2,095 research outputs found
Rigid Rotor as a Toy Model for Hodge Theory
We apply the superfield approach to the toy model of a rigid rotor and show
the existence of the nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, under
which, the kinetic term and action remain invariant. Furthermore, we also
derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST
symmetry transformations, under which, the gauge-fixing term and Lagrangian
remain invariant. The anticommutator of the above nilpotent symmetry
transformations leads to the derivation of a bosonic symmetry transformation,
under which, the ghost terms and action remain invariant. Together, the above
transformations (and their corresponding generators) respect an algebra that
turns out to be a physical realization of the algebra obeyed by the de Rham
cohomological operators of differential geometry. Thus, our present model is a
toy model for the Hodge theory.Comment: LaTeX file, 22 page
Abelian 2-form gauge theory: superfield formalism
We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for {\it all} the fields of a free Abelian
2-form gauge theory by exploiting the geometrical superfield approach to BRST
formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a
(4, 2)-dimensional supermanifold parameterized by the four even spacetime
variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian
variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta
\bar\theta + \bar\theta \theta = 0). One of the salient features of our present
investigation is that the above nilpotent (anti-)BRST symmetry transformations
turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari
(CF) type of restriction. The latter condition emerges due to the application
of our present superfield formalism. The actual CF condition, as is well-known,
is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that
our present 4D Abelian 2-form gauge theory imbibes some of the key signatures
of the 4D non-Abelian 1-form gauge theory. We briefly comment on the
generalization of our supperfield approach to the case of Abelian 3-form gauge
theory in four (3 + 1)-dimensions of spacetime.Comment: LaTeX file, 23 pages, journal versio
Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory
We demonstrate the existence of the nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the
four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory
that is described by the coupled Lagrangian densities (which incorporate the
celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-)
BRST symmetry transformations is ensured by the existence of a Curci-Ferrari
type restriction that emerges from the superfield formalism as well as from the
equations of motion that are derived from the above coupled Lagrangian
densities. We show the invariance of the action from the point of view of the
symmetry considerations as well as superfield formulation. We discuss,
furthermore, the topological term within the framework of superfield formalism
and provide the geometrical meaning of its invariance under the (anti-) BRST
symmetry transformations.Comment: LaTeX file, 22 pages, journal versio
Novel symmetries in N = 2 supersymmetric quantum mechanical models
We demonstrate the existence of a novel set of discrete symmetries in the
context of N = 2 supersymmetric (SUSY) quantum mechanical model with a
potential function f(x) that is a generalization of the potential of the 1D
SUSY harmonic oscillator. We perform the same exercise for the motion of a
charged particle in the X-Y plane under the influence of a magnetic field in
the Z-direction. We derive the underlying algebra of the existing continuous
symmetry transformations (and corresponding conserved charges) and establish
its relevance to the algebraic structures of the de Rham cohomological
operators of differential geometry. We show that the discrete symmetry
transformations of our present general theories correspond to the Hodge duality
operation. Ultimately, we conjecture that any arbitrary N = 2 SUSY quantum
mechanical system can be shown to be a tractable model for the Hodge theory.Comment: LaTeX file, 23 pages, Title and Abstract changed, Text modified,
version to appear in Annals of Physic
Recommended from our members
Bench-Scale Testing of Attrition Resistant Moving Bed Sorbents
Integrated Gasification Combined Cycle (IGCC) systems with cold-gas cleanup have now reached the early stages of commercialization. The foundation for this was successful completion of the Cool Water Coal Gasification Program several years ago. Destec Energy, Inc., a subsidiary of Dow Chemical Company, has a plant in operation in Louisiana, and the 2 Wabash River Plant in Indiana is now starting up. A similar plant based on the Shell gasification technology is operating in the Netherlands. In two new plants now under construction, the Tampa Electric Plant in Florida and the Sierra Pacific Power Plant in Nevada, incorporating hot-gas cleanup technology is desirable. Unfortunately, some nagging problems remain with both sulfur sorbent and particle filter technology that may result in the use of cold-gas, rather than hot-gas, cleanup in these plants. With sulfur sorbents, the main problems are with mechanical property degradation and/or loss of sulfur capacity over many sulfidation-regeneration cycles. The sorbents receiving the most attention are all zinc based. They include various zinc titanate formulations and proprietary materials developed by the U.S. Department of Energy/Morgantown Energy Technology Center (DOE/METC) staff and the Phillips Petroleum Company. The investigators on this project are now completing their third year of effort on a superstrong zinc titanate sorbent. Prior to this year, various formulations were prepared and evaluated for their potential use in fixed- and fluidized-bed hot-gas desulfurization systems. A unique feature, the reason for the high strength, is that the zinc titanate is contained in a matrix of titanium dioxide. Its crush strength is more than 6 times that prior investigators achieved
On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories
We demonstrate a few striking similarities and some glaring differences
between (i) the free four (3 + 1)-dimensional (4D) Abelian 2-form gauge theory,
and (ii) the anomalous two (1 + 1)-dimensional (2D) Abelian 1-form gauge
theory, within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We
demonstrate that the Lagrangian densities of the above two theories transform
in a similar fashion under a set of symmetry transformations even though they
are endowed with a drastically different variety of constraint structures.
