Download Titles and Abstracts

Poster Session
Titles and Abstracts
Sylvain Carrozza (Albert Einstein Institute, Golm, Germany & Laboratoire de
Physique Theorique, Orsay, France)
Title: Renormalizability in Group Field Theory
Abstract: I will present a recent work on renormalization in GFT, which extends
previous results to models implementing the so-called closure constraint. In particular,
superrenormalizability of a 4d model on U(1) could be proven, and there are hints that
just renormalizable models with higher dimensional groups might exist.
Vincent Genest (Universit de Montreal, Canada)
Title: The Bannai-Ito polynomials as Racah coefficients of the -1 sl(2) algebra
Abstract: The Bannai-Ito polynomials are shown to arise as Racah coefficients for -1
sl(2). This Hopf algebra has four generators including an involution and is defined
with both commutation and anticommutation relations. It is also equivalent to the
parabosonic oscillator algebra. The coproduct is used to show that the Bannai-Ito
algebra acts as the hidden symmetry algebra of the Racah problem for -1 sl(2). The
Racah coefficients are recovered from a related Leonard pair.
Jacek Jurkowski (Nicolaus Copernicus University, Poland)
Title: Quantum Discord Derived from Tsallis Entropy
Abstract: Due to some ambiguity in the definition of mutual Tsallis entropy in
classical probability theory, its generalization to quantum theory is discussed. We
define a $q$-discord originating from the $q$-expectation value of mutual Tsallis
entropy. $q$-discords for two-qubit Werner and isotropic states are calculated and it is
shown that both are positive, at least for states under investigation, for all $q>0$.
Finally, an analytical expression for $q$-discord of certain family of two-qubit X
states is presented.
Seiichi Kuwata (Hiroshima City University, Japan)
Title: Generalized associativity in the Cayley numbers
Abstract: The Cayley numbers, which are closely related to the exceptional Lie
groups, have been applied to Lorentz geometry and supersymmetry. However, the
Cayley number is somewhat difficult to deal with, due to the lack of its associativity,
where the associativity can be represented by the commutativity between the right
multiplication R_x and left multiplication L_y. Here we generalize the associativity of
the Cayley numbers by extending the commutator between R_x and L_y. The
resultant identity, which is quite different from the Moufang identitiy, depends on the
geometrical configuration between x and y.
Zhanna Kuznetsova (Federal University of ABC, Brazil)
Title: Twist-induced versus fondamental non-commutativity.
Abstract: Non-commutative quantum mechanics is first quantized. The noncommutative parameter can be assumed either fundamental or derived (induced by a
Drinfeld twist). The two frameworks are equivalent for the single-particle sector,
producing the same single-particle spectrum, but differ in multi-particle sector.
Quantum mechanics based on fundamental non-commutative parameter is additive
while NC quantum mechanics derived from a Drinfeld twist is non-additive. The
non-additive terms in the multi-particle Hamiltonian are determined and made
compatible by the Hopf algebra structures. An abelian twist induces a constant noncommutativity while the Jordanian twist induces a Snyder type non-commutativity.
Zhong-Qi Ma (Institute of High Energy Physics, CAS, China)
Title: The rotational invariants constructed by the products of three spherical
harmonic polynomials
Abstract: H. Weyl (1946) established a theorem on the important structure for
rotational invariants. Biedenharn and Louck in their famous Encyclopedia of
Mathematics on Angular Momentum in Quantum Physics (1981) studied the most
important case (n=3) of the general theorem in some detail. However, they pointed out
in their book: ``Unfortunately, the expression for the general coefficient has not been
given in the literature and one has had to work out these invariant polynomials from
the definition". We have solved completely the problem raised by Biedenharn and
Louck and present the expressions for the coefficients generally and explicitly in this
talk. The paper arXiv-1203-6702-math-ph is in submission.
Amir Moghaddam (The University of Queensland, Australia)
Title: A non–Hermitian BCS Hamiltonian and generalised exclusion statistics
Abstract: The Bethe ansatz is a key tool in the area of quantum integrable and exactly
solvable models. For each such model, understanding the nature of the roots of the
Bethe ansatz equations is central to understanding the mathematical physics
underpinning the model’s behaviour. Here we analyse an exactly solvable,
non-hermitian BCS pairing Hamiltonian dependent on a real-valued coupling
parameter. The Hamiltonian displays a real spectrum for all values of this coupling
parameter. The roots of the Bethe ansatz equations can be categorized into two classes,
those which are dependent on the coupling parameter and those which are not. We
will discuss how those roots which are independent of the coupling parameter can be
associated to exotic quasi-particles obeying generalised exclusion statistics, in the
sense proposed by Haldane in 1991.
Claudio Parmeggiani (University of Milan, Italy)
Title: Quantum Interferometers, Euler angles, Unitary Representations of SU(2)
Abstract: The "one particle" or "two particles" interferometers can be (quantum
mechanically) described in terms of Hilbert spaces of states and scattering operators.
Then the scattering operators realize an unitary representation of SU(2) and the Euler
angles of the SU(2) group are related to the interferometers parameters (transmission
coefficient, phase shift).
Peter S. Turner (University of Tokyo, Japan)
Title: The curious nonexistence of Gaussian 2-designs
Abstract: We report a surprising distinction between measurements in finite and
infinite dimensional Hilbert spaces. It is based on the observation that the overlaps of
arbitrary Gaussian states in the number basis are strictly decreasing functions of
excitation number, and therefore no convex combination thereof can be proportional
to a projection operator. We connect this observation with the construction of
t-designs, important ensembles of states that reproduce the t-th moments of the
unitarily uniform ensemble. We show that despite the fact that the uniform
subensemble of unsqueezed Gaussians forms a 1-design, and despite satisfying the
same necessary and sufficient representation theoretic property as in the well
understood finite dimensional case for the Heisenberg-Weyl and symplectic groups,
the uniform ensemble -- indeed, any ensemble -- of all pure Gaussian states in infinite
dimensions cannot comprise a 2-design in this way. This has important consequences
for quantum optical tomography, where 2-designs are powerful tools.
William Zeng (Oxford University, UK)
Title: Diagramming Quantum Algorithms: The Fourier Transform
Abstract: The Quantum Fourier transform is the fundamental mechanism in effective
known quantum algorithms. Here we present some preliminary attempts to locate
this Fourier transform in a more general structural context by building representation
theory into the monoidal categories and graphical reasoning of categorical quantum
mechanics.
Bin Zhou (Beijing Normal University, China)
Title: Solution Spaces of the Klein-Gordon equation and the Maxwell equations on
dS/AdS
Abstract: By virtue of the theory of Lie groups and Lie algebras, we can give
coordinate systems adapted to the Cartan subalgebras, then obtain finite dimensional
solution spaces of the Klein-Gordon equation and that of the Maxwell equations on de
Sitter spacetime and anti-de Sitter spacetime. Correspondingly, the mass spectrum of
the Klein-Gordon scalars can be obtained, too. In the de Sitter background, the
squared mass is -N(N + 3) with N a non-negative integer; in the anti-de Sitter
background, the squared mass is N(N + 3).