1,085 research outputs found
Covariant Quantum Fields on Noncommutative Spacetimes
A spinless covariant field on Minkowski spacetime \M^{d+1} obeys the
relation where
is an element of the Poincar\'e group \Pg and is its unitary representation on quantum vector states. It
expresses the fact that Poincar\'e transformations are being unitary
implemented. It has a classical analogy where field covariance shows that
Poincar\'e transformations are canonically implemented. Covariance is
self-reproducing: products of covariant fields are covariant. We recall these
properties and use them to formulate the notion of covariant quantum fields on
noncommutative spacetimes. In this way all our earlier results on dressing,
statistics, etc. for Moyal spacetimes are derived transparently. For the Voros
algebra, covariance and the *-operation are in conflict so that there are no
covariant Voros fields compatible with *, a result we found earlier. The notion
of Drinfel'd twist underlying much of the preceding discussion is extended to
discrete abelian and nonabelian groups such as the mapping class groups of
topological geons. For twists involving nonabelian groups the emergent
spacetimes are nonassociative.Comment: 20 page
Bosonic Description of Spinning Strings in Dimensions
We write down a general action principle for spinning strings in 2+1
dimensional space-time without introducing Grassmann variables. The action is
written solely in terms of coordinates taking values in the 2+1 Poincare group,
and it has the usual string symmetries, i.e. it is invariant under a)
diffeomorphisms of the world sheet and b) Poincare transformations. The system
can be generalized to an arbitrary number of space-time dimensions, and also to
spinning membranes and p-branes.Comment: Latex, 12 page
On Time-Space Noncommutativity for Transition Processes and Noncommutative Symmetries
We explore the consequences of time-space noncommutativity in the quantum
mechanics of atoms and molecules, focusing on the Moyal plane with just
time-space noncommutativity (,
\theta_{0i}\neqq 0, ). Space rotations and parity are not
automorphisms of this algebra and are not symmetries of quantum physics. Still,
when there are spectral degeneracies of a time-independent Hamiltonian on a
commutative space-time which are due to symmetries, they persist when
\theta_{0i}\neqq 0; they do not depend at all on . They give no
clue about rotation and parity violation when \theta_{0i}\neqq 0. The
persistence of degeneracies for \theta_{0i}\neqq 0 can be understood in terms
of invariance under deformed noncommutative ``rotations'' and ``parity''. They
are not spatial rotations and reflection. We explain such deformed symmetries.
We emphasize the significance of time-dependent perturbations (for example, due
to time-dependent electromagnetic fields) to observe noncommutativity. The
formalism for treating transition processes is illustrated by the example of
nonrelativistic hydrogen atom interacting with quantized electromagnetic field.
In the tree approximation, the transition for hydrogen is
zero in the commutative case. As an example, we show that it is zero in the
same approximation for . The importance of the deformed
rotational symmetry is commented upon further using the decay
as an example.Comment: 13 pages, revised version, references adde
Properties of Quantum Hall Skyrmions from Anomalies
It is well known that the Fractional Quantum Hall Effect (FQHE) may be
effectively represented by a Chern-Simons theory. In order to incorporate QH
Skyrmions, we couple this theory to the topological spin current, and include
the Hopf term. The cancellation of anomalies for chiral edge states, and the
proviso that Skyrmions may be created and destroyed at the edge, fixes the
coefficients of these new terms. Consequently, the charge and the spin of the
Skyrmion are uniquely determined. For those two quantities we find the values
and , respectively, where is electron charge,
is the filling fraction and is the Skyrmion winding number. We
also add terms to the action so that the classical spin fluctuations in the
bulk satisfy the standard equations of a ferromagnet, with spin waves that
propagate with the classical drift velocity of the electron.Comment: 8 pages, LaTeX file; Some remarks are included to clarify the
physical results obtained, and the role of the Landau-Lifshitz equation is
emphasized. Some references adde
Dual Response Models for the Fractional Quantum Hall Effect
It is shown that the Jain mapping between states of integer and fractional
quantum Hall systems can be described dynamically as a perturbative
renormalization of an effective Chern-Simons field theory. The effects of
mirror duality symmetries of toroidally compactified string theory on this
system are studied and it is shown that, when the gauge group is compact, the
mirror map has the same effect as the Jain map. The extrinsic ingredients of
the Jain construction appear naturally as topologically non-trivial field
configurations of the compact gauge theory giving a dynamical origin for the
Jain hierarchy of fractional quantum Hall states.Comment: 8 pages LaTe
Scalar Field Theory on Fuzzy S^4
Scalar fields are studied on fuzzy and a solution is found for the
elimination of the unwanted degrees of freedom that occur in the model. The
resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4
in the fuzzy context.Comment: 16 pages, LaTe
A transform of complementary aspects with applications to entropic uncertainty relations
Even though mutually unbiased bases and entropic uncertainty relations play
an important role in quantum cryptographic protocols they remain ill
understood. Here, we construct special sets of up to 2n+1 mutually unbiased
bases (MUBs) in dimension d=2^n which have particularly beautiful symmetry
properties derived from the Clifford algebra. More precisely, we show that
there exists a unitary transformation that cyclically permutes such bases. This
unitary can be understood as a generalization of the Fourier transform, which
exchanges two MUBs, to multiple complementary aspects. We proceed to prove a
lower bound for min-entropic entropic uncertainty relations for any set of
MUBs, and show that symmetry plays a central role in obtaining tight bounds.
For example, we obtain for the first time a tight bound for four MUBs in
dimension d=4, which is attained by an eigenstate of our complementarity
transform. Finally, we discuss the relation to other symmetries obtained by
transformations in discrete phase space, and note that the extrema of discrete
Wigner functions are directly related to min-entropic uncertainty relations for
MUBs.Comment: 16 pages, 2 figures, v2: published version, clarified ref [30
Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
We discuss the symmetry properties of the reparametrization invariant model
of an interacting relativistic particle where the electromagnetic field is
taken as the constant background field. The direct coupling between the
relativistic particle and the electromagnetic {\it gauge} field is a special
case of the above with a specific set of subtleties involved in it. For the
above model, we demonstrate the existence of a time-space noncommutativity (NC)
in the spacetime structure from the symmetry considerations alone. We further
show that the NC and commutativity properties of this model are different
aspects of a unique continuous {\it gauge} symmetry that is derived from the
non-standard gauge-type symmetry transformations by requiring their consistency
with (i) the equations of motion, and (ii) the expressions for the canonical
momenta, derived from the Lagrangians. We provide a detailed discussion on the
noncommutative deformation of the Poincar{\'e} algebra.Comment: LaTeX file, 23 pages, journal reference is give
Semi-superfluid strings in High Density QCD
We show that topological superfluid strings/vortices with flux tubes exist in
the color-flavor locked (CFL) phase of color superconductors. Using a
Ginzburg-Landau free energy we find the configurations of these strings. These
strings can form during the transition from the normal phase to the CFL phase
at the core of very dense stars. We discuss an interesting scenario for a
network of strings and its evolution at the core of dense stars.Comment: minor changes in the tex
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