22 research outputs found
Gravitoelectromagnetic knot fields
We construct a class of knot solutions of the gravitoelectromagnetic (GEM)
equations in vacuum in the linearized gravity approximation by analogy with the
Ra\~{n}ada-Hopf fields. For these solutions, the dual metric tensors of the
bi-metric geometry of the gravitational vacuum with knot perturbations are
given and the geodesic equation as a function of two complex parameters of the
GEM knots are calculated. Finally, the Landau--Lifshitz pseudo-tensor and a
scalar invariant of the GEM knots are computed.Comment: 22 pages. Published in the Special Issue "Frame-Dragging and
Gravitomagnetism
Normal ordering and boundary conditions in open bosonic strings
Boundary conditions play a non trivial role in string theory. For instance
the rich structure of D-branes is generated by choosing appropriate
combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an
antisymmetric background is present at the string end-points (corresponding to
mixed boundary conditions) space time becomes non-commutative there.
We show here how to build up normal ordered products for bosonic string
position operators that satisfy both equations of motion and open string
boundary conditions at quantum level. We also calculate the equal time
commutator of these normal ordered products in the presence of antisymmetric
tensor background.Comment: 7 pages no figures, References adde
Normal ordering and boundary conditions for fermionic string coordinates
We build up normal ordered products for fermionic open string coordinates
consistent with boundary conditions. The results are obtained considering the
presence of antisymmetric tensor fields. We find a discontinuity of the normal
ordered products at string endpoints even in the absence of the background. We
discuss how the energy momentum tensor also changes at the world-sheet boundary
in such a way that the central charge keeps the standard value at string end
points.Comment: In this revised version we clarify the issue of consistency between
supersymmetry and boundary conditions and stress the fact that we are
considering flat space. we also add two more reference
Fermionic anticommutators for open superstrings in the presence of antisymmetric tensor field
We build up the anticommutator algebra for the fermionic coordinates of open
superstrings attached to branes with antisymmetric tensor fields. We use both
Dirac quantization and the symplectic Faddeev Jackiw approach. In the
symplectic case we find a way of generating the boundary conditions as zero
modes of the symplectic matrix by taking a discretized form of the action and
adding terms that vanish in the continuous limit. This way boundary conditions
can be handled as constraints.Comment: Revision: passage from discrete to continuous clarified, comment on
previous results using Dirac quantization included, typos corrected. Version
to appear in Phys. Lett.
Canonical Transformations and Gauge Fixing in the Triplectic Quantization
We show that the generators of canonical transformations in the triplectic
manifold must satisfy constraints that have no parallel in the usual field
antifield quantization. A general form for these transformations is presented.
Then we consider gauge fixing by means of canonical transformations in this
Sp(2) covariant scheme, finding a relation between generators and gauge fixing
functions. The existence of a wide class of solutions to this relation nicely
reflects the large freedom of the gauge fixing process in the triplectic
quantization. Some solutions for the generators are discussed. Our results are
then illustrated by the example of Yang Mills theory.Comment: A new section about the cohomological approach to the extended BRST
quantization has been included. Some new references were added too. Final
version to appear in Nucl. Phys.B. 12 pages, LATE
Extending the D'Alembert Solution to Space-Time Modified Riemann-Liouville Fractional Wave Equations
In the realm of complexity, it is argued that adequate modeling of
TeV-physics demands an approach based on fractal operators and fractional
calculus (FC). Non-local theories and memory effects are connected to
complexity and the FC. The non-differentiable nature of the microscopic
dynamics may be connected with time scales. Based on the Modified
Riemann-Liouville definition of fractional derivatives, we have worked out
explicit solutions to a fractional wave equation with suitable initial
conditions to carefully understand the time evolution of classical fields with
a fractional dynamics. First, by considering space-time partial fractional
derivatives of the same order in time and space, a generalized fractional
D'Alembertian is introduced and by means of a transformation of variables to
light-cone coordinates, an explicit analytical solution is obtained. To address
the situation of different orders in the time and space derivatives, we adopt
different approaches, as it will become clear throughout the paper. Aspects
connected to Lorentz symmetry are analyzed in both approaches.Comment: 8 page
Extended BRST invariance in topological Yang Mills theory revisited
Extended BRST invariance (BRST plus anti-BRST invariances) provides in
principle a natural way of introducing the complete gauge fixing structure
associated to a gauge field theory in the minimum representation of the
algebra. However, as it happens in topological Yang Mills theory, not all gauge
fixings can be obtained from a symmetrical extended BRST algebra, where
antighosts belong to the same representation of the Lorentz group of the
corresponding ghosts. We show here that, at non interacting level, a simple
field redefinition makes it possible to start with an extended BRST algebra
with symmetric ghost antighost spectrum and arrive at the gauge fixing action
of topological Yang Mills theory.Comment: Interaction terms heve been included in all the calculations. Two
references added. Version to be published in Phys. Rev. D. 7 pages, Latex, no
figure
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.