800 research outputs found
Inequivalent Quantizations of Gauge Theories
It is known that the quantization of a system defined on a topologically
non-trivial configuration space is ambiguous in that many inequivalent quantum
systems are possible. This is the case for multiply connected spaces as well as
for coset spaces. Recently, a new framework for these inequivalent
quantizations approach has been proposed by McMullan and Tsutsui, which is
based on a generalized Dirac approach. We employ this framework for the
quantization of the Yang-Mills theory in the simplest fashion. The resulting
inequivalent quantum sectors are labelled by quantized non-dynamical
topological charges.Comment: 24 pages, LaTeX, to be publ. in Int.J.Mod.Phys.
Path Integrals on Riemannian Manifolds with Symmetry and Induced Gauge Structure
We formulate path integrals on any Riemannian manifold which admits the
action of a compact Lie group by isometric transformations. We consider a path
integral on a Riemannian manifold M on which a Lie group G acts isometrically.
Then we show that the path integral on M is reduced to a family of path
integrals on a quotient space Q=M/G and that the reduced path integrals are
completely classified by irreducible unitary representations of G. It is not
necessary to assume that the action of G on M is either free or transitive.
Hence our formulation is applicable to a wide class of manifolds, which
includes inhomogeneous spaces, and it covers all the inequivalent
quantizations. To describe the path integral on inhomogeneous space,
stratification geometry, which is a generalization of the concept of principal
fiber bundle, is necessarily introduced. Using it we show that the path
integral is expressed as a product of three factors; the rotational energy
amplitude, the vibrational energy amplitude, and the holonomy factor. When a
singular point arises in , we determine the boundary condition of the path
integral kernel for a path which runs through the singularity.Comment: 20 pages, no figur
An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold
It is well known that the inequivalent unitary irreducible representations
(UIR's) of the mapping class group of a 3-manifold give rise to ``theta
sectors'' in theories of quantum gravity with fixed spatial topology. In this
paper, we study several families of UIR's of and attempt to understand the
physical implications of the resulting quantum sectors. The mapping class group
of a three-manifold which is the connected sum of with a finite number
of identical irreducible primes is a semi-direct product group. Following
Mackey's theory of induced representations, we provide an analysis of the
structure of the general finite dimensional UIR of such a group. In the picture
of quantized primes as particles (topological geons), this general
group-theoretic analysis enables one to draw several interesting qualitative
conclusions about the geons' behavior in different quantum sectors, without
requiring an explicit knowledge of the UIR's corresponding to the individual
primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an
appendix proving the semi-direct product structure of the MCG, corrected an
error in the characterization of the slide subgroup, reworded extensively.
All our analysis and conclusions remain as befor
Behaviour of three charged particles on a plane under perpendicular magnetic field
We consider the problem of three identical charged particles on a plane under
a perpendicular magnetic field and interacting through Coulomb repulsion. This
problem is treated within Taut's framework, in the limit of vanishing center of
mass vector , which corresponds to the strong magnetic
field limit, occuring for example in the Fractional Quantum Hall Effect. Using
the solutions of the biconfluent Heun equation, we compute the eigenstates and
show that there is two sets of solutions. The first one corresponds to a system
of three independent anyons which have their angular momenta fixed by the value
of the magnetic field and specified by a dimensionless parameter , the ratio of , the magnetic length, over , the Bohr
radius. This anyonic character, consistent with quantum mechanics of identical
particles in two dimensions, is induced by competing physical forces. The
second one corresponds to the case of the Landau problem when .
Finally we compare these states with the quantum Hall states and find that the
Laughlin wave functions are special cases of our solutions under certains
conditions.Comment: 15 pages, 3 figures, Accepeted in JP
On a Modification of the Boundary State Formalism in Off-shell String Theory
We examine the application of boundary states in computing amplitudes in
off-shell open string theory. We find a straightforward generalization of
boundary state which produces the correct matrix elements with on-shell closed
string states.Comment: Latex, 10 pages, refs added, minor typos correcte
A natural biogenic fluorapatite as a new biomaterial for orthopedics and dentistry: antibacterial activity of lingula seashell and its use for nanostructured biomimetic coatings
Calcium phosphates are widely studied in orthopedics and dentistry, to obtain biomimetic and antibacterial implants. However, the multi-substituted composition of mineralized tissues is not fully reproducible from synthetic procedures. Here, for the first time, we investigate the possible use of a natural, fluorapatite-based material, i.e., Lingula anatina seashell, resembling the composition of bone and enamel, as a biomaterial source for orthopedics and dentistry. Indeed, thanks to its unique mineralization process and conditions, L. anatina seashell is among the few natural apatite-based shells, and naturally contains ions having possible antibacterial efficacy, i.e., fluorine and zinc. After characterization, we explore its deposition by ionized jet deposition (IJD), to obtain nanostructured coatings for implantable devices. For the first time, we demonstrate that L. anatina seashells have strong antibacterial properties. Indeed, they significantly inhibit planktonic growth and cell adhesion of both Gram-positive Staphylococcus aureus and Gram-negative Escherichia coli. The two strains show different susceptibility to the mineral and organic parts of the seashells, the first being more susceptible to zinc and fluorine in the mineral part, and the second to the organic (chitin-based) component. Upon deposition by IJD, all films exhibit a nanostructured morphology and sub-micrometric thickness. The multi-doped, complex composition of the target is maintained in the coating, demonstrating the feasibility of deposition of coatings starting from biogenic precursors (seashells). In conclusion, Lingula seashell-based coatings are non-cytotoxic with strong antimicrobial capability, especially against Gram-positive strains, consistently with their higher susceptibility to fluorine and zinc. Importantly, these properties are improved compared to synthetic fluorapatite, showing that the films are promising for antimicrobial applications.Lingula anatina seashell is an apatite-based shells, and naturally contains fluorine and zinc alongside an organic part (chitin). For the first time, we demonstrate that it has strong antibacterial properties, and that it can be used as nanostructured coatings for orthopaedics and dentistry
The Boundary State Formalism and Conformal Invariance in Off-shell String Theory
We present a generalization of the boundary state formalism for the bosonic
string that allows us to calculate the overlap of the boundary state with
arbitrary closed string states. We show that this generalization exactly
reproduces world-sheet sigma model calculations, thus giving the correct
overlap with both on- and off-shell string states, and that this new boundary
state automatically satisfies the requirement for integrated vertex operators
in the case of non-conformally invariant boundary interactions.Comment: 19 pages, 0 figure
Remarks on the Configuration Space Approach to Spin-Statistics
The angular momentum operators for a system of two spin-zero
indistinguishable particles are constructed, using Isham's Canonical Group
Quantization method. This mathematically rigorous method provides a hint at the
correct definition of (total) angular momentum operators, for arbitrary spin,
in a system of indistinguishable particles. The connection with other
configuration space approaches to spin-statistics is discussed, as well as the
relevance of the obtained results in view of a possible alternative proof of
the spin-statistics theorem.Comment: 18 page
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing
the inner product/Hilbert space for the Witten-Carlip holonomy formulation;
the proof of unitary equivalence of the metric and holonomy formulations is
then completed. Other additions include discussion of relation of canonical
and unitary transformations. Title/abstract change.
Classical phase space and statistical mechanics of identical particles
Starting from the quantum theory of identical particles, we show how to
define a classical mechanics that retains information about the quantum
statistics. We consider two examples of relevance for the quantum Hall effect:
identical particles in the lowest Landau level, and vortices in the
Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical}
statistical mechanics is shown to be a nontrivial classical limit of Haldane's
exclusion statistics.Comment: 40 pages, Late
- …