252 research outputs found
On Rotations as Spin Matrix Polynomials
Recent results for rotations expressed as polynomials of spin matrices are
derived here by elementary differential equation methods. Structural features
of the results are then examined in the framework of biorthogonal systems, to
obtain an alternate derivation. The central factorial numbers play key roles in
both derivations.Comment: 6 Figures. References updated in v2, along with some editing of tex
Branes, Strings, and Odd Quantum Nambu Brackets
The dynamics of topological open branes is controlled by Nambu Brackets.
Thus, they might be quantized through the consistent quantization of the
underlying Nambu brackets, including odd ones: these are reachable
systematically from even brackets, whose more tractable properties have been
detailed before.Comment: 12 pp, 1 fig, LateX2e/WS-procs9x6 macros. Contribution to the
proceedings of QTS3, 10-14 Sep 2003, Cincinnati, World Scientific (SPIRES
conf C03/09/10
Massive Dual Spin 2 Revisited
We reconsider a massive dual spin 2 field theory in four spacetime
dimensions. We obtain the Lagrangian that describes the lowest order coupling
of the field to the four-dimensional curl of its own energy-momentum tensor. We
then find some static solutions for the dual field produced by other
energy-momentum sources and we compare these to similar static solutions for
non-dual "finite range" gravity. Finally, through use of a nonlinear field
redefinition, we show the theory is the exact dual of the
Ogievetsky-Polubarinov model for a massive spin 2 field.Comment: Modified titl
Massive Dual Gravity in N Spacetime Dimensions
We describe a field theory for "massive dual gravity" in N spacetime
dimensions. We obtain a Lagrangian that gives the lowest order coupling of the
field to the N-dimensional curl of its own energy-momentum tensor. We then
briefly discuss classical solutions. Finally, we show the theory is the exact
dual of the Ogievetsky-Polubarinov model generalized to any N.Comment: In tribute to Peter Freund, with additional reference
Quantization with maximally degenerate Poisson brackets: The harmonic oscillator!
Nambu's construction of multi-linear brackets for super-integrable systems
can be thought of as degenerate Poisson brackets with a maximal set of Casimirs
in their kernel. By introducing privileged coordinates in phase space these
degenerate Poisson brackets are brought to the form of Heisenberg's equations.
We propose a definition for constructing quantum operators for classical
functions which enables us to turn the maximally degenerate Poisson brackets
into operators. They pose a set of eigenvalue problems for a new state vector.
The requirement of the single valuedness of this eigenfunction leads to
quantization. The example of the harmonic oscillator is used to illustrate this
general procedure for quantizing a class of maximally super-integrable systems
Canonical nonabelian dual transformations in supersymmetric field theories
A generating functional F is found for a canonical nonabelian dual transformation which maps the supersymmetric chiral O(4) \sigma-model to an equivalent supersymmetric extension of the dual \sigma-model. This F produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {\em symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional T which relates wavefunctions in the two quantum theories is argued to be {\em exactly} given by T=\exp(iF)
Generalized N = 2 Super Landau Models
We generalize previous results for the superplane Landau model to exhibit an
explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any
two-dimensional manifold. Starting from an off-shell N = 2 superfield
formalism, we discuss the quantization procedure in the general case
characterized by two independent potentials on the manifold and show that the
relevant Hamiltonians are factorizable. In the restricted case when both the
Gauss curvature and the magnetic field are constant over the manifold and, as a
consequence, the underlying potentials are related, the Hamiltonians admit
infinite series of factorization chains implying the integrability of the
associated systems. We explicitly determine the spectrum and eigenvectors for
the particular model with CP^1 as the bosonic manifold.Comment: 26 page
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