10,498 research outputs found
Some Characterizations of a Normal Subgroup of a Group
Let G be a group and H be a subgroup of G which is either finite or of finite
index in G. In this note, we give some characterizations for normality of H in
G. As a consequence we get a very short and elementary proof of the Main
Theorem of [5], which avoids the use of the classification of finite simple
group
Superspace Unitary Operator in QED with Dirac and Complex Scalar Fields: Superfield Approach
We exploit the strength of the superspace (SUSP) unitary operator to obtain
the results of the application of the horizontality condition (HC) within the
framework of augmented version of superfield formalism that is applied to the
interacting systems of Abelian 1-form gauge theories where the U(1) Abelian
1-form gauge field couples to the Dirac and complex scalar fields in the
physical four (3 + 1)-dimensions of spacetime. These interacting theories are
generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the
four (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannian
variables. To derive the (anti-)BRST symmetries for the matter fields, we
impose the gauge invariant restrictions (GIRs) on the superfields defined on
the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge
out from our knowledge of the SUSP unitary operator and its hermitian
conjugate. The latter operator is derived without imposing any operation of
hermitian conjugation on the parameters and fields of our theory from outside.
This is an interesting observation in our present investigation.Comment: LaTeX file, 11 pages, journal versio
Self-Dual Chiral Boson: Augmented Superfield Approach
We exploit the standard tools and techniques of the augmented version of
Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and
absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry
transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian
density of a self-dual bosonic system. In the derivation of the full set of the
above transformations, we invoke the (dual-)horizontality conditions,
(anti-)BRST and (anti-)co-BRST invariant restrictions on the superfields that
are defined on the (2, 2)-dimensional supermanifold. The latter is
parameterized by the bosonic variable x^\mu\,(\mu = 0,\, 1) and a pair of
Grassmanian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0
and \theta\bar\theta + \bar\theta\theta = 0). The dynamics of this system is
such that, instead of the full (2, 2) dimensional superspace coordinates
(x^\mu, \theta, \bar\theta), we require only the specific (1, 2)-dimensional
super-subspace variables (t, \theta, \bar\theta) for its description. This is a
novel observation in the context of superfield approach to BRST formalism. The
application of the dual-horizontality condition, in the derivation of a set of
proper (anti-)co-BRST symmetries, is also one of the new ingredients of our
present endeavor where we have exploited the augmented version of superfield
formalism which is geometrically very intuitive.Comment: LaTeX file, 27 pages, minor modifications, Journal reference is give
Curci-Ferrari Type Condition in Hamiltonian Formalism: A Free Spinning Relativistic Particle
The Curci-Ferrari (CF)-type of restriction emerges in the description of a
free spinning relativistic particle within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and
absolutely anticommuting (anti-)BRST symmetry transformations for this system
are derived from the application of horizontality condition (HC) and its
supersymmetric generalization (SUSY-HC) within the framework of superfield
formalism. We show that the above CF-condition, which turns out to be the
secondary constraint of our present theory, remains time-evolution invariant
within the framework of Hamiltonian formalism. This time-evolution invariance
(i) physically justifies the imposition of the (anti-)BRST invariant CF-type
condition on this system, and (ii) mathematically implies the linear
independence of BRST and anti-BRST symmetries of our present theory.Comment: LaTeX file, 11 Pages, journal versio
- …