Plenary Talks
Titles and Abstracts
Syed Twareque Ali (Concordia University, Canada)
Title: An overview of coherent states and coherent state quantization
Abstract: This talk will attempt to present an overview of the mathematical theory of
coherent states and coherent state quantization, emphasizing the role of group theory.
Some newer developments, involving coherent states on C*-Hilbert modules and
quaternionic Hilbert spaces will also be discussed. Coherent states feature in many
areas of quantum physics and mathematics. The emphasis in this talk will be more on
the mathematical aspects, with some mention of the historical physical backdrop.
Akito Arima (Shizuoka University of Art and Culture, Japan and Musashi Gakuen,
Japan)
Title: Dynamical Symmetries and Algebraic Methods in Nuclear Structure Physics
Abstract: Dynamical symmetries found in the nuclear structure physics are discussed.
Based on these symmetries, several algebraic methods are explained and shown how
powerful they are in order to predict nuclear excitation energies, and electro-magnetic
properties. These algebraic methods are very essential to understand the nature of
nuclear structure.
Especially two models, the interacting boson model (IBM) and the pseudo spin
scheme are discussed together with their microscopic interpretations. Finally their
application, for example, to the molecular structure and quantum phase transitions are
explained.
My talk consists of the following section.
1
1-1
1-2
1-3
1-4
2
2-1
2-2
3
4
5
6
6-1
6-2
6-3
7
Introduction
Early history of application of group theory in nuclear physics
Pairing interaction, seniority scheme and SU(2) symmetry
The Cooper Pair, BCS theory and its strong coupling limit
The harmonic oscillator shell model and collective motion in the sd shell; the Elliott model
The Interacting Boson Model
IBM 1
IBM 2 or the Neutron-Proton Interacting Boson Model
The pair approximation in nuclear shell model and a foundation of IBM
Application of IBM into molecular physics and phase transition
Recent study of γ-unstable nuclei
Pseudo Spin and Pseudo SU(3) scheme
Phenomenology
Application of pseudo spin scheme into well deformed nuclei
An explanation of the origin of the pseudo spin symmetry by J.Ginocchio
Conclusions
Murray Batchelor (Australian National University, Australia)
Title: The surprising connection between discrete holomorphicity and integrability
Abstract: This talk will be about exactly solved lattice models in statistical
mechanics, a richly rewarding area of mathematical physics which continues to
fascinate over many decades of activity. Over the past few years it has been
discovered that an "observable" can be set up on the lattice which obeys the discrete
Cauchy-Riemann equations. The ensuing condition of discrete holomorphicity leads
to a system of linear equations which can be solved to yield the Boltzmann weights of
the underlying lattice model. Surprisingly, these are the well known Boltzmann
weights which satisfy the star-triangle or Yang-Baxter equations at criticality. This
connection has been observed for a number of exactly solved models. In this talk I
will review these developments and discuss how this connection can be made explicit
in the context of the Z_N model. I will also discuss how discrete holomorphicity has
been used in recent breakthroughs in the rigorous proof of key results in the theory of
planar self-avoiding walks.
Edward Corrigan (University of York, UK)
Title: Aspects of defects in integrable quantum field theory
Abstract: Surprisingly, some integrable classical and quantum field theories allow
defects that do not destroy integrability. The main examples lie within affine Toda
field theory of which the sine-Gordon and Tzitzeica models are the simplest. A
suitable classical framework, together with infinite dimension representations of
quantum algebras needed for the description of defects, will be described.
Mo-Lin Ge (Nankai University, China)
Title: Yang-Baxter System and Quantum Information
Abstract: The braiding matrix related to the Bell basis can be Yang-Baxterized to
including spectral parameter u. The resultant u-dependent Ř(u)-matrix is called type-II
solution of YBE. In comparison with the familiar rational solution of YBE associated
with spin chain models, called the type-I, both of them belong to T-L algebra. The
loop value d is 2 for the type-I, whereas 2 for the type-II. Acting the T-L operators
on the topological basis it leads to, say, 2-dimensimal solution of YBE:
A(θ3)B(θ2,φ) A(θ1)= B(θ1,φ) A(θ2) B(θ3,φ)
where A stands for the braiding between 1 and 2, whereas B for 2 and 3. The
following results have been obtained:
(1) There holds Galilio velocity additivity for the type-I as expected, but Lorentzian
additivity for the type-II, i.e. two anyons may obey the Lorentz rule of velocity
additivity, if YBE holds.
(2) The existence of the two types may be due to the extremum of the L1-norm of the
Wigner D-functions.
