1,986 research outputs found
Inequivalence of the Massive Vector Meson and Higgs Models on a Manifold with Boundary
The exact quantization of two models, the massive vector meson model and the
Higgs model in the London limit, both describing massive photons, is presented.
Even though naive arguments (based on gauge-fixing) may indicate the
equivalence of these models, it is shown here that this is not true in general
when we consider these theories on manifolds with boundaries. We show, in
particular, that they are equivalent only for a special choice of the boundary
conditions that we are allowed to impose on the fields.Comment: 14 pages, LATEX File (revised with minor corrections
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
Quantum Geons and Noncommutative Spacetimes
Physical considerations strongly indicate that spacetime at Planck scales is
noncommutative. A popular model for such a spacetime is the Moyal plane. The
Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the
latter is not appropriate for more complicated spacetimes such as those
containing the Friedman-Sorkin (topological) geons. They have rich
diffeomorphism groups and in particular mapping class groups, so that the
statistics groups for N identical geons is strikingly different from the
permutation group . We generalise the Drinfel'd twist to (essentially)
generic groups including to finite and discrete ones and use it to modify the
commutative spacetime algebras of geons as well to noncommutative algebras. The
latter support twisted actions of diffeos of geon spacetimes and associated
twisted statistics. The notion of covariant fields for geons is formulated and
their twisted versions are constructed from their untwisted versions.
Non-associative spacetime algebras arise naturally in our analysis. Physical
consequences, such as the violation of Pauli principle, seem to be the outcomes
of such nonassociativity.
The richness of the statistics groups of identical geons comes from the
nontrivial fundamental groups of their spatial slices. As discussed long ago,
extended objects like rings and D-branes also have similar rich fundamental
groups. This work is recalled and its relevance to the present quantum geon
context is pointed out.Comment: 41 page
Edge States in Gauge Theories: Theory, Interpretations and Predictions
Gauge theories on manifolds with spatial boundaries are studied. It is shown
that observables localized at the boundaries (edge observables) can occur in
such models irrespective of the dimensionality of spacetime. The intimate
connection of these observables to charge fractionation, vertex operators and
topological field theories is described. The edge observables, however, may or
may not exist as well-defined operators in a fully quantized theory depending
on the boundary conditions imposed on the fields and their momenta. The latter
are obtained by requiring the Hamiltonian of the theory to be self-adjoint and
positive definite. We show that these boundary conditions can also have nice
physical interpretations in terms of certain experimental parameters such as
the penetration depth of the electromagnetic field in a surrounding
superconducting medium. The dependence of the spectrum on one such parameter is
explicitly exhibited for the Higgs model on a spatial disc in its London limit.
It should be possible to test such dependences experimentally, the above Higgs
model for example being a model for a superconductor. Boundary conditions for
the 3+1 dimensional system confined to a spatial ball are studied. Their
physical meaning is clarified and their influence on the edge states of this
system (known to exist under certain conditions) is discussed. It is pointed
out that edge states occur for topological solitons of gauge theories such as
the 't Hooft-Polyakov monopoles.Comment: 36 pages, LATEX File (revised because figures had problems
Edge States and Entanglement Entropy
It is known that gauge fields defined on manifolds with spatial boundaries
support states localized at the boundaries. In this paper, we demonstrate how
coarse-graining over these states can lead to an entanglement entropy. In
particular, we show that the entanglement entropy of the ground state for the
quantum Hall effect on a disk exhibits an approximate ``area " law.Comment: 16 pages, minor corrections and futher details adde
Discrete Time from Quantum Physics
't Hooft has recently developed a discretisation of (2+1) gravity which has a
multiple-valued Hamiltonian and which therefore admits quantum time evolution
only in discrete steps. In this paper, we describe several models in the
continuum with single-valued equations of motion in classical physics, but with
multiple-valued Hamiltonians. Their time displacements in quantum theory are
therefore obliged to be discrete. Classical models on smooth spatial manifolds
are also constructed with the property that spatial displacements can be
implemented only in discrete steps in quantum theory. All these models show
that quantization can profoundly affect classical topology.Comment: 21 pages with 2 figures, SU-4240-579 (figures corrected in this
version
Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
Recent work [hep-th/0504183,hep-th/0508002] indicates an approach to the
formulation of diffeomorphism invariant quantum field theories (qft's) on the
Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets
twisted and the S-matrix in the non-gauge qft's becomes independent of the
noncommutativity parameter theta^{\mu\nu}. Here we show that the noncommutative
algebra has a commutative spacetime algebra as a substructure: the Poincare,
diffeomorphism and gauge groups are based on this algebra in the twisted
approach as is known already from the earlier work of [hep-th/0510059]. It is
natural to base covariant derivatives for gauge and gravity fields as well on
this algebra. Such an approach will in particular introduce no additional gauge
fields as compared to the commutative case and also enable us to treat any
gauge group (and not just U(N)). Then classical gravity and gauge sectors are
the same as those for \theta^{\mu \nu}=0, but their interactions with matter
fields are sensitive to theta^{\mu \nu}. We construct quantum noncommutative
gauge theories (for arbitrary gauge groups) by requiring consistency of twisted
statistics and gauge invariance. In a subsequent paper (whose results are
summarized here), the locality and Lorentz invariance properties of the
S-matrices of these theories will be analyzed, and new non-trivial effects
coming from noncommutativity will be elaborated.
This paper contains further developments of [hep-th/0608138] and a new
formulation based on its approach.Comment: 17 pages, LaTeX, 1 figur
Edge states in Gravity and Black Hole Physics
We show in the context of Einstein gravity that the removal of a spatial
region leads to the appearance of an infinite set of observables and their
associated edge states localized at its boundary. Such a boundary occurs in
certain approaches to the physics of black holes like the one based on the
membrane paradigm. The edge states can contribute to black hole entropy in
these models. A ``complementarity principle" is also shown to emerge whereby
certain ``edge" observables are accessible only to certain observers. The
physical significance of edge observables and their states is discussed using
their similarities to the corresponding quantities in the quantum Hall effect.
The coupling of the edge states to the bulk gravitational field is demonstrated
in the context of (2+1) dimensional gravity.Comment: Revtex file, 22 pg. ( refs added , minor typos corrected
Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
Field theories on the Groenewold-Moyal(GM) plane are studied using the
Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields
is treated in detail. The S-matrix elements in this non-perturbative approach
are shown to be equal to the interaction representation S-matrix elements. This
is a new non-trivial result: in both cases, the S-operator is independent of
the noncommutative deformation parameter and the change in
scattering amplitudes due to noncommutativity is just a time delay. This result
is verified in two different ways. But the off-shell Green's functions do
depend on . In the course of this analysis, unitarity of the
non-perturbative S-matrix is proved as well.Comment: 18 pages, minor corrections, To appear in Phys. Rev. D, 201
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