300 research outputs found
Covariant hamiltonian dynamics
We discuss the covariant formulation of the dynamics of particles with
abelian and non-abelian gauge charges in external fields. Using this
formulation we develop an algorithm for the construction of constants of
motion, which makes use of a generalization of the concept of Killing vectors
and tensors in differential geometry. We apply the formalism to the motion of
classical charges in abelian and non-abelian monopole fieldsComment: 15 pages, no figure
Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
In spacetimes admitting Yano tensors the classical theory of the spinning
particle possesses enhanced worldline supersymmetry. Quantum mechanically
generators of extra supersymmetries correspond to operators that in the
classical limit commute with the Dirac operator and generate conserved
quantities. We show that the result is preserved in the full quantum theory,
that is, Yano symmetries are not anomalous. This was known for Yano tensors of
rank two, but our main result is to show that it extends to Yano tensors of
arbitrary rank. We also describe the conformal Yano equation and show that is
invariant under Hodge duality. There is a natural relationship between Yano
tensors and supergravity theories. As the simplest possible example, we show
that when the spacetime admits a Killing spinor then this generates Yano and
conformal Yano tensors. As an application, we construct Yano tensors on
maximally symmetric spaces: they are spanned by tensor products of Killing
vectors.Comment: 1+32 pages, no figures. Accepted for publication on Classical and
Quantum Gravity. New title and abstract. Some material has been moved to the
Appendix. Concrete formulas for Yano tensors on some special holonomy
manifolds have been provided. Some corrections included, bibliography
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Augmented Superfield Approach To Unique Nilpotent Symmetries For Complex Scalar Fields In QED
The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin
(BRST)- and anti-BRST symmetries for the matter fields, present in any
arbitrary interacting gauge theory, has been a long-standing problem in the
framework of superfield approach to BRST formalism. These nilpotent symmetry
transformations are deduced for the four (3 + 1)-dimensional (4D) complex
scalar fields, coupled to the U(1) gauge field, in the framework of augmented
superfield formalism. This interacting gauge theory (i.e. QED) is considered on
a six (4, 2)-dimensional supermanifold parametrized by four even spacetime
coordinates and a couple of odd elements of the Grassmann algebra. In addition
to the horizontality condition (that is responsible for the derivation of the
exact nilpotent symmetries for the gauge field and the (anti-)ghost fields), a
new restriction on the supermanifold, owing its origin to the (super) covariant
derivatives, has been invoked for the derivation of the exact nilpotent
symmetry transformations for the matter fields. The geometrical interpretations
for all the above nilpotent symmetries are discussed, too.Comment: LaTeX file, 17 pages, journal versio
Anomaly-Free Supersymmetric SO(2N+2)/U(N+1) sigma-Model Based on the SO(2N+1) Lie Algebra of the Fermion Operators
The extended supersymmetric (SUSY) sigma-model has been proposed on the bases
of SO(2N+1) Lie algebra spanned by fermion annihilation-creation operators and
pair operators. The canonical transformation, extension of an SO(2N) Bogoliubov
transformation to an SO(2N+1) group, is introduced. Embedding the SO(2N+1)
group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we have
investigated the SUSY sigma-model on the Kaehler manifold, the coset space
SO(2N+2)/U(N+1). We have constructed the Killing potential, extension of the
potential in the SO(2N)/U(N) coset space to that in the SO(2N+2)/U(N+1) coset
space. It is equivalent to the generalized density matrix whose diagonal-block
part is related to a reduced scalar potential with a Fayet-Ilipoulos term. The
f-deformed reduced scalar potential is optimized with respect to vacuum
expectation value of the sigma-model fields and a solution for one of the
SO(2N+1) group parameters has been obtained. The solution, however, is only a
small part of all solutions obtained from anomaly-free SUSY coset models. To
construct the coset models consistently, we must embed a coset coordinate in an
anomaly-free spinor representation (rep) of SO(2N+2) group and give
corresponding Kaehler and Killing potentials for an anomaly-free
SO(2N+2)/U(N+1) model based on each positive chiral spinor rep. Using such
mathematical manipulation we construct successfully the anomaly-free
SO(2N+2)/U(N+1) SUSY sigma-model and investigate new aspects which have never
been seen in the SUSY sigma-model on the Kaehler coset space SO(2N)/U(N). We
reach a f-deformed reduced scalar potential. It is minimized with respect to
the vacuum expectation value of anomaly-free SUSY sigma-model fields. Thus we
find an interesting f-deformed solution very different from the previous
solution for an anomaly-free SO(2.5+2)/(SU(5+1)*U(1)) SUSY sigma-model.Comment: 24 pages, no fiure
Nonrelativistic Chern-Simons Vortices on the Torus
A classification of all periodic self-dual static vortex solutions of the
Jackiw-Pi model is given. Physically acceptable solutions of the Liouville
equation are related to a class of functions which we term
Omega-quasi-elliptic. This class includes, in particular, the elliptic
functions and also contains a function previously investigated by Olesen. Some
examples of solutions are studied numerically and we point out a peculiar
phenomenon of lost vortex charge in the limit where the period lengths tend to
infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added
one referenc
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Dynamics of (SUSY) AdS Space Isometry Breaking
Actions governing the dynamics of the Nambu-Goldstone modes resulting from
the spontaneous breaking of the SO(4,2) and isometries of five
dimensional anti-de Sitter space () and SUSY
spaces respectively due to a restriction of the motion to embedded four
dimensional space and four dimensional Minkowski space () probe
branes are presented. The dilatonic Nambu-Goldstone mode governing the motion
of the space probe brane into the covolume of the SUSY
space is found to be unstable. No such instablility appears in the other cases.
Gauging these symmetries leads to an Einstein-Hilbert action containing, in
addition to the gravitational vierbein, a massive Abelian vector field coupled
to gravity.Comment: 6 pages, 0 figures, to appear in Proceedings of IRGAC 2006: 2nd
International Conference on Quantum Theories and Renormalization Group in
Gravity and Cosmology, Barcelon
Quantum 1/4 BPS Dyons
Classical properties of 1/4 BPS dyons were previously well understood both in
field theory context and in string theory context. Its quantum properties,
however, have been more difficult to probe, although the elementary information
of the supermultiplet structures is known from a perturbative construction.
Recently, a low energy effective theory of monopoles was constructed and argued
to contain these dyons as quantum bound states. In this paper, we find these
dyonic bound states explicitly in the N=4 supersymmetric low energy effective
theory. After identifying the correct angular momentum operators, we motivate
an anti-self-dual ansatz for all BPS bound states. The wavefunctions are found
explicitly, whose spin contents and degeneracies match exactly the expected
results.Comment: 20 pages, no figure
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