133 research outputs found
Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
Families of vector-like deformed relativistic quantum phase spaces and
corresponding realizations are analyzed. Method for general construction of
star product is presented. Corresponding twist, expressed in terms of phase
space coordinates, in Hopf algebroid sense is presented. General linear
realizations are considered and corresponding twists, in terms of momenta and
Poincar\'e-Weyl generators or generators, are constructed
and R-matrix is discussed. Classification of linear realizations leading to
vector-like deformed phase spaces is given. There are 3 types of spaces:
commutative spaces, -Minkowski spaces and -Snyder
spaces. Corresponding star products are associative and commutative (but
non-local), associative and non-commutative and non-associative
and non-commutative, respectively. Twisted symmetry algebras are considered.
Transposed twists and left-right dual algebras are presented. Finally, some
physical applications are discussed.Comment: 20 pages, version accepted for publication in EPJ
Analytical Results for Trapped Weakly Interacting Bosons in Two Dimensions
We consider a model of N two-dimensional bosons in a harmonic trap with
translational and rotational invariant, weak two-particle interaction. We
present in configuration space a systematical recursive method for constructing
all wave functions with angular momentum L and corresponding energies and apply
it to L\leq 6 for all N. The lower and the upper bounds for interaction energy
are estimated. We analitically confirm the conjecture of Smith et al. that
elementary symmetric polynomial is the ground state for repulsive delta
interaction, for all N\geq L up to L\leq 6. Additionally, we find that there
exist vanishing-energy solutions for L\geq N(N-1), signalizing the exclusive
statistics. Finally, we consider briefly the case of attractive power-like
potential r^k, k>-2, and prove that the lowest-energy state is still the one in
which all angular momentum is absorbed by the center-of-mass motion.Comment: RevTex, 13 page
Exponential Formulas and Lie Algebra Type Star Products
Given formal differential operators on polynomial algebra in several
variables , we discuss finding expressions determined by the
equation
and their applications. The expressions for are related to the coproducts
for deformed momenta for the noncommutative space-times of Lie algebra type and
also appear in the computations with a class of star products. We find
combinatorial recursions and derive formal differential equations for finding
. We elaborate an example for a Lie algebra , related to a quantum
gravity application from the literature
Generalized Quon Statistics
Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi,
and anyonic statistics are proposed. They follow from the R-matrix approach to
deformed associative algebras. It is proved that generalized quons have the
same main properties as quons. A new result for the number operator is
presented and some physical features of generalized quons are discussed in the
limit .Comment: 13+i pages, Latex, preprint RBI-TH-9
Parastatistics as Examples of the Extended Haldane Statistics
We show that for every algebra of creation and annihilation operators with a
Fock-like representation,one can define extended Haldane statistical parameters
in a unique way. Specially for parastatistics, we calculate extended Haldane
parameters and discuss the corresponding partition functions.Comment: Latex, 13 pages, no figures,to appear in Mod.Phys.Lett.
Unified view of multimode algebras with Fock-like representations
A unified view of general multimode oscillator algebras with Fock-like
representations is presented.It extends a previous analysis of the single-mode
oscillator algebras.The expansion of the operators is
extended to include all normally ordered terms in creation and annihilation
operators and we analyze their action on Fock-like states.We restrict ourselves
to the algebras compatible with number operators. The connection between these
algebras and generalized statistics is analyzed.We demonstrate our approach by
considering the algebras obtainable from the generalized Jordan-Wigner
transformation, the para-Bose and para-Fermi algebras, the Govorkov
"paraquantization" algebra and generalized quon algebra.Comment: Latex, 34 pages, no figures ( accepted in Int.J.Theor.Phys.A
Solutions of coupled BPS equations for two-family Calogero and matrix models
We consider a large N, two-family Calogero and matrix model in the
Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the
solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by
the static soliton configurations. We find all solutions close to constant and
construct exact one-parameter solutions in the strong-weak dual case. Full
classification of these solutions is presented.Comment: latex, 15 pages, no figure
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