720 research outputs found
Full hamiltonian structure for a parametric coupled Korteweg-de Vries system
We obtain the full hamiltonian structure for a parametric coupled KdV system.
The coupled system arises from four different real basic lagrangians. The
associated hamiltonian functionals and the corresponding Poisson structures
follow from the geometry of a constrained phase space by using the Dirac
approach for constrained systems. The overall algebraic structure for the
system is given in terms of two pencils of Poisson structures with associated
hamiltonians depending on the parameter of the Poisson pencils. The algebraic
construction we present admits the most general space of observables related to
the coupled system.Comment: 14 page
Poisson structure and stability analysis of a coupled system arising from the supersymmetric breaking of Super KdV
The Poisson structure of a coupled system arising from a supersymmetric
breaking of N=1 Super KdV equations is obtained. The supersymmetric breaking is
implemented by introducing a Clifford algebra instead of a Grassmann algebra.
The Poisson structure follows from the Dirac brackets obtained by the
constraint analysis of the hamiltonian of the system. The coupled system has
multisolitonic solutions. We show that the one soliton solutions are Liapunov
stable.Comment: Contribution to the Proceedings of the XXst International Coference
on Integrable systems and Quantum Symmetries (ISQS21)(12-16 June 2013,
Prague, Czech Republic), 7 page
Hamiltonian structure of an operator valued extension of Super KdV equations
An extension of the super Korteweg-de Vries integrable system in terms of
operator valued functions is obtained. In particular the extension contains the
Super KdV and coupled systems with functions valued on a symplectic
space. We introduce a Miura transformation for the extended system and obtain
its hamiltonian structure. We also obtain an extended Gardner transformation
which allows to find an infinite number of conserved quantities of the extended
system.Comment: Contribution to the Proceedings of the XXIst International Conference
on Integrable Systems and Quantum Symmetries(ISQS21)(June 11-16, 2013,
Prague, Czech Republic), 6 page
The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of Super KdV equations
A supersymmetric breaking procedure for Super KdV, using a Clifford
algebra, is implemented. Dirac's method for the determination of constraints is
used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting
solitonic system of coupled Korteweg-de Vries type system. It is shown that the
Hamiltonian obtained by this procedure is bounded from below and in that sense
represents a model which is physically admissible.Comment: 10 page
Gauge invariant formulation of systems with second class constraints
A covariant quantization method for physical systems with reducible
constraints is presented.Comment: 4 pages, XIX International Colloquium in Group Theoretical Methods in
Physics, Salamanca, Spain, 199
Covariant Quantization Of Green Schwarz Superstring
We describe a canonical covariant approach to the quantization of the
Green-Schwarz superstring. The approach is first applied to the canonical
covariant quantization of the Brink and Schwarz superparticle. The Kallosh
action is obtained in this case, with the correct BRST cohomology.Comment: 21 page
BF Topological Theories and Infinitely Reducible Systems
We present a rigurous disscusion for abelian theories in which the base
manifold of the bundle is homeomorphic to a Hilbert space. The theory
has an infinte number of stages of reducibility. We specify conditions on the
base manifold under which the covarinat quantization of the system can be
performed unambiguously. Applications of the formulation to the superparticle
and the supertstring are also discussed.Comment: 10 pages, Late
Membrane Solitons as Solitary Waves of Non-Linear Strings Dynamics
Families of solutions to the field equations of the covariant BRST invariant
effective action of the membrane theory are constructed. The equations are
discussed in a double dimensional reduction, they lead to a nonlinear equation
for a one dimensional extended object. One family of solutions of these
equations are solitary waves with several properties of solitonic solutions in
integrable systems, giving evidence that in this double dimensional reduction
the nonlinear equations are an integrable system. The other family of solutions
found, exploits the property that the non linear system under some assumptions
is equivalent to a non linear Schrdinger equation.Comment: 15 pages, latex=2
On the QFT relation between Donaldson-Witten invariants and Floer homology theory
A TQFT in terms of general gauge fixing functions is discussed. In a
covariant gauge it yields the Donaldson-Witten TQFT. The theory is formulated
on a generalized phase space where a simplectic structure is introduced. The
Hamiltonian is expressed as the anticommutator of off-shell nilpotent BRST and
anti-BRST charges. Following original ideas of Witten a time reversal operation
is introduced and an inner product is defined in terms of it. A non-covariant
gauge fixing is presented giving rise to a manifestly time reversal invariant
Lagrangean and a positive definite Hamiltonian, with the inner product
previously introduced. As a consequence, the indefiniteness problem of some of
the kinetic terms of the Witten's action is resolved. The construction allows
then a consistent interpretation of Floer groups in terms of the cohomology of
the BRST charge which is explicitly independent of the background metric.
The relation between the BRST cohomology and the ground states of the
Hamiltonian is then completely stablished. The topological theories arising
from the covariant, Donaldson-Witten, and non-covariant gauge fixing are shown
to be quantum equivalent by using the operatorial approach.Comment: 27 pages, latex, no figure
Minimal Immersions and the Spectrum of Supermembranes
We describe the minimal configurations of the compact D=11 Supermembrane and
D-branes when the spatial part of the world-volume is a K\"ahler manifold. The
minima of the corresponding hamiltonians arise at immersions into the target
space minimizing the K\"ahler volume. Minimal immersions of particular K\"ahler
manifolds into a given target space are known to exist. They have associated to
them a symplectic matrix of central charges. We reexpress the Hamiltonian of
the D=11 Supermembrane with a symplectic matrix of central charges, in the
light cone gauge, using the minimal immersions as backgrounds and the
Sp\parent{2g,\mathbb{Z}} symmetry of the resulting theory, being the
genus of the K\"ahler manifold. The resulting theory is a symplectic
noncommutative Yang-Mills theory coupled with the scalar fields transverse to
the Supermembrane. We prove that both theories are exactly equivalent. A
similar construction may be performed for the Born-Infeld action. Finally, the
noncommutative formulation is used to show that the spectrum of the reguralized
Hamiltonian of the above mentioned D=11 Supermembrane is a discrete set of
eigenvalues with finite multiplicity
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