391 research outputs found
Negative Probability and Uncertainty Relations
A concise derivation of all uncertainty relations is given entirely within
the context of phase-space quantization, without recourse to operator methods,
to the direct use of Weyl's correspondence, or to marginal distributions of x
and p.Comment: RevTeX, 4 page
Grounded Hyperspheres as Squashed Wormholes
We compute exterior Green functions for equipotential, grounded hyperspheres
in N-dimensional electrostatics by squashing Riemannian wormholes, where an
image charge is placed in the branch of the wormhole opposite the branch
containing the source charge, thereby providing a vivid geometrical approach to
a method first suggested in 1897 by Sommerfeld. We compare and contrast the
strength and location of the image charge in the wormhole approach with that of
the conventional Euclidean solution where an image charge of reduced magnitude
is located inside the hypersphere. While the two approaches give mathematically
equivalent Green functions, we believe they provide strikingly different
physics perspectives.Comment: Companion paper for arXiv:1805.11147 with minor typos corrected in
version 2. To appear in J Math Phy
Currents, Charges, and Canonical Structure of Pseudodual Chiral Models
We discuss the pseudodual chiral model to illustrate a class of
two-dimensional theories which have an infinite number of conservation laws but
allow particle production, at variance with naive expectations. We describe the
symmetries of the pseudodual model, both local and nonlocal, as transmutations
of the symmetries of the usual chiral model. We refine the conventional
algorithm to more efficiently produce the nonlocal symmetries of the model, and
we discuss the complete local current algebra for the pseudodual theory. We
also exhibit the canonical transformation which connects the usual chiral model
to its fully equivalent dual, further distinguishing the pseudodual theory.Comment: 15 pages, ANL-HEP-PR-93-85,Miami-TH-1-93,Revtex (references updated,
format improved to Revtex
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
Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space
Wigner's quasi-probability distribution function in phase-space is a special
(Weyl) representation of the density matrix. It has been useful in describing
quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum
computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It
is also of importance in signal processing.
Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal,
has only emerged in the last quarter-century: It furnishes a third,
alternative, formulation of Quantum Mechanics, independent of the conventional
Hilbert Space, or Path Integral formulations. In this logically complete and
self-standing formulation, one need not choose sides--coordinate or momentum
space. It works in full phase-space, accommodating the uncertainty principle.
This is an introductory overview of the formulation with simple illustrations.Comment: LaTeX, 22 pages, 2 figure
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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