23 research outputs found
Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
The effects of noncommutativity and of the existence of a minimal length on
the phase space of a dilatonic cosmological model are investigated. The
existence of a minimum length, results in the Generalized Uncertainty Principle
(GUP), which is a deformed Heisenberg algebra between the minisuperspace
variables and their momenta operators. We extend these deformed commutating
relations to the corresponding deformed Poisson algebra. For an exponential
dilaton potential, the exact classical and quantum solutions in the commutative
and noncommutative cases, and some approximate analytical solutions in the case
of GUP, are presented and compared.Comment: 16 pages, 3 figures, typos correcte
Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
We study the effects of noncommutativity, in the form of a Lie-algebraically
deformed Poisson commutation relations, on the evolution of a Bianchi type I
cosmological model with a positive cosmological constant. The phase space
variables turn out to correspond to the scale factors of this model in ,
and directions. According to the conditions that the structure constants
(deformation parameters) should satisfy, we argue that there are two types of
noncommutative phase space with Lie-algebraic structure. The exact classical
solutions in commutative and type I noncommutative cases are presented. In the
framework of this type of deformed phase space, we investigate the possibility
of building a Bianchi I model with cyclic scale factors in which the size of
the universe in each direction experiences an endless sequence of contractions
and re-expansions. We also obtain some approximate solutions for the type II
noncommutative structure by numerical methods and show that the cyclic behavior
is repeated as well. These results are compared with the standard commutative
case, and similarities and differences of these solutions are discussed.Comment: 13 pages, to appear in PRD, typos corrected, Refs. adde
Examples of q-regularization
An Introduction to Hopf algebras as a tool for the regularization of relavent
quantities in quantum field theory is given. We deform algebraic spaces by
introducing q as a regulator of a non-commutative and non-cocommutative Hopf
algebra. Relevant quantities are finite provided q\neq 1 and diverge in the
limit q\rightarrow 1. We discuss q-regularization on different q-deformed
spaces for \lambda\phi^4 theory as example to illustrate the idea.Comment: 17 pages, LaTex, to be published in IJTP 1995.1
Noncommutativity, generalized uncertainty principle and FRW cosmology
We consider the effects of noncommutativity and the generalized uncertainty
principle on the FRW cosmology with a scalar field. We show that, the
cosmological constant problem and removability of initial curvature singularity
find natural solutions in this scenarios.Comment: 8 pages, to appear in IJT
A coherent-state-based path integral for quantum mechanics on the Moyal plane
Inspired by a recent work that proposes using coherent states to evaluate the
Feynman kernel in noncommutative space, we provide an independent formulation
of the path-integral approach for quantum mechanics on the Moyal plane, with
the transition amplitude defined between two coherent states of mean position
coordinates. In our approach, we invoke solely a representation of the of the
noncommutative algebra in terms of commutative variables. The kernel expression
for a general Hamiltonian was found to contain gaussian-like damping terms, and
it is non-perturbative in the sense that it does not reduce to the commutative
theory in the limit of vanishing - the noncommutative parameter. As an
example, we studied the free particle's propagator which turned out to be
oscillating with period being the product of its mass and . Further, it
satisfies the Pauli equation for a charged particle with its spin aligned to a
constant, orthogonal field in the ordinary Landau problem, thus providing
an interesting evidence of how noncommutativity can induce spin-like effects at
the quantum mechanical level.Comment: 15 page