Commutation Relations of Vertex Operators Related with the Spin Representation of U Q (d
نویسنده
چکیده
A new scheme to study the XXZ spin chain in massive regime is introduced by Davies et al in [1]. In this scheme, which is called “quantum symmetry approach”, the space of states is identified with some Uq(A (1) 1 )-module. Under this identification, the XXZ Hamiltonian can be constructed on this module as an operator which commutes with the action of Uq(A (1) 1 ). Furthermore, the row transfer matrix and creation (annihilation) operators can be constructed by using vertex operators. In a similar way to [1], the higher spin chain [2] and the models related to the vector representation of Uq(A (1) n ) [3], Uq(B (1) n ), Uq(D (1) n ) [5] are studied. In this paper, we consider the model related with the spin representation of Uq(D (1) n ). In physics the model that we consider here is explained as follows. It is a one dimensional quantum spin chain model constructed from the spin representation of Uq(D (1) n ). The Hamiltonian acts on the space of the infinite tensor product
منابع مشابه
-vertex Model: Creation Algebras and Quasi-particles I
The infinite configuration space of an integrable vertex model based on Uq gl(2|2) 1 is studied at q = 0. Allowing four particular boundary conditions, the infinite configurations are mapped onto the semi-standard supertableaux of pairs of infinite border strips. By means of this map, a weight-preserving one-to-one correspondence between the infinite configurations and the normal forms of a pai...
متن کاملOn the Fock representation of the q-commutation relations
We consider the C*-algebraRq generated by the representation of the q-commutation relations on the twisted Fock space. We construct a canonical unitary U (= U(q)) from the twisted Fock space to the usual Fock space, such that URqU∗ contains the extended Cuntz algebra R0, for all q ∈ (−1, 1). We prove the equality URqU∗ = R0 for q satisfying: q < 1− 2|q|+ 2|q| − 2|q| + · · ·+ 2(−1)k|q|k2 + · · ·...
متن کاملStructure of the space of states in RSOS models
The restricted solid-on-solid models in the anti-ferromagnetic regime is studied in the framework of quantum affine algebras. Following the line developed recently for vertex models, a representation theoretical picture is presented for the structure of the space of states. The local operators and the creation/annihilation operators of quasi-particles are defined using vertex operators, and the...
متن کاملEdge pair sum labeling of some cycle related graphs
Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...
متن کاملThe U(1)-invariant Field Theories with Normal Field Operators
In this paper we consider a very general U(1)-invariant field theory such that a field operator commutes with its adjoint, what corresponds to a theory of a charged bosonic particle. We show that from such an invariance follows the existence of particles and antiparticles associated to the same physical state. The field operator always turns out to be a sum of a particle creation and an antipar...
متن کامل