93 research outputs found
Integrability of Superconformal Field Theory and SUSY N=1 KdV
The quantum SUSY N=1 hierarchy based on twisted affine
superalgebra is considered. The construction of the corresponding Baxter's
Q-operators and fusion relations is outlined. The relation with the
superconformal field theory is discussed.Comment: LaTeX2e, cargese.cls, 4 pages, Subm. to String Theory: from Gauge
Interactions to Cosmology, NATO Advanced Study Institute, Proc. of Cargese
Summer School, NATO Science series C, 200
Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet
We consider a finite sub-chain on an interval of the infinite XXX model in
the ground state. The density matrix for such a subsystem was described in our
previous works for the model with inhomogeneous spectral parameters. In the
present paper, we give a compact formula for the physically interesting case of
the homogeneous model.Comment: 6 pages, some formulas are refine
Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral
Different analogs of quasiclassical limit for a q-oscillator which result in
different (commutative and non-commutative) algebras of ``classical''
observables are derived. In particular, this gives the q-deformed Poisson
brackets in terms of variables on the quantum planes. We consider the
Hamiltonian made of special combination of operators (the analog of even
operators in Grassmann algebra) and discuss q-path integrals constructed with
the help of contracted ``classical'' algebras.Comment: 19 pages, Late
On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
By invoking the concept of twisted Poincar\' e symmetry of the algebra of
functions on a Minkowski space-time, we demonstrate that the noncommutative
space-time with the commutation relations ,
where is a {\it constant} real antisymmetric matrix, can be
interpreted in a Lorentz-invariant way. The implications of the twisted
Poincar\'e symmetry on QFT on such a space-time is briefly discussed. The
presence of the twisted symmetry gives justification to all the previous
treatments within NC QFT using Lorentz invariant quantities and the
representations of the usual Poincar\'e symmetry.Comment: 12 pages, one reference adde
Coherent States in Null-Plane Q.E.D
Light front field theories are known to have the usual infra-red divergences
of the equal time theories, as wellas new `spurious' infra-red divergences. The
formar kind of IR divergences are usually treated by giving a small mass to the
gauge particle. An alternative method to deal with these divergences is to
calculate the transition matrix elements in a coherent state basis. In this
paper we present, as a model calculation the lowest order correction to the
three point vertex in QED using a coherent state basis in the light cone
formalism. The relevant transition matrix element is shown to be free of the
true IR divergences up to .Comment: 20 pages and two figures, REVTEX, ITP-SB-93-7
On the physical contents of q-deformed Minkowski spaces
Some physical aspects of -deformed spacetimes are discussed. It is pointed
out that, under certain standard assumptions relating deformation and
quantization, the classical limit (Poisson bracket description) of the dynamics
is bound to contain unusual features. At the same time, it is argued that the
formulation of an associated -deformed field theory is fraught with serious
difficulties.Comment: some changes mad
Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
There are two fundamental problems studied by the theory of hamiltonian
integrable systems: integration of equations of motion, and construction of
action-angle variables. The third problem, however, should be added to the
list: separation of variables. Though much simpler than two others, it has
important relations to the quantum integrability. Separation of variables is
constructed for the magnetic chain --- an example of integrable model
associated to a nonhyperelliptic algebraic curve.Comment: 13 page
Finite-dimensional representations of the quantum superalgebra and related q-identities
Explicit expressions for the generators of the quantum superalgebra
acting on a class of irreducible representations are given. The
class under consideration consists of all essentially typical representations:
for these a Gel'fand-Zetlin basis is known. The verification of the quantum
superalgebra relations to be satisfied is shown to reduce to a set of
-number identities.Comment: 12 page
Looking at the Haldane Conjecture from a Grouptheoretical Point of View
Based on the Lieb-Schultz-Mattis construction we present a five parameter
family of Spin-1 Hamiltonians with degenerate groundstate. Starting from the
critical symmetric Hamiltonian, we look for those perturbations of the
symmetry, which leave the groundstate degenerate. We also discuss the
spin-3/2 -case.Comment: 9 pages RevTex 3.
Determinant Representations of Correlation Functions for the Supersymmetric t-J Model
Working in the -basis provided by the factorizing -matrix, the scalar
products of Bethe states for the supersymmetric t-J model are represented by
determinants. By means of these results, we obtain determinant representations
of correlation functions for the model.Comment: Latex File, 41 pages, no figure; V2: minor typos corrected, V3: This
version will appear in Commun. Math. Phy
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