On the Integrable Structure of the Ising Model

Starting from the lattice $A_3$ realization of the Ising model defined on a strip with integrable boundary conditions, the exact spectrum (including excited states) of all the local integrals of motion is derived in the continuum limit by means of TBA techniques. It is also possible to follow the massive flow of this spectrum between the UV $c=1/2$ conformal fixed point and the massive IR theory. The UV expression of the eigenstates of such integrals of motion in terms of Virasoro modes is found to have only rational coefficients and their fermionic representation turns out to be simply related to the quantum numbers describing the spectrum.Comment: 18 pages, no figure

The gl(M|N) Super Yangian and Its Finite Dimensional Representations

Methods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y(gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite dimensional irreducible representation of Y(gl(M|N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite dimensional are given.Comment: 14 pages plain late

Неэмпирические расчеты минимальных энергетических путей реакций присоединения молекулы HF к молекулам ацетилена и метилацетилена.

Potential energy surfaces of gas-phased synchronous addition of HF to acetylene and methylacetylene. A non-empirical Harthree-Fock-Ruthane method (Gaussian-03, G-31++G** basis) with electronic correlation consideration in MP2 approximation (Moeller-Plesseth 2nd grade) was used. Reaction heats and activation energies were calculated. Reaction heat of HF addition to acetylene molecule is -19.5 kcal/mol, activation energy is 52.3 kcal/mol. Reaction heats of HF addition to methylacetylene according to Markovnikov's rule and against it comprise -20.7 and -16.1 kcal/mol; activation energies are 48.0 and 53.5 kcal/mol accordingly. It was established that HF addition to methylacetylene molecule with formation of 2-fluoropropene is more energetically advantageous according to Markovnikov's rule kinetically as well as thermodynamically.Исследованы поверхности потенциальной энергии газофазных реакций синхронного присоединения молекулы HF к молекулам ацетилена и метилацетилена. Использованы неэмпирический метод Хартри-Фока-Рутана, программа Gaussian-03, базис 6-31++G** с учетом электронной корреляции в приближении МП2 (Меллера-Плессета 2-го порядка). Рассчитаны теплоты и энергии активации реакций. Установлено, что как кинетически, так и термодинамически более выгодно присоединение молекулы HF к молекуле метилацетилена по правилу Марковникова с образованием 2-фторпропена

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the Quantum Inverse Scattering Method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.Comment: 14 pages, latex, no figure

Branching rules of semi-simple Lie algebras using affine extensions

We present a closed formula for the branching coefficients of an embedding p in g of two finite-dimensional semi-simple Lie algebras. The formula is based on the untwisted affine extension of p. It leads to an alternative proof of a simple algorithm for the computation of branching rules which is an analog of the Racah-Speiser algorithm for tensor products. We present some simple applications and describe how integral representations for branching coefficients can be obtained. In the last part we comment on the relation of our approach to the theory of NIM-reps of the fusion rings of WZW models with chiral algebra g_k. In fact, it turns out that for these models each embedding p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps can be be extended to finite level, we obtain a Verlinde-like formula for branching coefficients.Comment: 11 pages, LaTeX, v2: one reference added, v3: Clarified proof of Theorem 2, completely rewrote and extended Section 5 (relation to CFT), added various references. Accepted for publication in J. Phys.

Kinematics of a relativistic particle with de Sitter momentum space

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.Comment: RevTeX, 12 pages, no figure

Coherent States for Quantum Compact Groups

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the $q$--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}Comment: 25 page

Неэмпирические расчеты минимальных энергетических путей реакций присоединения молекул H2F2 и H2Cl2 к молекулам ацетилена и метилацетилена

Surfaces of potential energy of gas phase addition reactions of H2F2 and H2Cl2 molecules to acetylene and methyl acetylene molecules were examined. An ab initio calculation of H2F2 and H2Cl2 molecules was carried out. A non-empirical Hartree-Fock-Roothaan method, 6-31 ++G** basis, taking into account electronic correlation in MP2 approximation (Møller-Plesset 2nd order) and Gaussian–03 software were used. Reaction heats and activation energies were calculated. It was established that addition of H2F2 and H2Cl2 molecules to a methyl acetylene molecule according to Markovnikov’s rule with the formation of 2-fluoropropene and HF and 2-chloropropene and HCl respectively is more advantageous both kinetically and thermodynamically.Исследованы поверхности потенциальной энергии газофазных реакций присоединения молекул H2 F2 и H2 Cl2 к молекулам ацетилена и метилацетилена. Проведен ab initio расчет молекул H2 F2 и H2 Cl2.. Использованы неэмпирический метод Хартри-Фока-Рутана, базис 6-31++ G ** с учетом электронной корреляции в приближении МП2 (Меллера-Плессета 2-го порядка), программа Gaussian -03. Рассчитаны теплоты и энергии активации реакций. Установлено, что как кинетически, так и термодинамически более выгодно присоединение молекул H2 F2 и H2 Cl2 к молекуле метилацетилена по правилу Марковникова с образованием 2-фторпропена и HF и соответственно 2-хлорпропена и HCl

Commensurate-Incommensurate Phase Transitions for Multichain Quantum Spin Models: Exact Results

The behavior in an external magnetic field is studied for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate-incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent. A scenario for the transition from one to two space dimensions for the integrable multichain models is proposed. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The exponents for the gaps caused by relevant perturbations of the models are calculated.Comment: 23 pages, LaTeX, typos correcte