15,917 research outputs found
Irreducible Hamiltonian BRST approach to topologically coupled abelian forms
An irreducible Hamiltonian BRST approach to topologically coupled p- and
(p+1)-forms is developed. The irreducible setting is enforced by means of
constructing an irreducible Hamiltonian first-class model that is equivalent
from the BRST point of view to the original redundant theory. The irreducible
path integral can be brought to a manifestly Lorentz covariant form.Comment: 29 pages, LaTeX 2.0
Foundations of Relational Particle Dynamics
Relational particle dynamics include the dynamics of pure shape and cases in
which absolute scale or absolute rotation are additionally meaningful. These
are interesting as regards the absolute versus relative motion debate as well
as discussion of conceptual issues connected with the problem of time in
quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces
of shapes are n-spheres and complex projective spaces, from which knowledge I
construct natural mechanics on these spaces. I also show that these coincide
with Barbour's indirectly-constructed relational dynamics by performing a full
reduction on the latter. Then the identification of the configuration spaces as
n-spheres and complex projective spaces, for which spaces much mathematics is
available, significantly advances the understanding of Barbour's relational
theory in spatial dimensions 1 and 2. I also provide the parallel study of a
new theory for which positon and scale are purely relative but orientation is
absolute. The configuration space for this is an n-sphere regardless of the
spatial dimension, which renders this theory a more tractable arena for
investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update
A Geometric Approach to Massive p-form Duality
Massive theories of abelian p-forms are quantized in a generalized
path-representation that leads to a description of the phase space in terms of
a pair of dual non-local operators analogous to the Wilson Loop and the 't
Hooft disorder operators. Special atention is devoted to the study of the
duality between the Topologically Massive and the Self-Dual models in 2+1
dimensions. It is shown that these models share a geometric representation in
which just one non local operator suffices to describe the observables.Comment: 26 pages, LaTeX. The discussion about the equivalence between the
Proca model and two seldual models, with opposite spins, was eliminated.
Typos correcte
An intrinsic Hamiltonian formulation of the dynamics of LC-circuits
First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduce
Robot's hand and expansions in non-integer bases
We study a robot hand model in the framework of the theory of expansions in
non-integer bases. We investigate the reachable workspace and we study some
configurations enjoying form closure properties.Comment: 22 pages, 10 figure
Dispersionless Toda hierarchy and two-dimensional string theory
The dispersionless Toda hierarchy turns out to lie in the heart of a recently
proposed Landau-Ginzburg formulation of two-dimensional string theory at
self-dual compactification radius. The dynamics of massless tachyons with
discrete momenta is shown to be encoded into the structure of a special
solution of this integrable hierarchy. This solution is obtained by solving a
Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by
deriving recursion relations of tachyon correlation functions in the machinery
of the dispersionless Toda hierarchy. Fundamental ingredients of the
Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon
Landau-Ginzburg fields, are translated into the language of the Lax formalism.
Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert
problem, and speculations on its possible role as generators of ``extra''
states and fields are presented.Comment: LaTeX 21 pages, KUCP-0067 (typos are corrected and a brief note is
added
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