4,794 research outputs found
Positronium Spectroscopy in a Magnetic Field
Hyperfine spectroscopy of positronium formed in the presence of a static
magnetic field is considered. Generalising the situation hitherto developed in
the literature, the magnetic field is not assumed to be parallel to the
momentum of incoming polarised positrons, while the possibility of electron
polarisation is also included in the analysis. The results are of application
to high sensitivity positron polarimeters used in current decay
experiments.Comment: 17 pages (LateX file; no extra macros needed
Quantisation without Gauge Fixing: Avoiding Gribov Ambiguities through the Physical Projector
The quantisation of gauge invariant systems usually proceeds through some
gauge fixing procedure of one type or another. Typically for most cases, such
gauge fixings are plagued by Gribov ambiguities, while it is only for an
admissible gauge fixing that the correct dynamical description of the system is
represented, especially with regards to non perturbative phenomena. However,
any gauge fixing procedure whatsoever may be avoided altogether, by using
rather a recently proposed new approach based on the projection operator onto
physical gauge invariant states only, which is necessarily free on any such
issues. These different aspects of gauge invariant systems are explicitely
analysed within a solvable U(1) gauge invariant quantum mechanical model
related to the dimensional reduction of Yang-Mills theory.Comment: 22 pages, no figures, plain LaTeX fil
Solving Gauge Invariant Systems without Gauge Fixing: the Physical Projector in 0+1 Dimensional Theories
The projector onto gauge invariant physical states was recently constructed
for arbitrary constrained systems. This approach, which does not require gauge
fixing nor any additional degrees of freedom beyond the original ones---two
characteristic features of all other available methods for quantising
constrained dynamics---is put to work in the context of a general class of
quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge
groups are considered specifically, and a comprehensive understanding of the
corresponding physical spectra is achieved in a straightforward manner, using
only standard methods of coherent states and group theory which are directly
amenable to generalisation to other Lie algebras. Results extend by far the few
examples available in the literature from much more subtle and delicate
analyses implying gauge fixing and the characterization of modular space.Comment: 32 pages, LaTeX fil
Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings
It is shown that background fields of a topological character usually
introduced as such in compactified string theories correspond to quantum
degrees of freedom which parametrise the freedom in choosing a representation
of the zero mode quantum algebra in the presence of non-trivial topology. One
consequence would appear to be that the values of such quantum degrees of
freedom, in other words of the associated topological background fields, cannot
be determined by the nonperturbative string dynamics.Comment: 1+10 pages, no figure
Noncommuting Coordinates and Magnetic Monopoles
The appearance of noncommuting spatial coordinates is studied in quantum
systems containing a magnetic monopole and under the influence of a radial
potential. We derive expressions for the commutators of the coordinates that
have been restricted to the lowest energy level. Quantum corrections are found
to previous results by Frenkel and Pereira based on quantizing the Dirac
brackets of the classical theory. For two different potentials, the modified
harmonic oscillator potential and the modified Coulomb potential, we also
calculate the commutators for a projection to a fixed energy level.Comment: 8 pages, Late
Noncommutative Spherically Symmetric Spaces
We examine some noncommutative spherically symmetric spaces in three space
dimensions. A generalization of Snyder's noncommutative (Euclidean) space
allows the inclusion of the generator of dilations into the defining algebra of
the coordinate and rotation operators. We then construct a spherically
symmetric noncommutative Laplacian on this space having the correct limiting
spectrum. This is presented via a creation and annihilation operator
realization of the algebra, which may lend itself to a truncation of the
Hilbert space.Comment: 9 pages, revtex, matches Phys.Rev.D versio
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