1,361 research outputs found
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
On tree form-factors in (supersymmetric) Yang-Mills theory
{\it Perturbiner}, that is, the solution of field equations which is a
generating function for tree form-factors in N=3 supersymmetric
Yang-Mills theory, is studied in the framework of twistor formulation of the
N=3 superfield equations. In the case, when all one-particle asymptotic states
belong to the same type of N=3 supermultiplets (without any restriction on
kinematics), the solution is described very explicitly. It happens to be a
natural supersymmetrization of the self-dual perturbiner in non-supersymmetric
Yang-Mills theory, designed to describe the Parke-Taylor amplitudes. In the
general case, we reduce the problem to a neatly formulated algebraic geometry
problem (see Eqs(\ref{5.15i}),(\ref{5.15ii}),(\ref{5.15iii})) and propose an
iterative algorithm for solving it, however we have not been able to find a
closed-form solution. Solution of this problem would, of course, produce a
description of all tree form-factors in non-supersymmetric Yang-Mills theory as
well. In this context, the N=3 superfield formalism may be considered as a
convenient way to describe a solution of the non-supersymmetric Yang-Mills
theory, very much in the spirit of works by E.Witten \cite{Witten} and by
J.Isenberg, P.B.Yasskin and P.S.Green \cite{2}.Comment: 17 pages, Latex, the form of citation in the abstract have been
corrected by xxx.lanl.gov reques
Geometry and Physics on Orbits
We apply the coadjoint orbit technique to the group of area preserving
diffeomorphisms (APD) of a 2D manifold, particularly to the APD of the
semi-infinite cylinder which is identified with . The geometrical
action obtained is relevant to both gravity and 2D turbulence. For the
latter we describe the hamiltonian, which appears to be given by the Schwinger
mass term, and discuss some possible developments within our approach. Next we
show that the set of highest weight orbits of splits into subsets,
each of which consists of highest weight orbits of for a given N.
We specify the general APD geometric action to an orbit of and
describe an appropriate set of observables, thus getting an action and
observables for gravity. We compute also the Ricci form on the
orbits, what gives us the critical central charge of the
string, which appears to be the same as the one of the
string.Comment: 19 pages, LATEX, with notation changed to , with 3
more references and with note added in proo
Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs
We discuss possibilities of application of Numerical Analysis methods to
proving computability, in the sense of the TTE approach, of solution operators
of boundary-value problems for systems of PDEs. We prove computability of the
solution operator for a symmetric hyperbolic system with computable real
coefficients and dissipative boundary conditions, and of the Cauchy problem for
the same system (we also prove computable dependence on the coefficients) in a
cube . Such systems describe a wide variety of physical
processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many
boundary-value problems for the wave equation also can be reduced to this case,
thus we partially answer a question raised in Weihrauch and Zhong (2002).
Compared with most of other existing methods of proving computability for PDEs,
this method does not require existence of explicit solution formulas and is
thus applicable to a broader class of (systems of) equations.Comment: 31 page
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