269 research outputs found
Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory
We derive the nilpotent (anti-)BRST symmetry transformations for the Dirac
(matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian
gauge theory by applying the theoretical arsenal of augmented superfield
formalism where (i) the horizontality condition, and (ii) the equality of a
gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are
exploited together. The above supermanifold is parameterized by four bosonic
spacetime coordinates x^\mu (with \mu = 0,1,2,3) and a couple of Grassmannian
variables \theta and \bar{\theta}. The on-shell nilpotent BRST symmetry
transformations for all the fields of the theory are derived by considering the
chiral superfields on the five (4, 1)-dimensional super sub-manifold and the
off-shell nilpotent symmetry transformations emerge from the consideration of
the general superfields on the full six (4, 2)-dimensional supermanifold.
Geometrical interpretations for all the above nilpotent symmetry
transformations are also discussed in the framework of augmented superfield
formalism.Comment: LaTeX file, 19 pages, journal-versio
Field dependent nilpotent symmetry for gauge theories
We construct the field dependent mixed BRST (combination of BRST and
anti-BRST) transformations for pure gauge theories. These are shown to be an
exact nilpotent symmetry of both the effective action as well as the generating
functional for certain choices of the field dependent parameters. We show that
the Jacobian contributions for path integral measure in the definition of
generating functional arising from BRST and anti-BRST part compensate each
other. The field dependent mixed BRST transformations are also considered in
field/antifield formulation to show that the solutions of quantum master
equation remain invariant under these. Our results are supported by several
explicit examples.Comment: 25 pages, No figures, Revte
Development of an approximate method for quantum optical models and their pseudo-Hermicity
An approximate method is suggested to obtain analytical expressions for the
eigenvalues and eigenfunctions of the some quantum optical models. The method
is based on the Lie-type transformation of the Hamiltonians. In a particular
case it is demonstrated that Jahn-Teller Hamiltonian can
easily be solved within the framework of the suggested approximation. The
method presented here is conceptually simple and can easily be extended to the
other quantum optical models. We also show that for a purely imaginary coupling
the Hamiltonian becomes non-Hermitian but -symmetric. Possible generalization of this approach is outlined.Comment: Paper prepared fo the "3rd International Workshop on Pseudo-Hermitian
Hamiltonians in Quantum Physics" June 2005 Istanbul. To be published in
Czechoslovak Journal of Physic
Polynomial Solution of Non-Central Potentials
We show that the exact energy eigenvalues and eigenfunctions of the
Schrodinger equation for charged particles moving in certain class of
non-central potentials can be easily calculated analytically in a simple and
elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the
generalized Coulomb and harmonic oscillator systems. We study the Hartmann
Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials
as special cases. The results are in exact agreement with other methods.Comment: 18 page
-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
A class of spherically symmetric non-Hermitian Hamiltonians and their
\eta-weak-pseudo-Hermiticity generators are presented. An operators-based
procedure is introduced so that the results for the 1D Schrodinger Hamiltonian
may very well be reproduced. A generalization beyond the nodeless states is
proposed. Our illustrative examples include \eta-weak-pseudo-Hermiticity
generators for the non-Hermitian weakly perturbed 1D and radial oscillators,
the non-Hermitian perturbed radial Coulomb, and the non-Hermitian radial Morse
models.Comment: 14 pages, content revised/regularized to cover 1D and 3D case
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