12 research outputs found
Gravitational non-commutativity and G\"odel-like spacetimes
We derive general conditions under which geodesics of stationary spacetimes
resemble trajectories of charged particles in an electromagnetic field. For
large curvatures (analogous to strong magnetic fields), the quantum
mechanicical states of these particles are confined to gravitational analogs of
{\it lowest Landau levels}. Furthermore, there is an effective
non-commutativity between their spatial coordinates. We point out that the
Som-Raychaudhuri and G\"odel spacetime and its generalisations are precisely of
the above type and compute the effective non-commutativities that they induce.
We show that the non-commutativity for G\"odel spacetime is identical to that
on the fuzzy sphere. Finally, we show how the star product naturally emerges in
Som-Raychaudhuri spacetimes.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the
star product). 10 pages, Revtex. To appear in General Relativity and
Gravitatio
Poincare covariant mechanics on noncommutative space
The Dirac approach to constrained systems can be adapted to construct
relativistic invariant theories on a noncommutative (NC) space. As an example,
we propose and discuss relativistic invariant NC particle coupled to
electromagnetic field by means of the standard term . Poincare
invariance implies deformation of the free particle NC algebra in the
interaction theory. The corresponding corrections survive in the
nonrelativistic limit.Comment: 7 pages, JHEP style, final versio
Symplectic Quantization of Open Strings and Noncommutativity in Branes
We show how to translate boundary conditions into constraints in the
symplectic quantization method by an appropriate choice of generalized
variables. This way the symplectic quantization of an open string attached to a
brane in the presence of an antisymmetric background field reproduces the non
commutativity of the brane coordinates.Comment: We included a comparison with previous results obtained from Dirac
quantization, emphasizing the fact that in the symplectic case the boundary
conditions, that lead to the non commutativity, show up from the direct
application of the standard method. Version to appear in Phys. Rev.
Geometric Quantization of Topological Gauge Theories
We study the symplectic quantization of Abelian gauge theories in
space-time dimensions with the introduction of a topological Chern-Simons term.Comment: 13 pages, plain TEX, IF/UFRJ/9
Knot soliton in Weinberg-Salam model
We study numerically the topological knot solution suggested recently in the
Weinberg-Salam model. Applying the SU(2) gauge invariant Abelian projection we
demonstrate that the restricted part of the Weinberg-Salam Lagrangian
containing the interaction of the neutral boson with the Higgs scalar can be
reduced to the Ginzburg-Landau model with the hidden SU(2) symmetry. The energy
of the knot composed from the neutral boson and Higgs field has been evaluated
by using the variational method with a modified Ward ansatz. The obtained
numerical value is 39 Tev which provides the upper bound on the electroweak
knot energy.Comment: 6 pages, 3 figures, analysis of stability adde
Time-Space Noncommutativity in Gravitational Quantum Well scenario
A novel approach to the analysis of the gravitational well problem from a
second quantised description has been discussed. The second quantised formalism
enables us to study the effect of time space noncommutativity in the
gravitational well scenario which is hitherto unavailable in the literature.
The corresponding first quantized theory reveals a leading order perturbation
term of noncommutative origin. Latest experimental findings are used to
estimate an upper bound on the time--space noncommutative parameter. Our
results are found to be consistent with the order of magnitude estimations of
other NC parameters reported earlier.Comment: 7 pages, revTe
Abstract kinetic equations with positive collision operators
We consider "forward-backward" parabolic equations in the abstract form , , where and are
operators in a Hilbert space such that , , and
. The following theorem is proved: if the operator is
similar to a self-adjoint operator, then associated half-range boundary
problems have unique solutions. We apply this theorem to corresponding
nonhomogeneous equations, to the time-independent Fokker-Plank equation , , , as well as to
other parabolic equations of the "forward-backward" type. The abstract kinetic
equation , where is injective and
satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in
the introductio