223 research outputs found
The Dirac operator and gamma matrices for quantum Minkowski spaces
Gamma matrices for quantum Minkowski spaces are found. The invariance of the
corresponding Dirac operator is proven. We introduce momenta for spin 1/2
particles and get (in certain cases) formal solutions of the Dirac equation.Comment: 25 pages, LaTeX fil
Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
Coquasitriangular universal matrices on quantum Lorentz and
quantum Poincar\'e groups are classified. The results extend (under certain
assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on
those objects are described.Comment: 18 pages, LaTeX file, minor change
Representations of derived from quantum flag manifolds
A relationship between quantum flag and Grassmann manifolds is revealed. This
enables a formal diagonalization of quantum positive matrices. The requirement
that this diagonalization defines a homomorphism leads to a left \Uh -- module
structure on the algebra generated by quantum antiholomorphic coordinate
functions living on the flag manifold. The module is defined by prescribing the
action on the unit and then extending it to all polynomials using a quantum
version of Leibniz rule. Leibniz rule is shown to be induced by the dressing
transformation. For discrete values of parameters occuring in the
diagonalization one can extract finite-dimensional irreducible representations
of \Uh as cyclic submodules.Comment: LaTeX file, JMP (to appear
Quantum Chains with Symmetry
Usually quantum chains with quantum group symmetry are associated with
representations of quantized universal algebras . Here we propose a
method for constructing quantum chains with global symmetry , where
is the algebra of functions on the quantum group. In particular we
will construct a quantum chain with symmetry which interpolates
between two classical Ising chains.It is shown that the Hamiltonian of this
chain satisfies in the generalised braid group algebra.Comment: 7 pages,latex,this is the completely revised version of my paper
which is submitted for publicatio
Wigner-Eckart theorem for tensor operators of Hopf algebras
We prove Wigner-Eckart theorem for the irreducible tensor operators for
arbitrary Hopf algebras, provided that tensor product of their irreducible
representation is completely reducible. The proof is based on the properties of
the irreducible representations of Hopf algebras, in particular on Schur lemma.
Two classes of tensor operators for the Hopf algebra U(su(2)) are
considered. The reduced matrix elements for the class of irreducible tensor
operators are calculated. A construction of some elements of the center of
U(su(2)) is given.Comment: 14 pages, late
Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems
To provide tools, especially L-operators, for use in studies of rational
Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N)
(b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices,
this paper develops a presentation of these Lie algebras convenient for the
context, and derives many properties of the matrices of their defining
representations and of the ad-invariant tensors that enter their multiplication
laws. Metaplectic-type representations of sp(2n) and so(N) on bosonic and on
fermionic Fock spaces respectively are constructed. Concise general expressions
(see (5.2) and (5.5) below) for their L-operators are obtained, and used to
derive simple formulas for the T operators of the rational RTT algebra of the
associated integral systems, thereby enabling their efficient treatment by
means of the algebraic Bethe ansatz.Comment: 24 pages, LaTe
The Gell-Mann-Okubo and Colemann-Glashow relations for octet and decuplet baryons in the quantum algebra
The q-deformed Clebsch-Gordan coefficients corresponding to the
\lrpy{3}\times\lrpy{21} reduction of the quantum algebra are
computed. From these results and using the quantum Clebsch-Gordan coefficients
for the \lrpy{21}\times\lrpy{21} reduction found by Zhong Qi Ma, the
q-deformed Gell-Mann-Okubo mass relations for octet and decuplet baryons are
determined by generalizing the procedure used for the SU(3) algebra. We also
determine the Coleman-Glashow relations for octet and decuplet baryons in the
algebra. Finally, by using the experimental particle masses of the
octet and decuplet baryons, two values of the -parameter are found and
adjusted for the predicted masses expressions (one for the Gell-Mann-Okubo mass
relations and the other for the Coleman-Glashow relations) and a possible
physical interpretation is given.Comment: 19 pages, 4 figures. Corrected typo
Quantum Jacobi-Trudi and Giambelli Formulae for from Analytic Bethe Ansatz
Analytic Bethe ansatz is executed for a wide class of finite dimensional
modules. They are labeled by skew-Young diagrams which, in
general, contain a fragment corresponding to the spin representation. For the
transfer matrix spectra of the relevant vertex models, we establish a number of
formulae, which are analogues of the classical ones due to
Jacobi-Trudi and Giambelli on Schur functions. They yield a full solution to
the previously proposed functional relation (-system), which is a Toda
equationComment: Plain Tex(macro included), 18 pages. 7 figures are compressed and
attache
Representations of Super Yangian
We present in detail the classification of the finite dimensional irreducible
representations of the super Yangian associated with the Lie superalgebra
.Comment: 14 pages, plain latex, no figur
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