(3) The type-II solution of YBE may be simulated with quantum optics.
(4) The 3-dimonsional topological basis related to the Birman-Wenzl-Murakami
algebra has been constructed. The physical application is discussed.
This is a joint work with Kang Xue.
Razvan Gurau (Perimeter Institute for Theoretical Physics, Canada)
Title: The large N limit of Tensor Models
Abstract: Matrix models are a highly successful framework for the analytic study of
random two dimensional surfaces with applications to quantum gravity in two
dimensions, string theory, conformal field theory, statistical physics in random
geometry, etc. . The size of the matrix, N , endows a matrix model with a small
parameter, 1/N , and its perturbative expansion can be reorganised as series in 1/N .
The leading order contribution represents planar surfaces. As the leading order is
summable, matrix models undergo a phase transition to a continuum theory of random,
infinitely refined, surfaces.
In higher dimensions matrix models generalise to tensor models. In the absence of a
viable 1/N expansion tensor models have for a long time been less successful in
providing an analytically controlled theory of random higher dimensional topological
spaces. This situation has drastically changed recently. Models for a generic complex
tensor have been shown to admit a 1/N expansion dominated by graphs of spherical
topology in arbitrary dimensions and to undergo a phase transition to a continuum
theory. I will present an overview of these results and discuss their implications to
statistical mechanics, integrable systems, quantum field theory, random discrete
geometries and probability theory.
Jerzy Lewandowski (Uniwersytet Warszawski, Poland)
Title: Loop Quantizable Gravity
Abstract: For several models of gravity coupled to other fields, the algorithm of the
canonical quantization has been completed and performed to an end. It gave rise to
well defined, exact quantum theories. The Dirac observables are provided by the
relational and the deparametrization frameworks. The quantum states, Hilbert spaces
and concrete quantum operators are furnished by the canonical Loop Quantum
Gravity framework. The models are not confirmed experimentally and admit
ambiguities, but they are there, available for farther study and applications.
Alden Mead (University of Minnesota, USA)
Title: Permutation Symmetry for Molecular Systems with Identical Nuclei
Abstract: The development of the study of degeneracy manifolds which contain
symmetry manifolds as submanifolds in molecular systems of identical nuclei is
reviewed, particularly with respect to the symmetry of electronic wave functions
under permutations of identical nuclei. Early progress has been mainly in the systems
X3 and X4, for which there are two simplifying features, viz: The number of
internuclear distances is the same as the number of internal coordinates, and the
deviations from degeneracy can often be described in terms of a two-dimensional
irreducible representation of the relevant permutation group.
We consider the study of systems of more than four identical nuclei, concentrating on
the X5 system. We show that for such system there exists no internal coordinate
system that treats all identical nuclei equivalently. The problem of constructing
electronic wave functions which are single-valued with respect to the nuclear
coordinates is discussed, both for the integer and half-odd integer electronic spin
cases.
Jun Murakami (Waseda University, Japan)
Title: Quantum invariants of knots and the hyperbolic volume
Abstract: Recently, several quantum invariants are constructed from the restricted
quantum groups. I would like to review these constructions, to explain their relation to
the hyperbolic volume, and to give some applications.
Vincent Rivasseau (University Paris-Sud XI, France)
Title: Tensor Field theories
Abstract: We present an approach to emergent space-time and quantum gravity which
is based on recent progress on the analysis of large random tensors, with particular
emphasis on the construction of renormalizable tensor field theories.
Daniel Treille (CERN and ETHZ, Switzerland)
Title: Towards the origin?
Abstract: The young expanding Universe, at its first moments, went through a series
of transitions which shaped its present structure. Our understanding of these phases
comes from direct observation of the Cosmos, using various messengers from the past.
It also comes from experiments performed at colliders, allowing to re-create at small
scale the physics which prevailed at a given time in the evolution of the Universe.
Facts are reasonably well established until the first picosecond (10**-12 s). At shorter
times one needs to extrapolate within various models, and hypotheses replace
certainties, in particular concerning the short win of matter over antimatter. The
present status of our understanding will be reviewed. Special attention will be given to
results from the LHC collider including the recently announced discovery of a new
particle, as well as to recent advances in neutrino physics.
Zhenghan Wang (Microsoft Station Q, USA)
Title: Building a Quantum Computer: A Microsoft Approach
Abstract: Topological phases of matter can be used to build inherently fault-tolerant
quantum computers. I will give an introduction to this approach as pursued in
Microsoft Station Q, where quantum algebraic structures such as quantum groups or
modular categories play an essential role.