48 research outputs found
Type II vertex operators for the face model
Presented is a free boson representation of the type II vertex operators for
the face model. Using the bosonization, we derive some
properties of the type II vertex operators, such as commutation, inversion and
duality relations.Comment: 20 pages, LaTEX 2
The SU(n) invariant massive Thirring model with boundary reflection
We study the SU(n) invariant massive Thirring model with boundary reflection.
Our approach is based on the free field approach. We construct the free field
realizations of the boundary state and its dual. For an application of these
realizations, we present integral representations for the form factors of the
local operators.Comment: LaTEX2e file, 27 page
Vertex operator approach to semi-infinite spin chain : recent progress
Vertex operator approach is a powerful method to study exactly solvable
models. We review recent progress of vertex operator approach to semi-infinite
spin chain. (1) The first progress is a generalization of boundary condition.
We study spin chain with a triangular boundary, which
gives a generalization of diagonal boundary [Baseilhac and Belliard 2013,
Baseilhac and Kojima 2014]. We give a bosonization of the boundary vacuum
state. As an application, we derive a summation formulae of boundary
magnetization. (2) The second progress is a generalization of hidden symmetry.
We study supersymmetry spin chain with a diagonal
boundary [Kojima 2013]. By now we have studied spin chain with a boundary,
associated with symmetry , and
[Furutsu-Kojima 2000, Yang-Zhang 2001, Kojima 2011,
Miwa-Weston 1997, Kojima 2011], where bosonizations of vertex operators are
realized by "monomial" . However the vertex operator for
is realized by "sum", a bosonization of boundary
vacuum state is realized by "monomial".Comment: Proceedings of 10-th Lie Theory and its Applications in Physics,
LaTEX, 10 page
Difference equations for the higher rank XXZ model with a boundary
The higher rank analogue of the XXZ model with a boundary is considered on
the basis of the vertex operator approach. We derive difference equations of
the quantum Knizhnik-Zamolodchikov type for 2N-point correlations of the model.
We present infinite product formulae of two point functions with free boundary
condition by solving those difference equations with N=1.Comment: LaTEX 16 page
Diagonalization of infinite transfer matrix of boundary face model
We study infinitely many commuting operators , which we call infinite
transfer matrix of boundary face model. We diagonalize
infinite transfer matrix by using free field realizations of the
vertex operators of the elliptic quantum group .Comment: 36 pages, Dedicated to Professor Etsuro Date on the occassion of the
60th birthda
Vertex operator approach for form factors of Belavin's -symmetric model
Belavin's -symmetric model is considered on the
basis of bosonization of vertex operators in the model and
vertex-face transformation. Free field representations of nonlocal tail
operators are constructed for off diagonal matrix elements with respect to the
ground state sectors. As a result, integral formulae for form factors of any
local operators in the -symmetric model can be
obtained, in principle.Comment: 24 pages, 4 figures, published in J. Phys. A: Math. Theor. 43 (2010)
085202. For the next thirty days from Feb 5 2010, the full text of the
article will be completely free to access through our 'This Month's Papers'
service (www.iop.org/journals/thismonth), helping you to benefit from maximum
visibilit
-analog of the XXZ chain with a boundary
We study analog of the XXZ spin chain with a boundary
magnetic field h. We construct explicit bosonic formulas of the vacuum vector
and the dual vacuum vector with a boundary magnetic field. We derive integral
formulas of the correlation functions.Comment: 24 pages, LaTEX2
Free field approach to diagonalization of boundary transfer matrix : recent advances
We diagonalize infinitely many commuting operators . We call these
operators the boundary transfer matrix associated with the quantum
group and the elliptic quantum group. The boundary transfer matrix is related
to the solvable model with a boundary. When we diagonalize the boundary
transfer matrix, we can calculate the correlation functions for the solvable
model with a boundary. We review the free field approach to diagonalization of
the boundary transfer matrix associated with and
. We construct the free field realizations of the
eigenvectors of the boundary transfer matrix . This paper includes new
unpublished formula of the eigenvector for . It is thought that
this diagonalization method can be extended to more general quantum group
and elliptic quantum group .Comment: To appear in Group 28 : Group Theoretical Method in Physic
Elliptic Deformed Superalgebra
We introduce the elliptic superalgebra as one
parameter deformation of the quantum superalgebra . For an
arbitrary level we give the bosonization of the elliptic
superalgebra and the screening currents that commute
with modulo total difference.Comment: LaTEX, 25 page
Unitary representations of nilpotent super Lie groups
We show that irreducible unitary representations of nilpotent super Lie
groups can be obtained by induction from a distinguished class of sub super Lie
groups. These sub super Lie groups are natural analogues of polarizing
subgroups that appear in classical Kirillov theory. We obtain a concrete
geometric parametrization of irreducible unitary representations by nonnegative
definite coadjoint orbits. As an application, we prove an analytic
generalization of the Stone-von Neumann theorem for Heisenberg-Clifford super
Lie groups