23,216 research outputs found
BRST cohomology and Hodge decomposition theorem in Abelian gauge theory
We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge
decomposition theorem for the two dimensional free U(1) gauge theory. In
addition to the usual BRST charge, we derive a local, conserved and nilpotent
co(dual)-BRST charge under which the gauge-fixing term remains invariant. We
express the Hodge decomposition theorem in terms of these charges and the
Laplacian operator. We take a single photon state in the quantum Hilbert space
and demonstrate the notion of gauge invariance, no-(anti)ghost theorem,
transversality of photon and establish the topological nature of this theory by
exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In
fact, the topological nature of this theory is encoded in the vanishing of the
Laplacian operator when equations of motion are exploited. On the two
dimensional compact manifold, we derive two sets of topological invariants with
respect to the conserved and nilpotent BRST- and co-BRST charges and express
the Lagrangian density of the theory as the sum of terms that are BRST- and
co-BRST invariants. Mathematically, this theory captures together some of the
key features of both Witten- and Schwarz type of topological field theories.Comment: 20 pages, LaTeX, no figures, Title and text have been changed,
Journal reference is given, some references have been adde
Gauge Transformations, BRST Cohomology and Wigner's Little Group
We discuss the (dual-)gauge transformations and BRST cohomology for the two
(1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional
(4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries
(and their corresponding generators) for the Lagrangian densities of these
theories. For the 4D free 2-form gauge theory, we show that the changes on the
antisymmetric polarization tensor e^{\mu\nu} (k) due to (i) the (dual-)gauge
transformations corresponding to the internal symmetry group, and (ii) the
translation subgroup T(2) of the Wigner's little group, are connected with
each-other for the specific relationships among the parameters of these
transformation groups. In the language of BRST cohomology defined w.r.t. the
conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states
turn out to be the sum of the original state and the (co-)BRST exact states. We
comment on (i) the quasi-topological nature of the 4D free 2-form gauge theory
from the degrees of freedom count on e^{\mu\nu} (k), and (ii) the Wigner's
little group and the BRST cohomology for the 2D one-form gauge theory {\it
vis-{\`a}-vis} our analysis for the 4D 2-form gauge theory.Comment: LaTeX file, 29 pages, misprints in (3.7), (3.8), (3.9), (3.13) and
(4.14)corrected and communicated to IJMPA as ``Erratum'
Production of in electron positron collisions
is an atom of simple hydrogenlike structure similar to
positronium and . In this paper energy levels and
decay widths of different decay channels of are given. Cross
section of production of this atomic system in annihilation taking
into account radiative corrections is calculated. According to our estimates
886 atoms may be produced at BEPCII and 29
atoms are produced at VEPP-4M under the present experimental
conditions.Comment: 5 pages, submitted to Int. Jour. Mod. Phys.
Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory
We derive the complete set of off-shell nilpotent and absolutely
anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST
symmetry transformations for all the fields of the modified version of two
(1+1)-dimensional (2D) Proca theory by exploiting the "augmented" superfield
formalism where the (dual-)horizontality conditions and (dual-)gauge-invariant
restrictions are exploited together. We capture the (anti-)BRST and
(anti-)co-BRST invariance of the Lagrangian density in the language of
superfield formalism. We also express the nilpotency and absolute
anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the
framework of augmented superfield formalism. This exercise leads to some novel
observations which have, hitherto, not been pointed out in the literature
within the framework of superfield approach to BRST formalism. For the sake of
completeness, we also mention, very briefly, a unique bosonic symmetry, the
ghost-scale symmetry and discrete symmetries of the theory and show that the
algebra of conserved charges captures the cohomological aspects of differential
geometry. Thus, our present modified 2D Proca theory is a model for the Hodge
Theory.Comment: LaTeX file, 32 pages, journal reference give
Ultracold neutron depolarization in magnetic bottles
We analyze the depolarization of ultracold neutrons confined in a magnetic
field configuration similar to those used in existing or proposed
magneto-gravitational storage experiments aiming at a precise measurement of
the neutron lifetime. We use an extension of the semi-classical Majorana
approach as well as an approximate quantum mechanical analysis, both pioneered
by Walstrom et al. [Nucl. Instr. Meth. Phys. Res. A 599, 82 (2009)]. In
contrast with this previous work we do not restrict the analysis to purely
vertical modes of neutron motion. The lateral motion is shown to cause the
predominant depolarization loss in a magnetic storage trap. The system studied
also allowed us to estimate the depolarization loss suffered by ultracold
neutrons totally reflected on a non-magnetic mirror immersed in a magnetic
field. This problem is of preeminent importance in polarized neutron decay
studies such as the measurement of the asymmetry parameter A using ultracold
neutrons, and it may limit the efficiency of ultracold neutron polarizers based
on passage through a high magnetic field.Comment: 18 pages, 6 figure
Spin flip loss in magnetic storage of ultracold neutrons
We analyze the depolarization of ultracold neutrons confined in a magnetic
field configuration similar to those used in existing or proposed
magneto-gravitational storage experiments aiming at a precise measurement of
the neutron lifetime. We use an approximate quantum mechanical analysis such as
pioneered by Walstrom \emph{et al} [Nucl. Instrum. Methods Phys. Res. A 599, 82
(2009)]. Our analysis is not restricted to purely vertical modes of neutron
motion. The lateral motion is shown to cause the predominant depolarization
loss in a magnetic storage trap.Comment: 12 pages, 3 figures, for Proceedings of Neutron Lifetime Worksho
Topological aspects in non-Abelian gauge theory
We discuss the BRST cohomology and exhibit a connection between the Hodge
decomposition theorem and the topological properties of a two dimensional free
non-Abelian gauge theory having no interaction with matter fields. The
topological nature of this theory is encoded in the vanishing of the Laplacian
operator when equations of motion are exploited. We obtain two sets of
topological invariants with respect to BRST and co-BRST charges on the two
dimensional manifold and show that the Lagrangian density of the theory can be
expressed as the sum of terms that are BRST- and co-BRST invariants.Comment: (1+11) pages, LaTeX, no figure
Suppressing Super-Horizon Curvature Perturbations?
We consider the possibility of suppressing superhorizon curvature
perturbations after the end of the ordinary slow-roll inflationary stage. This
is the opposite of the curvaton limit. We assume that large curvature
perturbations are created by the inflaton and investigate if they can be
diluted or suppressed by a second very homogeneous field which starts to
dominate the energy density of the universe shortly after the end of inflation.
We show explicit that the gravitational sourcing of inhomogeneities from the
more inhomogeneous fluid to the more homogeneous fluid makes the suppression
difficult if not impossible to achieve.Comment: 10 pages, 1 figure. Important revision. Conclusions more negativ
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