588 research outputs found
Hopf solitons and area preserving diffeomorphisms of the sphere
We consider a (3+1)-dimensional local field theory defined on the sphere. The
model possesses exact soliton solutions with non trivial Hopf topological
charges, and infinite number of local conserved currents. We show that the
Poisson bracket algebra of the corresponding charges is isomorphic to that of
the area preserving diffeomorphisms of the sphere. We also show that the
conserved currents under consideration are the Noether currents associated to
the invariance of the Lagrangian under that infinite group of diffeomorphisms.
We indicate possible generalizations of the model.Comment: 6 pages, LaTe
On Z-graded loop Lie algebras, loop groups, and Toda equations
Toda equations associated with twisted loop groups are considered. Such
equations are specified by Z-gradations of the corresponding twisted loop Lie
algebras. The classification of Toda equations related to twisted loop Lie
algebras with integrable Z-gradations is discussed.Comment: 24 pages, talk given at the Workshop "Classical and Quantum
Integrable Systems" (Dubna, January, 2007
Bose-Einstein correlations in thermal field theory
Two-particle correlation functions are calculated for bosons emitted from a
localized thermal source (the ``glow'' of a ``hot spot''). In contrast to
existing work, non-equilibrium effects up to first order in gradients of the
particle distribution function are taken into account. The spectral width of
the bosons is shown to be an important quantity: If it is too small, they do
not equilibrate locally and therefore strongly increase the measured
correlation radius. In memoriam of Eugene Wigner and Hiroomi Umezawa.Comment: Paper in LaTeX. Figures and complete paper available via anonymous
ftp, ftp://tpri6c.gsi.de/pub/phenning/hhbr9
Photon intensity interferometry of systems in local equilibrium
Using Quantum Field Theory we derive a general formula for the double inclusive spectra of photons radiated by a system in local equilibrium. The derived expression differs significantly from the one mostly used up to now in photon intensity interferometry of heavy--ion collisions. We present a covariant expression for double inclusive spectra adapted for usage in numerical simulations. Application to a schematic model with a Bj\o rken type expansion gives strong evidence for the need of reinvestigating of photon--photon correlations for expanding sources
Multidimensional Toda type systems
On the base of Lie algebraic and differential geometry methods, a wide class
of multidimensional nonlinear systems is obtained, and the integration scheme
for such equations is proposed.Comment: 29 pages, LaTeX fil
Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems
We associate to an arbitrary -gradation of the Lie algebra of a
Lie group a system of Riccati-type first order differential equations. The
particular cases under consideration are the ordinary Riccati and the matrix
Riccati equations. The multidimensional extension of these equations is given.
The generalisation of the associated Redheffer--Reid differential systems
appears in a natural way. The connection between the Toda systems and the
Riccati-type equations in lower and higher dimensions is established. Within
this context the integrability problem for those equations is studied. As an
illustration, some examples of the integrable multidimensional Riccati-type
equations related to the maximally nonabelian Toda systems are given.Comment: LaTeX2e, 18 page
A staggered fermion chain with supersymmetry on open intervals
A strongly-interacting fermion chain with supersymmetry on the lattice and
open boundary conditions is analysed. The local coupling constants of the model
are staggered, and the properties of the ground states as a function of the
staggering parameter are examined. In particular, a connection between certain
ground-state components and solutions of non-linear recursion relations
associated with the Painlev\'e VI equation is conjectured. Moreover, various
local occupation probabilities in the ground state have the so-called
scale-free property, and allow for an exact resummation in the limit of
infinite system size.Comment: 21 pages, no figures; v2: typos correcte
Ground-state properties of a supersymmetric fermion chain
We analyze the ground state of a strongly interacting fermion chain with a
supersymmetry. We conjecture a number of exact results, such as a hidden
duality between weak and strong couplings. By exploiting a scale free property
of the perturbative expansions, we find exact expressions for the order
parameters, yielding the critical exponents. We show that the ground state of
this fermion chain and another model in the same universality class, the XYZ
chain along a line of couplings, are both written in terms of the same
polynomials. We demonstrate this explicitly for up to N = 24 sites, and provide
consistency checks for large N. These polynomials satisfy a recursion relation
related to the Painlev\'e VI differential equation, and using a scale-free
property of these polynomials, we derive a simple and exact formula for their
limit as N goes to infinity.Comment: v2: added more information on scaling function, fixed typo
Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices
The integrable loop model with mixed boundary conditions based on the
1-boundary extended Temperley--Lieb algebra with loop weight 1 is considered.
The corresponding qKZ equation is introduced and its minimal degree solution
described. As a result, the sum of the properly normalized components of the
ground state in size L is computed and shown to be equal to the number of
Horizontally and Vertically Symmetric Alternating Sign Matrices of size 2L+3. A
refined counting is also considered
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