17,150 research outputs found
Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D non-Abelian 1-Form Gauge Theory
We exploit the theoretical strength of augmented version of superfield
approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the
nilpotency and absolute anticommutativity properties of the (anti-)BRST and
(anti-)co-BRST conserved charges for the two -dimensional (2D)
non-Abelian 1-form gauge theory (without any interaction with matter fields) in
the language of superspace variables, their derivatives and suitable
superfields. In the proof of absolute anticommutativity property, we invoke the
strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such
outside condition/restriction is required in the proof of absolute
anticommutativity of the (anti-)co-BRST conserved charges. The latter
observation (as well as other observations) connected with (anti-)co-BRST
symmetries and corresponding conserved charges are novel results of our present
investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry
invariance of the appropriate Lagrangian densities within the framework of
AVSA. In addition, we dwell a bit on the derivation of the above fermionic
(nilpotent) symmetries by applying the AVSA to BRST formaism where only the
(anti-)chiral superfields are used.Comment: LaTeX file, 33 pages, journal referenc
Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss
mainly the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and
some discrete dual-symmetries of the appropriate Lagrangian densities for a two
(1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory
without any interaction with matter fields. One of the novel observations of
our present investigation is the existence of some kinds of restrictions in the
case of our present St\"{u}ckelberg-modified version of the 2D Proca theory
which is not like the standard Curci-Ferrari (CF)-condition of a non-Abelian
1-form gauge theory. Some kinds of similarities and a few differences between
them have been pointed out in our present investigation. To establish the
sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST
symmetries, we derive them by using our newly proposed (anti-)chiral superfield
formalism where a few specific and appropriate sets of invariant quantities
play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved
charges in terms of the superfields that are obtained after the applications of
(anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell
nilpotency and absolute anticommutativity properties, too. Finally, we make
some comments on (i) the novelty of our restrictions/obstructions, and (ii) the
physics behind the negative kinetic term associated with the pseudo-scalar
field of our present theory.Comment: LaTeX file, 58 pages, Journal reference give
Superfield approach to symmetry invariance in QED with complex scalar fields
We show that the Grassmannian independence of the super Lagrangian density,
expressed in terms of the superfields defined on a (4, 2)-dimensional
supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST)
and anti-BRST invariance of the corresoponding four (3 + 1)-dimensional (4D)
Lagrangian density that describes the interaction between the U(1) gauge field
and the charged complex scalar fields. The above 4D field theoretical model is
considered on a (4, 2)-dimensional supermanifold parametrized by the ordinary
four spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of
Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,
\theta \bar\theta + \bar\theta \theta = 0). Geometrically, the (anti-)BRST
invariance is encoded in the translation of the super Lagrangian density along
the Grassmannian directions of the above supermanifold such that the outcome of
this shift operation is zero.Comment: LaTeX file, 14 pages, minor changes in the title and text, version to
appear in ``Pramana - Journal of Physics'
Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism
In the framework of augmented superfield approach, we provide the geometrical
origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST
charges and a non-nilpotent bosonic charge. Together, these local and conserved
charges turn out to be responsible for a clear and cogent definition of the
Hodge decomposition theorem in the quantum Hilbert space of states. The above
charges owe their origin to the de Rham cohomological operators of differential
geometry which are found to be at the heart of some of the key concepts
associated with the interacting gauge theories. For our present review, we
choose the two -dimensional (2D) quantum electrodynamics (QED) as a
prototype field theoretical model to derive all the nilpotent symmetries for
all the fields present in this interacting gauge theory in the framework of
augmented superfield formulation and show that this theory is a {\it unique}
example of an interacting gauge theory which provides a tractable field
theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the
Journal are give
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