1,481 research outputs found
Quasideterminants
The determinant is a main organizing tool in commutative linear algebra. In
this review we present a theory of the quasideterminants defined for matrices
over a division algebra. We believe that the notion of quasideterminants should
be one of main organizing tools in noncommutative algebra giving them the same
role determinants play in commutative algebra.Comment: amstex; final version; to appear in Advances in Mat
Recursion relations and branching rules for simple Lie algebras
The branching rules between simple Lie algebras and its regular (maximal)
simple subalgebras are studied. Two types of recursion relations for anomalous
relative multiplicities are obtained. One of them is proved to be the
factorized version of the other. The factorization property is based on the
existence of the set of weights specific for each injection. The
structure of is easily deduced from the correspondence between the
root systems of algebra and subalgebra. The recursion relations thus obtained
give rise to simple and effective algorithm for branching rules. The details
are exposed by performing the explicit decomposition procedure for injection.Comment: 15p.,LaTe
A uniform reconstruction formula in integral geometry
A general method for analytic inversion in integral geometry is proposed. All
classical and some new reconstruction formulas of Radon-John type are obtained
by this method. No harmonic analysis and PDE is used
Noncommutative symmetric functions and Laplace operators for classical Lie algebras
New systems of Laplace (Casimir) operators for the orthogonal and symplectic
Lie algebras are constructed. The operators are expressed in terms of paths in
graphs related to matrices formed by the generators of these Lie algebras with
the use of some properties of the noncommutative symmetric functions associated
with a matrix. The decomposition of the Sklyanin determinant into a product of
quasi-determinants play the main role in the construction. Analogous
decomposition for the quantum determinant provides an alternative proof of the
known construction for the Lie algebra gl(N).Comment: 25 page
An Effective Field Theory Look at Deep Inelastic Scattering
This talk discusses the effective field theory view of deep inelastic
scattering. In such an approach, the standard factorization formula of a hard
coefficient multiplied by a parton distribution function arises from matching
of QCD onto an effective field theory. The DGLAP equations can then be viewed
as the standard renormalization group equations that determines the cut-off
dependence of the non-local operator whose forward matrix element is the parton
distribution function. As an example, the non-singlet quark splitting functions
is derived directly from the renormalization properties of the non-local
operator itself. This approach, although discussed in the literature, does not
appear to be well known to the larger high energy community. In this talk we
give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters
Invariant and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants,
determinants, characteristic polynomials and polynomial identities for matrices
of higher rank. We define permutation tensors and in term of them we construct
discriminants and the determinant as the discriminant of order , where
is the dimension of the matrix. The characteristic polynomials and the
Cayley--Hamilton theorem for higher rank matrices are obtained there from
The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator
A new approach is proposed to the solution of the quantum mechanical inverse
scattering problem at fixed energy. The method relates the fixed energy phase
shifts to those arising in an auxiliary Sturm-Liouville problem via the
interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko
equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure
Nonlinear equations for p-adic open, closed, and open-closed strings
We investigate the structure of solutions of boundary value problems for a
one-dimensional nonlinear system of pseudodifferential equations describing the
dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar
tachyon field using the method of successive approximations. For an open-closed
string, we prove that the method converges for odd values of p of the form
p=4n+1 under the condition that the solution for the closed string is known.
For p=2, we discuss the questions of the existence and the nonexistence of
solutions of boundary value problems and indicate the possibility of
discontinuous solutions appearing.Comment: 16 pages, 3 figure
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