1,355 research outputs found
The Jacobian Conjecture as a Problem of Perturbative Quantum Field Theory
The Jacobian conjecture is an old unsolved problem in mathematics, which has
been unsuccessfully attacked from many different angles. We add here another
point of view pertaining to the so called formal inverse approach, that of
perturbative quantum field theory.Comment: 22 pages, 13 diagram
Bosonic Monocluster Expansion
We compute connected Green's functions of a Bosonic field theory with cutoffs
by means of a ``minimal'' expansion which in a single move, interpolating a
generalized propagator, performs the usual tasks of the cluster and Mayer
expansion. In this way it allows a direct construction of the infinite volume
or thermodynamic limit and it brings constructive Bosonic expansions closer to
constructive Fermionic expansions and to perturbation theory.Comment: 30 pages, 1 figur
RTT relations, a modified braid equation and noncommutative planes
With the known group relations for the elements of a quantum
matrix as input a general solution of the relations is sought without
imposing the Yang - Baxter constraint for or the braid equation for
. For three biparametric deformatios, and , the standard,the nonstandard and the
hybrid one respectively, or is found to depend, apart from the
two parameters defining the deformation in question, on an extra free parameter
,such that only for two values of , given explicitly for each case, one
has the braid equation. Arbitray corresponds to a class (conserving the
group relations independent of ) of the MQYBE or modified quantum YB
equations studied by Gerstenhaber, Giaquinto and Schak. Various properties of
the triparametric , and are
studied. In the larger space of the modified braid equation (MBE) even
can satisfy outside braid equation (BE)
subspace. A generalized, - dependent, Hecke condition is satisfied by each
3-parameter . The role of in noncommutative geometries of the
, and deformed planes is studied. K is found to
introduce a "soft symmetry breaking", preserving most interesting properties
and leading to new interesting ones. Further aspects to be explored are
indicated.Comment: Latex, 17 pages, minor change
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