Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane

Recent work [hep-th/0504183,hep-th/0508002] indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets twisted and the S-matrix in the non-gauge qft's becomes independent of the noncommutativity parameter theta^{\mu\nu}. Here we show that the noncommutative algebra has a commutative spacetime algebra as a substructure: the Poincare, diffeomorphism and gauge groups are based on this algebra in the twisted approach as is known already from the earlier work of [hep-th/0510059]. It is natural to base covariant derivatives for gauge and gravity fields as well on this algebra. Such an approach will in particular introduce no additional gauge fields as compared to the commutative case and also enable us to treat any gauge group (and not just U(N)). Then classical gravity and gauge sectors are the same as those for \theta^{\mu \nu}=0, but their interactions with matter fields are sensitive to theta^{\mu \nu}. We construct quantum noncommutative gauge theories (for arbitrary gauge groups) by requiring consistency of twisted statistics and gauge invariance. In a subsequent paper (whose results are summarized here), the locality and Lorentz invariance properties of the S-matrices of these theories will be analyzed, and new non-trivial effects coming from noncommutativity will be elaborated. This paper contains further developments of [hep-th/0608138] and a new formulation based on its approach.Comment: 17 pages, LaTeX, 1 figur

Bosonic Description of Spinning Strings in 2+12+1 Dimensions

We write down a general action principle for spinning strings in 2+1 dimensional space-time without introducing Grassmann variables. The action is written solely in terms of coordinates taking values in the 2+1 Poincare group, and it has the usual string symmetries, i.e. it is invariant under a) diffeomorphisms of the world sheet and b) Poincare transformations. The system can be generalized to an arbitrary number of space-time dimensions, and also to spinning membranes and p-branes.Comment: Latex, 12 page

Structural study, NCA, FTIR, FT-Raman spectral investigations, NBO analysis and thermodynamic functions of N-benzyloxy carbonyl-L-alanine

The FTIR and FT-Raman spectra of N-benzyloxy carbonyl-L-alanine have been recorded and analyzed. Natural bond orbital analysis has been carried out for various intra-molecular interactions that are responsible for the stabilization of the molecule. HOMO-LUMO energy gap has been computed with the help of density functional theory. The statistical thermodynamic functions (heat capacity, entropy, vibrational partition function and Gibbs energy) have been obtained for the range of temperature 100-1000 K. The infrared and Raman spectra have been also predicted from the calculated intensities. Comparison of the experimental and theoretical spectra values provides important information about the ability of the computational method to describe the vibrational modes. In addition to these, Mulliken’s atomic charges associated with each atom have also been reported and mapped molecular electrostatic potential (MEP) surfaces have also been performed with the same level of DFT

Vibrational (FT-IR and FT-Raman) spectra and quantum chemical studies on the molecular structure of p-hydroxy-N-(p-methoxy benzylidene) aniline

The FT-IR and FT-Raman spectra of p-hydroxy-N-(p-methoxy benzylidene) aniline have been recorded in the region 4000-400 cm−1 and 3500-100 cm−1, respectively. The optimized molecular geometry, vibrational frequencies in ground state have been calculated using density functional B3LYP methods (DFT) with 6-31+G(d,p) and 6-311++G(d,p) basis sets. The observed FT-IR and FT-Raman vibrational frequencies have been analysed and compared with theoretically predicted vibrational frequencies. The geometries and normal modes of vibration obtained from B3LYP/6-311+G(d,p) and B3LYP/6-311++G(d,p) methods are reliable compared with the experimental data. The natural bonding orbital (NBO) analysis of the investigated molecule have been computed using DFT/ B3LYP/6-311++G(d,p) calculations. The calculated HOMO and LUMO energies show that charge transfer occurs within molecule

Influence of dissipation on extreme oscillations of a forced anharmonic oscillator

