56,487 research outputs found
Hamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the
one-dimensional homogeneous potential, , where and
are continuously varying parameters. In the non-relativistic case, the
exact analytical solution is determined in terms of , and the total
energy . It is also shown that the non-linear equation of motion can be
linearized by constructing a hypergeometric differential equation for the
inverse problem . A variable transformation reducing the general problem
to that one of a particle subjected to a linear force is also established. For
any value of , it leads to a simple harmonic oscillator if , an
"anti-oscillator" if , or a free particle if E=0. However, such a
reduction is not possible in the relativistic case. For a bounded relativistic
motion, the first order correction to the period is determined for any value of
. For , it is found that the correction is just twice that one
deduced for the simple harmonic oscillator (), and does not depend on the
specific value of .Comment: 12 pages, Late
Integral representations for a generalized Hermite linear functional
In this paper we find new integral representations for the {\it generalized
Hermite linear functional} in the real line and the complex plane. As
application, new integral representations for the Euler Gamma function are
given.Comment: 4 figure
Lorentz-violating Yang-Mills theory: discussing the Chern-Simons-like term generation
We analyze the Chern-Simons-like term generation in the CPT-odd
Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we
study the anomalies of this model as well as its quantum stability. The whole
analysis is performed within the algebraic renormalization theory, which is
independent of the renormalization scheme. In addition, all results are valid
to all orders in perturbation theory. We find that the Chern-Simons-like term
is not generated by radiative corrections, just like its Abelian version.
Additionally, the model is also free of gauge anomalies and quantum stable.Comment: 16 pages. No figures. Final version to appear in the Eur.Phys.J.
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