Taking the help of our understanding of the 4D Abelian 2-form gauge theory, we
prove that the gauge invariant version of the anomalous 2D Abelian 1-form gauge
theory is a new field-theoretic model for the Hodge theory where all the de
Rham cohomological operators of differential geometry find their physical
realizations in the language of proper symmetry transformations. The
corresponding conserved charges obey an algebra that is reminiscent of the
algebra of the cohomological operators. We briefly comment on the consistency
of the 2D anomalous 1-form gauge theory in the language of restrictions on the
harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the
above 2D theory.Comment: LaTeX file, 37 pages, version to appear in EPJ
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Bench-Scale Development of Fluidized-Bed Spray-Dried Sorbents
Successful development of regenerable mixed-metal oxide sorbents for removal of reduced sulfur species (such as H{sub 2}S and COS) from coal-derived fuel gas streams at high=temperature, high-pressure (HTHP) conditions is a key to commercialization of the integrated-gasification-combined-cycle (IGCC) power systems. Among the various available coal-to-electricity pathways, IGCC power plants have the most potential with high thermal efficiency, simple system configuration, low emissions of SO{sub 2}, NO{sub x} and other contaminants, modular design, and low capital cost. Due to these advantages, the power plants of the 21st century are projected to utilize IGCC technology worldwide. Sorbents developed for sulfur removal are primarily zinc oxide-based inorganic materials, because of their ability to reduce fuel gas sulfur level to a few parts-per-million (ppm). This project extends the prior work on the development of fluidizable zinc titanate particles using a spray-drying technique to impart high reactivity and attrition resistance. Specific objectives are to develop highly reactive and attrition-resistant zinc titanate sorbents in 40- to 150-{mu}m particle size range for transport reactor applications using semicommercial- to full commercial-scale spray dryers, to transfer sorbent production technology to private sector, and to provide technical support for Sierra Pacific`s Clean Coal Technology Demonstration plant and METC`s hot-gas desulfurization process development unit (PDU), both employing a transport reactor system
The vector-valued big q-Jacobi transform
Big -Jacobi functions are eigenfunctions of a second order -difference
operator . We study as an unbounded self-adjoint operator on an
-space of functions on with a discrete measure. We describe
explicitly the spectral decomposition of using an integral transform
with two different big -Jacobi functions as a kernel, and we
construct the inverse of .Comment: 35 pages, corrected an error and typo
A field-theoretic model for Hodge theory
We demonstrate that the four (3 + 1)-dimensional free Abelian 2-form gauge
theory presents a tractable field theoretical model for the Hodge theory where
the well-defined symmetry transformations correspond to the de Rham
cohomological operators of differential geometry. The conserved charges,
corresponding to the above continuous symmetry transformations, obey an algebra
that is reminiscent of the algebra obeyed by the cohomological operators. The
discrete symmetry transformation of the theory represents the realization of
the Hodge duality operation that exists in the relationship between the
exterior and co-exterior derivatives of differential geometry. Thus, we provide
the realizations of all the mathematical quantities, associated with the de
Rham cohomological operators, in the language of the symmetries of the present
4D free Abelian 2-form gauge theory.Comment: LaTeX file, 24 pages, journal reference is give
Massive gravity as a quantum gauge theory
We present a new point of view on the quantization of the massive
gravitational field, namely we use exclusively the quantum framework of the
second quantization. The Hilbert space of the many-gravitons system is a Fock
space where the one-particle Hilbert
space carries the direct sum of two unitary irreducible
representations of the Poincar\'e group corresponding to two particles of mass
and spins 2 and 0, respectively. This Hilbert space is canonically
isomorphic to a space of the type where is a gauge charge
defined in an extension of the Hilbert space
generated by the gravitational field and some ghosts fields
(which are vector Fermi fields) and (which
are vector field Bose fields.)
Then we study the self interaction of massive gravity in the causal
framework. We obtain a solution which goes smoothly to the zero-mass solution
of linear quantum gravity up to a term depending on the bosonic ghost field.
This solution depends on two real constants as it should be; these constants
are related to the gravitational constant and the cosmological constant. In the
second order of the perturbation theory we do not need a Higgs field, in sharp
contrast to Yang-Mills theory.Comment: 35 pages, no figur
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