Dynamics of a periodically forced anharmonic oscillator (AO) with cubic nonlinearity, linear damping, and nonlinear damping, is studied. To begin with, the authors examine the dynamics of an AO. Due to this symmetric nature, the system has two neutrally stable elliptic equilibrium points in positive and negative potential-wells. Hence, the unforced system can exhibit both single-well and double-well periodic oscillations depending on the initial conditions. Next, the authors include nonlinear damping into the system. Then, the symmetry of the system is broken instantly and the stability of the two elliptic points is altered to result in stable focus and unstable focus in the positive and negative potential-wells, respectively. Consequently, the system is dual-natured and is either non-dissipative or dissipative, depending on location in the phase space. Furthermore, when one includes a periodic external forcing with suitable parameter values into the nonlinearly damped AO system and starts to increase the damping strength, the symmetry of the system is not broken right away, but it occurs after the damping reaches a threshold value. As a result, the system undergoes a transition from double-well chaotic oscillations to single-well chaos mediated through extreme events (EEs). Furthermore, it is found that the large-amplitude oscillations developed in the system are completely eliminated if one incorporates linear damping into the system. The numerically calculated results are in good agreement with the theoretically obtained results on the basis of Melnikov's function. Further, it is demonstrated that when one includes linear damping into the system, this system has a dissipative nature throughout the entire phase space of the system. This is believed to be the key to the elimination of EEs.Comment: 15 pages, 9 figures. Accepted for publications in International Journal of Non-Linear Mechanic

On the quantization of SU(3)-skyrmions

The quantization condition derived previously for SU(2) solitons quantized with SU(3)-collective coordinates is generalized for SU(3) skyrmions with strangeness content different from zero. Quantization of the dipole-type configuration with large strangeness content found recently is considered as an example.Comment: 7 pages, 2 figures (available by request

Global Theory of Quantum Boundary Conditions and Topology Change

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold $M$ with regular boundary $\Gamma=\partial M$. The space \CM of self-adjoint extensions of the covariant Laplacian on $M$ is shown to have interesting geometrical and topological properties which are related to the different topological closures of $M$. In this sense, the change of topology of $M$ is connected with the non-trivial structure of \CM. The space \CM itself can be identified with the unitary group \CU(L^2(\Gamma,\C^N)) of the Hilbert space of boundary data L^2(\Gamma,\C^N). A particularly interesting family of boundary conditions, identified as the set of unitary operators which are singular under the Cayley transform, \CC_-\cap \CC_+ (the Cayley manifold), turns out to play a relevant role in topology change phenomena. The singularity of the Cayley transform implies that some energy levels, usually associated with edge states, acquire an infinity energy when by an adiabatic change the boundary condition reaches the Cayley submanifold \CC_-. In this sense topological transitions require an infinite amount of quantum energy to occur, although the description of the topological transition in the space \CM is smooth. This fact has relevant implications in string theory for possible scenarios with joint descriptions of open and closed strings. In the particular case of elliptic self--adjoint boundary conditions, the space \CC_- can be identified with a Lagrangian submanifold of the infinite dimensional Grassmannian. The corresponding Cayley manifold \CC_- is dual of the Maslov class of \CM.Comment: 29 pages, 2 figures, harvma

