825 research outputs found
A Geometric Model of Arbitrary Spin Massive Particle
A new model of relativistic massive particle with arbitrary spin
(()-particle) is suggested. Configuration space of the model is a product
of Minkowski space and two-dimensional sphere, . The system describes Zitterbewegung at the classical level.
Together with explicitly realized Poincar\'e symmetry, the action functional
turns out to be invariant under two types of gauge transformations having their
origin in the presence of two Abelian first-class constraints in the Hamilton
formalism. These constraints correspond to strong conservation for the
phase-space counterparts of the Casimir operators of the Poincar\'e group.
Canonical quantization of the model leads to equations on the wave functions
which prove to be equivalent to the relativistic wave equations for the massive
spin- field.Comment: 25 pages; v2: eq. (45.b) correcte
Massive spinning particle on anti-de Sitter space
To describe a massive particle with fixed, but arbitrary, spin on
anti-de Sitter space , we propose the point-particle model with
configuration space , where the sphere
corresponds to the spin degrees of freedom. The model possesses two gauge
symmetries expressing strong conservation of the phase-space counterparts of
the second- and fourth-order Casimir operators for . We prove that the
requirement of energy to have a global positive minimum over the
configuration space is equivalent to the relation , being the
particle's spin, what presents the classical counterpart of the quantum massive
condition. States with the minimal energy are studied in detail. The model is
shown to be exactly solvable. It can be straightforwardly generalized to
describe a spinning particle on -dimensional anti-de Sitter space ,
with the corresponding configuration
space.Comment: 23 pages, LaTe
Why the general Zakharov-Shabat equations form a hierarchy?
The totality of all Zakharov-Shabat equations (ZS), i.e., zero-curvature
equations with rational dependence on a spectral parameter, if properly
defined, can be considered as a hierarchy. The latter means a collection of
commuting vector fields in the same phase space. Further properties of the
hierarchy are discussed, such as additional symmetries, an analogue to the
string equation, a Grassmannian related to the ZS hierarchy, and a Grassmannian
definition of soliton solutions.Comment: 13p
Spectrum Generating Algebras for the free motion in
We construct the spectrum generating algebra (SGA) for a free particle in the
three dimensional sphere for both, classical and quantum descriptions. In
the classical approach, the SGA supplies time-dependent constants of motion
that allow to solve algebraically the motion. In the quantum case, the SGA
include the ladder operators that give the eigenstates of the free Hamiltonian.
We study this quantum case from two equivalent points of view.Comment: 29 pages, 1 figur
Spectral Difference Equations Satisfied by KP Soliton Wavefunctions
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the
KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring
of translational operators in the spectral parameter. In the rational limit,
these translational operators converge to the differential operators in the
spectral parameter previously discussed as part of the theory of
"bispectrality". Consequently, these translational operators can be seen as
demonstrating a form of bispectrality for the non-rational solitons as well.Comment: to appear in "Inverse Problems
Coherent (spin-)tensor fields on D=4 anti-de Sitter space
The coherent states associated to the discrete serie representations
of are constructed in terms of (spin-)tensor fields on
anti-de Sitter space. For the linear space
spanned by these states is proved to carry the unitary irreducible
representation . The -covariant generalized Fourier
transform in this space is exhibited. The quasiclassical properties of the
coherent states are analyzed. In particular, these states are shown to be
localized on the time-like geodesics of anti-de Sitter space.Comment: 15 pages, LaTe
Intertwining technique for a system of difference Schroedinger equations and new exactly solvable multichannel potentials
The intertwining operator technique is applied to difference Schroedinger
equations with operator-valued coefficients. It is shown that these equations
appear naturally when a discrete basis is used for solving a multichannel
Schroedinger equation. New families of exactly solvable multichannel
Hamiltonians are found
Geometry of W-algebras from the affine Lie algebra point of view
To classify the classical field theories with W-symmetry one has to classify
the symplectic leaves of the corresponding W-algebra, which are the
intersection of the defining constraint and the coadjoint orbit of the affine
Lie algebra if the W-algebra in question is obtained by reducing a WZNW model.
The fields that survive the reduction will obey non-linear Poisson bracket (or
commutator) relations in general. For example the Toda models are well-known
theories which possess such a non-linear W-symmetry and many features of these
models can only be understood if one investigates the reduction procedure. In
this paper we analyze the SL(n,R) case from which the so-called W_n-algebras
can be obtained. One advantage of the reduction viewpoint is that it gives a
constructive way to classify the symplectic leaves of the W-algebra which we
had done in the n=2 case which will correspond to the coadjoint orbits of the
Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov
algebra. Our method in principle is capable of constructing explicit
representatives on each leaf. Another attractive feature of this approach is
the fact that the global nature of the W-transformations can be explicitly
described. The reduction method also enables one to determine the ``classical
highest weight (h. w.) states'' which are the stable minima of the energy on a
W-leaf. These are important as only to those leaves can a highest weight
representation space of the W-algebra be associated which contains a
``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter
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