97 research outputs found
Some remarks on unilateral matrix equations
We briefly review the results of our paper hep-th/0009013: we study certain
perturbative solutions of left-unilateral matrix equations. These are algebraic
equations where the coefficients and the unknown are square matrices of the
same order, or, more abstractly, elements of an associative, but possibly
noncommutative algebra, and all coefficients are on the left. Recently such
equations have appeared in a discussion of generalized Born-Infeld theories. In
particular, two equations, their perturbative solutions and the relation
between them are studied, applying a unified approach based on the generalized
Bezout theorem for matrix polynomials.Comment: latex, 6 pages, 1 figure, talk given at the euroconference "Brane New
World and Noncommutative Geometry", Villa Gualino, Torino, Italy, Oct 2-7,
200
q-Deformed Minkowski Space based on a q-Lorentz Algebra
The Hilbert space representations of a non-commutative q-deformed Minkowski
space, its momenta and its Lorentz boosts are constructed. The spectrum of the
diagonalizable space elements shows a lattice-like structure with accumulation
points on the light-cone.Comment: 31 pages, 1 figur
The Seiberg-Witten Map for Noncommutative Gauge Theories
The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and
methods for its explicit construction are discussed which are valid for any
gauge group. In particular the use of the evolution equation is described in
some detail and its relation to the cohomological approach is elucidated.
Cohomological methods which are applicable to gauge theories requiring the
Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the
analogy of the Weyl-Moyal star product with the star product of open bosonic
string field theory and possible ramifications of this analogy are briefly
mentioned.Comment: 12 pages, talk presented at "Continuous Advances in QCD
2002/Arkadyfest", University of Minnesota, Minneapolis, May 17-23, 2002. A
few misprints correcte
On the Euler angles for SU(N)
In this paper we reconsider the problem of the Euler parametrization for the
unitary groups. After constructing the generic group element in terms of
generalized angles, we compute the invariant measure on SU(N) and then we
determine the full range of the parameters, using both topological and
geometrical methods. In particular, we show that the given parametrization
realizes the group as a fibration of U(N) over the complex projective
space . This justifies the interpretation of the parameters as
generalized Euler angles.Comment: 16 pages, references adde
Structure of the Three-dimensional Quantum Euclidean Space
As an example of a noncommutative space we discuss the quantum 3-dimensional
Euclidean space together with its symmetry structure in great detail.
The algebraic structure and the representation theory are clarified and
discrete spectra for the coordinates are found. The q-deformed Legendre
functions play a special role. A completeness relation is derived for these
functions.Comment: 22 pages, late
A Calculus Based on a q-deformed Heisenberg Algebra
We show how one can construct a differential calculus over an algebra where
position variables x and momentum variables p have be defined. As the simplest
example we consider the one-dimensional q-deformed Heisenberg algebra. This
algebra has a subalgebra generated by x and its inverse which we call the
coordinate algebra. A physical field is considered to be an element of the
completion of this algebra. We can construct a derivative which leaves
invariant the coordinate algebra and so takes physical fields into physical
fields. A generalized Leibniz rule for this algebra can be found. Based on this
derivative differential forms and an exterior differential calculus can be
constructed.Comment: latex-file, 23 page
Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity
In this paper we perform, in the spirit of the holographic correspondence, a
particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a
locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2)
invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory
considered in [Alvarez:2011gd] and featuring "unconventional local
supersymmetry". The model constructed in that reference describes the dynamics
of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to
be relevant for the description of graphene, near the Dirac points, for
specific spatial geometries. Our construction yields the model in
[Alvarez:2011gd] with a specific prescription on the parameters. In this
framework the Dirac spin-1/2 fermion originates from the radial components of
the gravitini in D=4.Comment: 23 page
The Quantum Theory of Chern-Simons Supergravity
We consider -extended Chern-Simons supergravity (\`a la
Achucarro-Tonswend) and we study its gauge symmetries. We promote those gauge
symmetries to a BRST symmetry and we perform its quantization by choosing
suitable gauge-fixings. The resulting quantum theories have different features
which we discuss in the present work. In particular, we show that a special
choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez,
Valenzuela and Zanelli for the graphene fermion.Comment: 25 pages. Some points clarified and conclusion section extended;
content of sections 3 and 4 reorganized. Version to be published on JHE
Bethe Ansatz solution of a new class of Hubbard-type models
We define one-dimensional particles with generalized exchange statistics. The
exact solution of a Hubbard-type Hamiltonian constructed with such particles is
achieved using the Coordinate Bethe Ansatz. The chosen deformation of the
statistics is equivalent to the presence of a magnetic field produced by the
particles themselves, which is present also in a ``free gas'' of these
particles.Comment: 4 pages, revtex. Essentially modified versio
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