7,972 research outputs found
Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics
Symmetries in quantum mechanics are realized by the projective
representations of the Lie group as physical states are defined only up to a
phase. A cornerstone theorem shows that these representations are equivalent to
the unitary representations of the central extension of the group. The
formulation of the inertial states of special relativistic quantum mechanics as
the projective representations of the inhomogeneous Lorentz group, and its
nonrelativistic limit in terms of the Galilei group, are fundamental examples.
Interestingly, neither of these symmetries includes the Weyl-Heisenberg group;
the hermitian representations of its algebra are the Heisenberg commutation
relations that are a foundation of quantum mechanics. The Weyl-Heisenberg group
is a one dimensional central extension of the abelian group and its unitary
representations are therefore a particular projective representation of the
abelian group of translations on phase space. A theorem involving the
automorphism group shows that the maximal symmetry that leaves invariant the
Heisenberg commutation relations are essentially projective representations of
the inhomogeneous symplectic group. In the nonrelativistic domain, we must also
have invariance of Newtonian time. This reduces the symmetry group to the
inhomogeneous Hamilton group that is a local noninertial symmetry of Hamilton's
equations. The projective representations of these groups are calculated using
the Mackey theorems for the general case of a nonabelian normal subgroup
Covariant spinor representation of and quantization of the spinning relativistic particle
A covariant spinor representation of is constructed for the
quantization of the spinning relativistic particle. It is found that, with
appropriately defined wavefunctions, this representation can be identified with
the state space arising from the canonical extended BFV-BRST quantization of
the spinning particle with admissible gauge fixing conditions after a
contraction procedure. For this model, the cohomological determination of
physical states can thus be obtained purely from the representation theory of
the algebra.Comment: Updated version with references included and covariant form of
equation 1. 23 pages, no figure
A class of quadratic deformations of Lie superalgebras
We study certain Z_2-graded, finite-dimensional polynomial algebras of degree
2 which are a special class of deformations of Lie superalgebras, which we call
quadratic Lie superalgebras. Starting from the formal definition, we discuss
the generalised Jacobi relations in the context of the Koszul property, and
give a proof of the PBW basis theorem. We give several concrete examples of
quadratic Lie superalgebras for low dimensional cases, and discuss aspects of
their structure constants for the `type I' class. We derive the equivalent of
the Kac module construction for typical and atypical modules, and a related
direct construction of irreducible modules due to Gould. We investigate in
detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie
superalgebra sl(n/1). We formulate the general atypicality conditions at level
1, and present an analysis of zero-and one-step atypical modules for a certain
family of Kac modules.Comment: 26pp, LaTeX. Original title: "Finite dimensional quadratic Lie
superalgebras"; abstract re-worded; text clarified; 3 references added;
rearrangement of minor appendices into text; new subsection 4.
A Selected Ion Flow Tube Study of the Reactions of Several Cations with the Group 6B Hexafluorides SF6, SeF6, and TeF6
The first investigation of the ion chemistry of SeF and TeF is presented. Using a selected ion flow tube, the thermal rate coefficients and ion product distributions have been determined at 300 K for the reactions of fourteen atomic and molecular cations, namely HO, CF, CF, CF, HO, NO, O, CO, CO, N, N, Ar, F and Ne (in order of increasing recombination energy), with SeF and TeF. The results are compared with those from the reactions of these ions with SF, for which the reactions with CF, CF, NO and F are reported for the first time. Several distinct processes are observed amongst the large number of reactions studied, including dissociative charge transfer, and F, F, F and F abstraction from the neutral reactant molecule to the reagent ion. The dissociative charge transfer channels are discussed in relation to vacuum ultraviolet photoelectron and threshold photoelectron-photoion coincidence spectra of XF (X = S, Se, and Te). For reagent ions whose recombination energies lie between the first dissociative ionisation limit, XF XF + F + e, and the onset of ionisation of the XF molecule, the results suggest that if dissociative charge transfer occurs, it proceeds via an intimate encounter. For those reagent ions whose recombination energies are greater than the onset of ionisation, long-range electron transfer may occur depending on whether certain physical factors apply, for example non-zero Franck-Condon overlap. From the reaction kinetics, limits for the heats of formation of SeF, SeF, TeF and TeF at 298 K have been obtained; H(SeF) < -369 kJ mol, H(SeF) < -621 kJ mol, H(TeF) > -570 kJ mol, and H(TeF) < -822 kJ mol
On the Structure of the Observable Algebra of QCD on the Lattice
The structure of the observable algebra of lattice
QCD in the Hamiltonian approach is investigated. As was shown earlier,
is isomorphic to the tensor product of a gluonic
-subalgebra, built from gauge fields and a hadronic subalgebra
constructed from gauge invariant combinations of quark fields. The gluonic
component is isomorphic to a standard CCR algebra over the group manifold
SU(3). The structure of the hadronic part, as presented in terms of a number of
generators and relations, is studied in detail. It is shown that its
irreducible representations are classified by triality. Using this, it is
proved that the hadronic algebra is isomorphic to the commutant of the triality
operator in the enveloping algebra of the Lie super algebra
(factorized by a certain ideal).Comment: 33 page
On Combining Lensing Shear Information from Multiple Filters
We consider the possible gain in the measurement of lensing shear from
imaging data in multiple filters. Galaxy shapes may differ significantly across
filters, so that the same galaxy offers multiple samples of the shear. On the
other extreme, if galaxy shapes are identical in different filters, one can
combine them to improve the signal-to-noise and thus increase the effective
number density of faint, high redshift galaxies. We use the GOODS dataset to
test these scenarios by calculating the covariance matrix of galaxy
ellipticities in four visual filters (B,V,i,z). We find that galaxy shapes are
highly correlated, and estimate the gain in galaxy number density by combining
their shapes.Comment: 8 pages, no figures, submitted to JCA
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