Supercavitating vehicle maneuvering with delay and non-steady planing

In this article, a general form of pitch-plane model for supercavitating vehicle dynamics is presented and used to study vehicle maneuvers. Vehicle motions into and out of the cavity are also considered and this allows for modeling of damping-force like components encountered during planing. The non-steady nature of the planing formulation allows for appropriate treatment of transient vehicle to cavity interactions. Since the vehicle planes on a cavity that is generated by previous cavitator positions, the memory effects play an important role in the model development. Unlike previous models, which are primarily intended for studies of vehicle motions in steady horizontal travel, the current form of the model makes it possible to evaluate transient maneuvers that may deviate considerably from straight and level trajectories. A numerical optimal-control approach is utilized to generate control inputs for maneuvers intended to reach a particular location. Comparisons with previous approaches are made and results obtained for maneuvering are included in this work.В статье описана обобщенная математическая модель динамиики суперкавитирующего аппарата в вертикальной плоскости, которая используется для исследования маневренности аппарата. Для расчета компонент демпфирующей силы при глиссировании рассмотрено движение аппарата внутри и вне каверны. При рассмотрении взаимодействия аппарата с каверной учитывается нестационарная природа глиссирования и эффект памяти каверны. В отличие от предыдущих математических моделей, которые предназначались в основном для изучения стационарного горизонтального движения аппаратов, предлагаемая модель позволяет рассматривать маневры аппарата с существенным отклонением от прямолинейных траекторий. Для генерации управляющих сигналов для маневров, предназначенных для достижения заданного положения, применены численные методы оптимального управления. Также в работе дано сравнение с предыдущими подходами и приведены результаты расчетов маневрирования суперкавитирующего аппарата.В статті описано узагальнену математичну модель динаміки суперкавітуючого апарату у вертикальній площині, яка використовується для дослідження маневреності апарата. Для розрахунку компонент демпфіpуючої сили при глісуванні розглянуто рух апарата усередині і зовні каверни. При розгляданні взаємодії апарата з каверною враховується нестаціонарна природа глісування і ефект пам'яті каверни. На відміну від попередніх математичних моделей, які призначались в основному для вивчення стаціонарного горизонтального руху апаратів, запропонована модель дозволяє розглядати маневри апарата з суттєвим відхиленням від прямолінійних траєкторій. Для генерації керуючих сигналів для маневрів, що призначені для досягнення заданого положення, застосовано чисельні методи оптимального керування. Також у роботі дано порівняння з попередніми підходами і наведено результати розрахунків маневрування суперкавітуючого апарата

Spectroscopic characterization and quantum chemical investigation of molecular structure and vibrational spectra of phthalazine-1(2H)-one

In this study, vibrational and electronic transition analysis of phthalazine-1(2H)-one have been presented using experimental techniques FT-IR, FT-Raman and density functional theory (DFT) calculation. The structural properties of the molecule in the ground state have been calculated using DFT employing B3LYP/6-311++G(d,p) basis set. Optimized geometrical parameters have been interpreted and compared with the experimental values. The complete assignments have been performed on the basis of the experimental data and potential energy distribution (PED) of the vibrational modes. The calculated HOMO and LUMO energies and energy difference (ΔEHOMO‒LUMO = − 4.876 eV), confirm that charge transfers occur within the molecule. The stability of the molecule arising from hyperconjugative interactions and the charge delocalization has been analyzed using natural bond orbital’s analysis (NBO). The specific heat, Gibb’s free energy, and entropy of molecule have been calculated as a function of temperature by using statistical mechanics coupled with quantum chemical calculation. Observed vibrational wave numbers have been compared with calculated values, and found to be in agreement with experimental results. The study of dielectric properties like dielectric constant at microwave frequency, static dielectric constant and dielectric constant at optical frequency of Phthalazine-1(2H)-one have been determined. The dielectric relaxation studies provide information about the molecular structure and intermolecular interaction between phthalazine-1(2H)-one and alcohol mixture

Hypernuclei as chiral solitons

The identification of flavored multiskyrmions with the ground states of known hypernuclei is successful for several of them, e.g. for isodoublet H(Lambda) - He(Lambda), A=4, isoscalars He(Lambda) (A=5) and Li(Lambda) (A=7). In other cases agreement is not so good, but the behaviour of the binding energy with increasing baryon number is in qualitative agreement with data. Charmed or beauty hypernuclei within this approach are predicted to be bound stronger than strange hypernuclei. This conclusion is stable against variation of poorly known heavy flavor decay constants.Comment: 9 pages, 1 Fig. Presented at the International Workshops on Nuclear and Particle Physics at 50-Gev PS, NP01 (KEK, Japan, December 2001) and NP02 (Kyoto, Japan, September 2002). Some additions and corrections of numerical results are mad