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In this paper we shall discuss some of the isomorphisms established between the approach to conformal field theory on P1 of [TK], and the topological construction of braid group representations of [L 1]. These approaches both lead, in the simplest cases, to the one-variable Jones polynomial invariant of links, but can be generalised to give other invariants. The case of higher spin representations...
The supersymmetric product of a SUSY-curve over a field is constructed with the aid of a theorem of invariants, and the notion of relative superdivisor is introduced. A universal superdivisor is defined in the supersymmetric product by means of Manin's superdiagonal, and it is proven that every superdivisor can be obtained in a unique way as a pullback of the universal superdivisor.
A super Krichever construction is used to produce solutions to the various super Kadomtsev-Petviashvili (SKP) hierarchies from geometric data consisting primarily of a suitable algebraic supercurve of genus g (generally not a super Riemann surface) and a line bundle of degree g-1 on it. The known SKP hierarchies deform both the supercurve and the bundle, in contrast to ordinary KP which deforms bundles...
We present a proof of renormalizability for a non-Riemannian model, based on gauging GL(4,R), in which Einstein's Gravity dominates the low-energy region through a Goldstone-Higgs spontaneous symmetry breakdown mechanism. In other renormalizble models of gravity, this is the result of 1/p4 unitarity-violating propagators, in this case it follows only from the Yang-Mills-like features of the theory.
Multi-soliton solutions of third order nonlinear evolution equations admitting a recursion operator as well as a Lax operator are here considered. Specifically, results obtained in [2,8], which give a method to construct the action-angle transformation on the so-called “multi-soliton” manifold [15], are briefly discussed. Crucial to achieve such a result is the nonlinear link between the eigenvectors...
An extension of the Hurwitz' transformation to a canonical transformation between the corresponding phase spaces allows conversion of the five-dimensional Kepler problem into that of a constrained Harmonic oscillator in eight-dimensions. Then following Dirac we quantize the extended phase space imposing non-Abelian constraint conditions as superselection rules. In that way the interchangeability of...
We exhibit the supergeometric meaning of the symbols or “generating functionals” considered by F. A. Berezin [1] of states and operators in Fock space.
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