108 research outputs found
Nonstandard coproducts and the Izergin-Korepin open spin chain
Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three
diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using
these R and K matrices, one can construct transfer matrices for open integrable
quantum spin chains. The transfer matrix corresponding to the identity matrix
K=1 is known to have U_q(o(3)) symmetry. We argue here that the transfer
matrices corresponding to the other two K matrices also have U_q(o(3))
symmetry, but with a nonstandard coproduct. We briefly explore some of the
consequences of this symmetry.Comment: 7 pages, LaTeX; v2 has one additional sentence on the degeneracy
patter
Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
The general solutions for the factorization equations of the reflection
matrices for the eight vertex and six vertex models (XYZ, XXZ
and XXX chains) are found. The associated integrable magnetic Hamiltonians are
explicitly derived, finding families dependig on several continuous as well as
discrete parameters.Comment: 13 page
Simplified Calculation of Boundary S Matrices
The antiferromagnetic Heisenberg spin chain with N spins has a sector with
N=odd, in which the number of excitations is odd. In particular, there is a
state with a single one-particle excitation. We exploit this fact to give a
simplified derivation of the boundary S matrix for the open antiferromagnetic
spin-1/2 Heisenberg spin chain with diagonal boundary magnetic fields.Comment: 8 pages, LaTeX, no figure
Berry's phase in noncommutative spaces
We introduce the perturbative aspects of noncommutative quantum mechanics.
Then we study the Berry's phase in the framework of noncommutative quantum
mechanics. The results show deviations from the usual quantum mechanics which
depend on the parameter of space/space noncommtativity.Comment: 7 pages, no figur
Classification of reflection matrices related to (super) Yangians and application to open spin chain models
We present a classification of diagonal, antidiagonal and mixed reflection
matrices related to Yangian and super-Yangian R matrices associated to the
infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe
Ansatz resolution for the so(m) and sp(n) open spin chains with boundary
conditions described by the diagonal solutions.Comment: 36 pages ; references added ; typos corrected, precisions adde
Space of State Vectors in PT Symmetrical Quantum Mechanics
Space of states of PT symmetrical quantum mechanics is examined. Requirement
that eigenstates with different eigenvalues must be orthogonal leads to the
conclusion that eigenfunctions belong to the space with an indefinite metric.
The self consistent expressions for the probability amplitude and average value
of operator are suggested. Further specification of space of state vectors
yield the superselection rule, redefining notion of the superposition
principle. The expression for the probability current density, satisfying
equation of continuity and vanishing for the bound state, is proposed.Comment: Revised version, explicit expressions for average values and
probability amplitude adde
Eigenvalues of PT-symmetric oscillators with polynomial potentials
We study the eigenvalue problem
with the boundary
conditions that decays to zero as tends to infinity along the rays
, where is a polynomial and integers . We provide an
asymptotic expansion of the eigenvalues as , and prove
that for each {\it real} polynomial , the eigenvalues are all real and
positive, with only finitely many exceptions.Comment: 23 pages, 1 figure. v2: equation (14) as well as a few subsequent
equations has been changed. v3: typos correcte
On the equivalence between real and superfield 5d formalisms
We explicitly prove the equivalence and construct a dictionary between two
different supersymmetric formalisms for five-dimensional theories commonly used
in the literature. One is the real formalism, which consists in doubling the
number of degrees of freedom and then imposing reality constraints and the
other is the usual superfield formalism.Comment: 19 page
Soft breaking of two-loop finite N = 1 supersymmetric gauge theories
The effect of soft supersymmetry-breaking terms on one-loop finite N = 1 supersymmetric gauge theories is investigated, and the general conditions that finiteness be preserved given. Particular attention is paid to the kinds of breakings which arise in low energy supergravity models, and it is shown that in this case the susy-breaking gaugino and scalar masses and cubic scalar interactions are related.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24636/1/0000047.pd
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