29,139 research outputs found
A superspace embedding of the Wess-Zumino model
We embed the Wess-Zumino (WZ) model in a wider superspace than the one
described by chiral and anti-chiral superfields.Comment: 5 pages, Revtex (multicol
Nonlinear Pendulum: A Simple Generalization
In this work we solve the nonlinear second order differential equation of the
simple pendulum with a general initial angular displacement
() and velocity (), obtaining a
closed-form solution in terms of the Jacobi elliptic function ,
and of the the incomplete elliptical integral of the first kind .
Such a problem can be used to introduce concepts like elliptical integrals and
functions to advanced undergraduate students, to motivate the use of Computer
Algebra Systems to analyze the solutions obtained, and may serve as an exercise
to show how to carry out a simple generalization, taking as a starting point
the paper of Bel\'endez \emph{et al} \cite{belendez}, where they have
considered the standard case
Reducible systems and embedding procedures in the canonical formalism
We propose a systematic method of dealing with the canonical constrained
structure of reducible systems in the Dirac and symplectic approaches which
involves an enlargement of phase and configuration spaces, respectively. It is
not necessary, as in the Dirac approach, to isolate the independent subset of
constraints or to introduce, as in the symplectic analysis, a series of
lagrange multipliers-for-lagrange multipiers. This analysis illuminates the
close connection between the Dirac and symplectic approaches of treating
reducible theories, which is otherwise lacking. The example of p-form gauge
fields (p=2,3) is analyzed in details.Comment: Latex 23 pages, some corrections and improvements in the text. To
appear in Annals of Physic
Axiomatic Local Metric Derivatives for Low-Level Fractionality with Mittag-Leffler Eigenfunctions
In this contribution, we build up an axiomatic local metric derivative that
exhibits the Mittag-Leffler as an eigenfunction and is valid for low-level
fractionality, whenever the order parameter is close to . This version of
deformed or metric derivative may be a possible alternative to the versions by
Jumarie and the inappropriately so-called local fractional derivative also
based on the Jumarie's approach. With rules similar to the classical ones, but
with a solid axiomatic basis in the limit pointed out here, we present our
results and some comments on the limits of validity for the controversial
formalism found in the literature of the area.Comment: 5 page
Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
In this work, we investigate aspects of the electron, muon and tau
gyromagnetic ratios (g-factor) in a fractional coarse-grained scenario, by
adopting a Modified Riemann-Liouville (MRL) fractional calculus. We point out
the possibility of mapping the experimental values of the specie's g-factors
into a theoretical parameter which accounts for fractionality, without
computing higher-order QED calculations. We wish to understand whether the
value of (g-2) may be traced back to a fractionality of space-time.The
justification for the difference between the experimental and the theoretical
value g=2 stemming from the Dirac equation is given in the terms of the
complexity of the interactions of the charged leptons, considered as
pseudo-particles and "dressed" by the interactions and the medium. Stepwise, we
build up a fractional Dirac equation from the fractional Weyl equation that, on
the other hand, was formulated exclusively in terms of the helicity operator.
From the fractional angular momentum algebra, in a coarse-grained scenario, we
work out the eigenvalues of the spin operator. Based on the standard
electromagnetic current, as an analogy case, we write down a fractional
Lagrangian density, with the electromagnetic field minimally coupled to the
particular charged lepton. We then study a fractional gauge-like invariance
symmetry, formulate the covariant fractional derivative and propose the spinor
field transformation. Finally, by taking the non-relativistic regime of the
fractional Dirac equation, the fractional Pauli equation is obtained and, from
that, an explicit expression for the fractional g-factor comes out that is
compared with the experimental CODATA value. Our claim is that the different
lepton species must probe space-time by experiencing different fractionalities,
once the latter may be associated to the effective interactions of the
different families with the medium.Comment: 15 page
BV QUANTIZATION OF A VECTOR-TENSOR GAUGE THEORY WITH TOPOLOGICAL COUPLING
We use the BV quantization method for a theory with coupled tensor and vector
gauge fields through a topological term. We consider in details the
reducibility of the tensorial sector as well as the appearance of a mass term
in the effective vectorial theory .Comment: 10 pages, Late
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