85 research outputs found
Einstein-Riemann Gravity on Deformed Spaces
A differential calculus, differential geometry and the E-R Gravity theory are
studied on noncommutative spaces. Noncommutativity is formulated in the star
product formalism. The basis for the gravity theory is the infinitesimal
algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find
that the deformed gravity is based on a deformation of the Hopf algebra.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
q-deformed Hermite Polynomials in q-Quantum Mechanics
The q-special functions appear naturally in q-deformed quantum mechanics and
both sides profit from this fact. Here we study the relation between the
q-deformed harmonic oscillator and the q-Hermite polynomials. We discuss:
recursion formula, generating function, Christoffel-Darboux identity,
orthogonality relations and the moment functional.Comment: latex, 8 pages, no figures. accepted for publication in European
Journal of Physics
Twisted Gauge Theories
Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant quantities. The connection will be enveloping algebra valued in a particular representation of the Lie algebra. This gives rise to additional fields, which couple only weakly via the deformation parameter and reduce in the commutative limit to free fields. Consistent field equations that lead to conservation laws are derived and some properties of such theories are discussed
Noncommutative Geometry and Gravity
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold.
The deformation is based on a general twist. This leads to a differential
geometry on a noncommutative algebra of functions whose product is a
star-product. The class of noncommutative spaces studied is very rich.
Non-anticommutative superspaces are also briefly considered.
The differential geometry developed is covariant under deformed
diffeomorphisms and it is coordinate independent. The main target of this work
is the construction of Einstein's equations for gravity on noncommutative
manifolds.Comment: 40pages; v2: references adde
External Fields as Intrinsic Geometry
There is an interesting dichotomy between a space-time metric considered as
external field in a flat background and the same considered as an intrinsic
part of the geometry of space-time. We shall describe and compare two other
external fields which can be absorbed into an appropriate redefinition of the
geometry, this time a noncommutative one. We shall also recall some previous
incidences of the same phenomena involving bosonic field theories. It is known
that some such theories on the commutative geometry of space-time can be
re-expressed as abelian-gauge theory in an appropriate noncommutative geometry.
The noncommutative structure can be considered as containing extra modes all of
whose dynamics are given by the one abelian action.Comment: 19 pages, Late
Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
An enveloping algebra valued gauge field is constructed, its components are
functions of the Lie algebra valued gauge field and can be constructed with the
Seiberg-Witten map. This allows the formulation of a dynamics for a finite
number of gauge field components on non-commutative spaces.Comment: 13 page
Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator
A --deformed anharmonic oscillator is defined within the framework of
--deformed quantum mechanics. It is shown that the Rayleigh--Schr\"odinger
perturbation series for the bounded spectrum converges to exact eigenstates and
eigenvalues, for close to 1. The radius of convergence becomes zero in the
undeformed limit.Comment: 14 pages, 2 figure using eps
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