19 research outputs found
Learning from Julius' star, *,
While collecting some personal memories about Julius Wess, I briefly describe
some aspects of my recent work on many particle quantum mechanics and second
quantization on noncommutative spaces obtained by twisting, and their
connection to him.Comment: Late2e file 13 pages. To appear in the Proceedings of the Workshop
"Scientific and Human Legacy of Julius Wess - JW2011", Donji Milanovac
(Serbia), August 27-29, 2011, International Journal of Modern Physics:
Conference Series. On-line at:
http://www.worldscientific.com/toc/ijmpcs/13/0
Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces
We introduce a new class of sine-Gordon models, for which interaction term is
present in a region different from the domain over which quadratic part is
defined. We develop a novel non-perturbative approach for calculating partition
functions of such models, which relies on mapping them to statistical
properties of random surfaces. As a specific application of our method, we
consider the problem of calculating the amplitude of interference fringes in
experiments with two independent low dimensional Bose gases. We calculate full
distribution functions of interference amplitude for 1D and 2D gases with
nonzero temperatures.Comment: final published versio
Band-Insulator-Metal-Mott-Insulator transition in the half--filled ionic-Hubbard chain
We investigate the ground state phase diagram of the half-filled
repulsive Hubbard model in the presence of a staggered ionic
potential , using the continuum-limit bosonization approach. We find,
that with increasing on-site-repulsion , depending on the value of the
next-nearest-hopping amplitude , the model shows three different
versions of the ground state phase diagram. For , the ground state phase diagram consists of the following
three insulating phases: Band-Insulator at , Ferroelectric Insulator
at . For
there is only one transition from a spin gapped
metallic phase at .
Finally, for intermediate values of the next-nearest-hopping amplitude
we find that with increasing
on-site repulsion, at the model undergoes a second-order
commensurate-incommensurate type transition from a band insulator into a
metallic state and at larger there is a Kosterlitz-Thouless type
transition from a metal into a ferroelectric insulator.Comment: 9 pages 3 figure
On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
We explore some general consequences of a proper, full enforcement of the
"twisted Poincare'" covariance of Chaichian et al. [14], Wess [50], Koch et al.
[34], Oeckl [41] upon many-particle quantum mechanics and field quantization on
a Moyal-Weyl noncommutative space(time). This entails the associated braided
tensor product with an involutive braiding (or -tensor product in the
parlance of Aschieri et al. [3,4]) prescription for any coordinates pair of
generating two different copies of the space(time); the associated
nontrivial commutation relations between them imply that is central and
its Poincar\'e transformation properties remain undeformed. As a consequence,
in QFT (even with space-time noncommutativity) one can reproduce notions (like
space-like separation, time- and normal-ordering, Wightman or Green's
functions, etc), impose constraints (Wightman axioms), and construct free or
interacting theories which essentially coincide with the undeformed ones, since
the only observable quantities involve coordinate differences. In other words,
one may thus well realize QM and QFT's where the effect of space(time)
noncommutativity amounts to a practically unobservable common noncommutative
translation of all reference frames.Comment: Latex file, 24 pages. Final version to appear in PR
A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
We make contact between the infinite-dimensional non-local symmetry of the
typeIIB superstring on AdS5xS5 worldsheet theory and a non-abelian
infinite-dimensional symmetry algebra for the weakly coupled superconformal
gauge theory. We explain why the planar limit of the one-loop dilatation
operator is the Hamiltonian of a spin chain, and show that it commutes with the
g*2 N = 0 limit of the non-abelian charges.Comment: 19 pages, harvma
The arctic curve of the domain-wall six-vertex model
The problem of the form of the `arctic' curve of the six-vertex model with
domain wall boundary conditions in its disordered regime is addressed. It is
well-known that in the scaling limit the model exhibits phase-separation, with
regions of order and disorder sharply separated by a smooth curve, called the
arctic curve. To find this curve, we study a multiple integral representation
for the emptiness formation probability, a correlation function devised to
detect spatial transition from order to disorder. We conjecture that the arctic
curve, for arbitrary choice of the vertex weights, can be characterized by the
condition of condensation of almost all roots of the corresponding saddle-point
equations at the same, known, value. In explicit calculations we restrict to
the disordered regime for which we have been able to compute the scaling limit
of certain generating function entering the saddle-point equations. The arctic
curve is obtained in parametric form and appears to be a non-algebraic curve in
general; it turns into an algebraic one in the so-called root-of-unity cases.
The arctic curve is also discussed in application to the limit shape of
-enumerated (with ) large alternating sign matrices. In
particular, as the limit shape tends to a nontrivial limiting curve,
given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction
On second quantization on noncommutative spaces with twisted symmetries
By application of the general twist-induced star-deformation procedure we
translate second quantization of a system of bosons/fermions on a symmetric
spacetime in a non-commutative language. The procedure deforms in a coordinated
way the spacetime algebra and its symmetries, the wave-mechanical description
of a system of n bosons/fermions, the algebra of creation and annihilation
operators and also the commutation relations of the latter with functions of
spacetime; our key requirement is the mode-decomposition independence of the
quantum field. In a conservative view, the use of noncommutative coordinates
can be seen just as a way to better express non-local interactions of a special
kind. In a non-conservative one, we obtain a covariant framework for QFT on the
corresponding noncommutative spacetime consistent with quantum mechanical
axioms and Bose-Fermi statistics. One distinguishing feature is that the field
commutation relations remain of the type "field (anti)commutator=a
distribution". We illustrate the results by choosing as examples interacting
non-relativistic and free relativistic QFT on Moyal space(time)s.Comment: Latex file, 45 pages. I have corrected a small typo present in 3
points of the previous version and in the version published also in JPA
(which had occurred via late careless serial replacements, with no
consequences on the results of the calculations): has
been corrected into $\beta^*=S(\beta^{-1})