21 research outputs found
Hilbert Space Representation of an Algebra of Observables for q-Deformed Relativistic Quantum Mechanics
Using a representation of the q-deformed Lorentz algebra as differential
operators on quantum Minkowski space, we define an algebra of observables for a
q-deformed relativistic quantum mechanics with spin zero. We construct a
Hilbert space representation of this algebra in which the square of the mass is diagonal.Comment: 13 pages, LMU-TPW 94-
-models on the quantum group manifolds , , and infinitesimal trasformations
The differential and variational calculus on the group is
constructed. The spontaneous breaking symmetry in the WZNW model with
quantum group symmetry and in the -models with
, quantum group symmetry is considered.
The Lagrangian formalism over the quantum group manifolds is discussed. The
classical solution of {}-model is obtained.Comment: LaTex, 7 page
Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction
By deriving and studying the coordinate representation for the two-spinon
wavefunction, we show that spinon excitations in the Haldane-Shastry model
interact. The interaction is given by a short-range attraction and causes a
resonant enhancement in the two-spinon wavefunction at short separations
between the spinons. We express the spin susceptibility for a finite lattice in
terms of the resonant enhancement, given by the two-spinon wavefunction at zero
separation. In the thermodynamic limit, the spinon attraction turns into the
square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure
Reduction and Realization in Toda and Volterra
We construct a new symplectic, bi-hamiltonian realization of the KM-system by
reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is
constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper
we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page
Strong Connections on Quantum Principal Bundles
A gauge invariant notion of a strong connection is presented and
characterized. It is then used to justify the way in which a global curvature
form is defined. Strong connections are interpreted as those that are induced
from the base space of a quantum bundle. Examples of both strong and non-strong
connections are provided. In particular, such connections are constructed on a
quantum deformation of the fibration . A certain class of strong
-connections on a trivial quantum principal bundle is shown to be
equivalent to the class of connections on a free module that are compatible
with the q-dependent hermitian metric. A particular form of the Yang-Mills
action on a trivial U\sb q(2)-bundle is investigated. It is proved to
coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel.
Furthermore, it is shown that the moduli space of critical points of this
action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections
over a quantum real projective spac
Hamilton's Formalism for Systems with Constraints
The main goal of these lectures is to introduce and review the Hamiltonian
formalism for classical constrained systems and in particular gauge theories.
Emphasis is put on the relation between local symmetries and constraints and on
the relation between Lagrangean and Hamiltonian symmetries.Comment: 52 pages, revised LATEX version, ETH-TH/93-48, Lectures given at the
Seminar "The Canonical Formalism in Classical and Quantum General
Relativity", Bad Honnef, September 9
Corrections to oblique parameters induced by anomalous vector boson couplings
We study quadratically divergent radiative corrections to the oblique
parameters at LEP1 induced by non-standard vector boson self-couplings. We work
in the Stueckelberg formalism and regulate the divergences through a
gauge-invariant higher derivative scheme. Using consistency arguments together
with the data we find a limit on the anomalous magnetic moment Delta kappa of
the W-boson, |Delta kappa| <= 0.26.Comment: 32 pages, LaTeX; cross reference corrected, minor beautifications,
version to be published in Phys.Rev.