164 research outputs found
(Anti-)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory
We exploit the beauty and strength of the symmetry invariant restrictions on
the (anti-)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST),
anti-BRST and (anti-)co-BRST symmetry transformations in the case of a two
(1+1)-dimensional (2D) self-dual chiral bosonic field theory within the
framework of augmented (anti-)chiral superfield formalism. Our 2D ordinary
theory is generalized onto a (2, 2)-dimensional supermanifold which is
parameterized by the superspace variable Z^M = (x^\mu, \theta, \bar\theta)
where x^\mu (with \mu = 0, 1) are the ordinary 2D bosonic coordinates and
(\theta,\, \bar\theta) are a pair of Grassmannian variables with their standard
relationships: \theta^2 = {\bar\theta}^2 =0, \theta\,\bar\theta +
\bar\theta\theta = 0. We impose the (anti-)BRST and (anti-)co-BRST invariant
restrictions on the (anti-)chiral superfields (defined on the (anti-)chiral (2,
1)-dimensional super-submanifolds of the above general (2, 2)-dimensional
supermanifold) to derive the above nilpotent symmetries. We do not exploit the
mathematical strength of the (dual-)horizontality conditions anywhere in our
present investigation. We also discuss the properties of nilpotency, absolute
anticommutativity and (anti-)BRST and (anti-)co-BRST symmetry invariance of the
Lagrangian density within the framework of our augmented (anti-)chiral
superfield formalism. Our observation of the absolute anticommutativity
property is a completely novel result in view of the fact that we have
considered only the (anti-)chiral superfields in our present endeavor.Comment: LaTeX file, 20 pages, journal reference is give
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
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
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
Novel symmetries in the modified version of two dimensional Proca theory
By exploiting Stueckelberg's approach, we obtain a gauge theory for the two
(1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed
with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST
symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the
total gauge-fixing term remains invariant. The anticommutator of the BRST and
co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique
bosonic symmetry in the theory, under which the ghost part of the Lagrangian
density remains invariant. To establish connections of the above symmetries
with the Hodge theory, we invoke a pseudo-scalar field in the theory.
Ultimately, we demonstrate that the full theory provides a field theoretic
example for the Hodge theory where the continuous symmetry transformations
provide a physical realization of the de Rham cohomological operators and
discrete symmetries of the theory lead to the physical realization of the Hodge
duality operation of differential geometry. We also mention the physical
implications and utility of our present investigation.Comment: LaTeX file, 21 pages, journal referenc
Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory
We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e., a rigid rotor) and provide the geometrical meaning and interpretation to them. Furthermore, we also derive the nilpotent (anti-)co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e., nilpotent and absolutely anticommuting) fermionic (anti-)co-BRST symmetries are completely novel results in our present investigation
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Benefits and pitfalls of GRACE data assimilation: A case study of terrestrial water storage depletion in India
This study investigates some of the benefits and drawbacks of assimilating terrestrial water storage (TWS) observations from the Gravity Recovery and Climate Experiment (GRACE) into a land surface model over India. GRACE observes TWS depletion associated with anthropogenic groundwater extraction in northwest India. The model, however, does not represent anthropogenic groundwater withdrawals and is not skillful in reproducing the interannual variability of groundwater. Assimilation of GRACE TWS introduces long-term trends and improves the interannual variability in groundwater. But the assimilation also introduces a negative trend in simulated evapotranspiration, whereas in reality evapotranspiration is likely enhanced by irrigation, which is also unmodeled. Moreover, in situ measurements of shallow groundwater show no trend, suggesting that the trends are erroneously introduced by the assimilation into the modeled shallow groundwater, when in reality the groundwater is depleted in deeper aquifers. The results emphasize the importance of representing anthropogenic processes in land surface modeling and data assimilation systems
Corrigendum to “Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory”
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