76 research outputs found
Topological Dilatonic Supergravity Theories
We present a central extension of the super-Poincar\'e algebra in two
dimensions. Besides the usual Poincar\'e generators and the
supersymmetry generators we have Grassmann generators, a bosonic
internal symmetry generator and a central charge. We then build up the
topological gauge theory associated to this algebra. We can solve the classical
field equations for the fields which do not belong to the supergravity
multiplet and to a Lagrange multiplier multiplet. The resulting topological
supergravity theory turns out to be non-local in the fermionic sector.Comment: 11 pages, plain TeX, IFUSP-P/112
The spin-statistics connection in classical field theory
The spin-statistics connection is obtained for a simple formulation of a
classical field theory containing even and odd Grassmann variables. To that
end, the construction of irreducible canonical realizations of the rotation
group corresponding to general causal fields is reviewed. The connection is
obtained by imposing local commutativity on the fields and exploiting the
parity operation to exchange spatial coordinates in the scalar product of
classical field evaluated at one spatial location with the same field evaluated
at a distinct location. The spin-statistics connection for irreducible
canonical realizations of the Poincar\'{e} group of spin is obtained in the
form: Classical fields and their conjugate momenta satisfy fundamental
field-theoretic Poisson bracket relations for 2 even, and fundamental
Poisson antibracket relations for 2 oddComment: 27 pages. Typos and sign error corrected; minor revisions to tex
Projective representation of k-Galilei group
The projective representations of k-Galilei group G_k are found by
contracting the relevant representations of k-Poincare group. The projective
multiplier is found. It is shown that it is not possible to replace the
projective representations of G_k by vector representations of some its
extension.Comment: 15 pages Latex fil
Single Boson Images Via an Extended Holstein Primakoff Mapping
The Holstein-Primakoff mapping for pairs of bosons is extended in order to
accommodate single boson mapping. The proposed extension allows a variety of
applications and especially puts the formalism at finite temperature on firm
grounds. The new mapping is applied to the O(N+1) anharmonic oscillator with
global symmetry broken down to O(N). It is explicitly demonstrated that
N-Goldstone modes appear. This result generalizes the Holstein-Primakoff
mapping for interacting boson as developed in ref.[1].Comment: 9 pages, LaTeX. Physical content unchanged. Unnecessary figure
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Interpolating Coherent States for Heisenberg-Weyl and Single-Photon SU(1,1) Algebras
New quantal states which interpolate between the coherent states of the
Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states
are obtained as the coherent states of a closed and symmetric algebra which
interpolates between the two algebras. The overcompleteness of the
interpolating coherent states is established. Differential operator
representations in suitable spaces of entire functions are given for the
generators of the algebra. A nonsymmetric set of operators to realize the
Heisenberg-Weyl algebra is provided and the relevant coherent states are
studied.Comment: 13 pages nd 5 ps figure
Graded Contractions of Affine Kac-Moody Algebras
The method of graded contractions, based on the preservation of the
automorphisms of finite order, is applied to the affine Kac-Moody algebras and
their representations, to yield a new class of infinite dimensional Lie
algebras and representations. After the introduction of the horizontal and
vertical gradings, and the algorithm to find the horizontal toroidal gradings,
I discuss some general properties of the graded contractions, and compare them
with the In\"on\"u-Wigner contractions. The example of is discussed
in detail.Comment: 23 pages, Ams-Te
Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras
A family of deformed Hopf algebras corresponding to the classical maximal
isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous
algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to
have a bicrossproduct structure. This is done for both the algebra and, in a
low-dimensional example, for the (dual) group aspects of the deformation.Comment: LaTeX file, 20 pages. Trivial changes. To appear in J. Phys.
Supergroup approach to the Hubbard model
Based on the revealed hidden supergroup structure, we develop a new approach
to the Hubbard model. We reveal a relation of even Hubbard operators to the
spinor representation of the generators of the rotation group of
four-dimensional spaces. We propose a procedure for constructing a matrix
representation of translation generators, yielding a curved space on which
dynamic superfields are defined. We construct a new deformed nonlinear
superalgebra for the regime of spinless Hubbard model fermions in the case of
large on-site repulsion and evaluate the effective functional for spinless
fermions.Comment: 17 pages, Theoretical and Mathematical Physics, V.166, n.2,
p.209-222,201
Expansions of algebras and superalgebras and some applications
After reviewing the three well-known methods to obtain Lie algebras and
superalgebras from given ones, namely, contractions, deformations and
extensions, we describe a fourth method recently introduced, the expansion of
Lie (super)algebras. Expanded (super)algebras have, in general, larger
dimensions than the original algebra, but also include the Inonu-Wigner and
generalized IW contractions as a particular case. As an example of a physical
application of expansions, we discuss the relation between the possible
underlying gauge symmetry of eleven-dimensional supergravity and the
superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in
Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches
Forschungsinstitut Oberwolfach, German
Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of
non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras.
We prove that every contracted QUEA in a certain class is a cochain twist of
the corresponding undeformed universal envelope. Consequently, these contracted
QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we
consider kappa-Poincare in 3 and 4 spacetime dimensions.Comment: 32 page
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