC
Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action
is carefully discussed. We then consider the higher-derivative modification
into the pure NC Chern-Simons Lagrangian density and evaluate the one-loop
correction to the pole of the photon propagator.Comment: 20 pages, published versio
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