956 research outputs found
A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula
We provide yet another proof of the classical Lagrange-Good multivariable
inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram
Atypical Representations of at Roots of Unity
We show how to adapt the Gelfand-Zetlin basis for describing the atypical
representation of when is root of
unity. The explicit construction of atypical representation is presented in
details for .Comment: 18 pages, Tex-file and 2 figures. Uuencoded, compressed and tared
archive of plain tex file and postscript figure file. Upon uudecoding,
uncompressing and taring, tex the file atypique.te
On Auxiliary Fields in BF Theories
We discuss the structure of auxiliary fields for non-Abelian BF theories in
arbitrary dimensions. By modifying the classical BRST operator, we build the
on-shell invariant complete quantum action. Therefore, we introduce the
auxiliary fields which close the BRST algebra and lead to the invariant
extension of the classical action.Comment: 7 pages, minor changes, typos in equations corrected and
acknowledgements adde
Analyticity of The Ground State Energy For Massless Nelson Models
We show that the ground state energy of the translationally invariant Nelson
model, describing a particle coupled to a relativistic field of massless
bosons, is an analytic function of the coupling constant and the total
momentum. We derive an explicit expression for the ground state energy which is
used to determine the effective mass.Comment: 33 pages, 1 figure, added a section on the calculation of the
effective mas
Deformations of the fermion realization of the sp(4) algebra and its subalgebras
With a view towards future applications in nuclear physics, the fermion
realization of the compact symplectic sp(4) algebra and its q-deformed versions
are investigated. Three important reduction chains of the sp(4) algebra are
explored in both the classical and deformed cases. The deformed realizations
are based on distinct deformations of the fermion creation and annihilation
operators. For the primary reduction, the su(2) sub-structure can be
interpreted as either the spin, isospin or angular momentum algebra, whereas
for the other two reductions su(2) can be associated with pairing between
fermions of the same type or pairing between two distinct fermion types. Each
reduction provides for a complete classification of the basis states. The
deformed induced u(2) representations are reducible in the action spaces of
sp(4) and are decomposed into irreducible representations.Comment: 28 pages, LaTeX 12pt article styl
General Gauss-Bonnet brane cosmology
We consider 5-dimensional spacetimes of constant 3-dimensional spatial
curvature in the presence of a bulk cosmological constant. We find the general
solution of such a configuration in the presence of a Gauss-Bonnet term. Two
classes of non-trivial bulk solutions are found. The first class is valid only
under a fine tuning relation between the Gauss-Bonnet coupling constant and the
cosmological constant of the bulk spacetime. The second class of solutions are
static and are the extensions of the AdS-Schwarzchild black holes. Hence in the
absence of a cosmological constant or if the fine tuning relation is not true,
the generalised Birkhoff's staticity theorem holds even in the presence of
Gauss-Bonnet curvature terms. We examine the consequences in brane world
cosmology obtaining the generalised Friedmann equations for a perfect fluid
3-brane and discuss how this modifies the usual scenario.Comment: 20 pages, no figures, typos corrected, refs added, section IV changed
yielding novel result
Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications
A multi-shell generalization of a fermion representation of the q-deformed
compact symplectic sp_q(4) algebra is introduced. An analytic form for the
action of two or more generators of the Sp_q(4) symmetry on the basis states is
determined and the result used to derive formulae for the overlap between
number preserving states as well as for matrix elements of a model Hamiltonian.
A second-order operator in the generators of Sp_q(4) is identified that is
diagonal in the basis set and that reduces to the Casimir invariant of the
sp(4) algebra in the non-deformed limit of the theory. The results can be used
in nuclear structure applications to calculate beta-decay transition
probabilities and to provide for a description of pairing and higher-order
interactions in systems with nucleons occupying more than a single-j orbital.Comment: 10 page
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index
{Let be a -dimensional fractional Brownian motion
with Hurst index , or more generally a Gaussian process whose paths
have the same local regularity. Defining properly iterated integrals of is
a difficult task because of the low H\"older regularity index of its paths. Yet
rough path theory shows it is the key to the construction of a stochastic
calculus with respect to , or to solving differential equations driven by
.
We intend to show in a series of papers how to desingularize iterated
integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure
defined by a limit in law procedure. Convergence is proved by using "standard"
tools of constructive field theory, in particular cluster expansions and
renormalization. These powerful tools allow optimal estimates, and call for an
extension of Gaussian tools such as for instance the Malliavin calculus.
After a first introductory paper \cite{MagUnt1}, this one concentrates on the
details of the constructive proof of convergence for second-order iterated
integrals, also known as L\'evy area
Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
Multiparametric quantum deformations of are studied through a
complete classification of Lie bialgebra structures. From them, the
non-relativistic limit leading to harmonic oscillator Lie bialgebras is
implemented by means of a contraction procedure. New quantum deformations of
together with their associated quantum -matrices are obtained and
other known quantizations are recovered and classified. Several connections
with integrable models are outlined.Comment: 21 pages, LaTeX. To appear in J. Phys. A. New contents adde
On realizations of nonlinear Lie algebras by differential operators
We study realizations of polynomial deformations of the sl(2,R)- Lie algebra
in terms of differential operators strongly related to bosonic operators. We
also distinguish their finite- and infinite-dimensional representations. The
linear, quadratic and cubic cases are explicitly visited but the method works
for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are
studied in the context of these ``nonlinear'' Lie algebras and some examples
dealing with quantum optics are pointed out.Comment: 21 pages, Latex; New examples added in Sect.
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