Non-Abelian Proca model based on the improved BFT formalism

We present the newly improved Batalin-Fradkin-Tyutin (BFT) Hamiltonian formalism and the generalization to the Lagrangian formulation, which provide the much more simple and transparent insight to the usual BFT method, with application to the non-Abelian Proca model which has been an difficult problem in the usual BFT method. The infinite terms of the effectively first class constraints can be made to be the regular power series forms by ingenious choice of $X_{\alpha \beta}$ and $\omega^{\alpha \beta}$-matrices. In this new method, the first class Hamiltonian, which also needs infinite correction terms is obtained simply by replacing the original variables in the original Hamiltonian with the BFT physical variables. Remarkably all the infinite correction terms can be expressed in the compact exponential form. We also show that in our model the Poisson brackets of the BFT physical variables in the extended phase space are the same structure as the Dirac brackets of the original phase space variables. With the help of both our newly developed Lagrangian formulation and Hamilton's equations of motion, we obtain the desired classical Lagrangian corresponding to the first class Hamiltonian which can be reduced to the generalized St\"uckelberg Lagrangian which is non-trivial conjecture in our infinitely many terms involved in Hamiltonian and Lagrangian.Comment: Notable improvements in Sec. I

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions

Self dual models and mass generation in planar field theory

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the lagrangian formalism. The implications of our results for bosonisation in three dimensions are discussed.Comment: 15 pages,Revtex, No figures; several changes; revised version to appear in Physical Review

On the constrained structure of duality symmetric Maxwell theory

The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more economical and elegant. Distinctions from the constrained analysis of the usual Maxwell theory are pointed out and their implications are also discussed.Comment: Latex, 12 page

Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories

We show that noncommuting electric fields occur naturally in $\theta$-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian formulations of these theories, is established. A comparison of results in different descriptions shows that this generalised map acts as canonical transformation in the physical subspace only. Finally, we apply the hamiltonian formulation to derive the gauge symmetries of the action.Comment: 16 pages, LaTex, considerably expanded version with a new section on `Gauge symmetries'; To appear in Phys. Rev.

Hamiltonian embedding of the massive Yang-Mills theory and the generalized St\"uckelberg formalism

Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert second class systems into first class ones, we present a gauge invariant formulation of the massive Yang-Mills theory by embedding it in an extended phase space. The infinite set of correction terms necessary for obtaining the involutive constraints and Hamiltonian is explicitly computed and expressed in a closed form. It is also shown that the extra fields introduced in the correction terms are exactly identified with the auxiliary scalars used in the generalized St\"uckelberg formalism for converting a gauge noninvariant Lagrangian into a gauge invariant form.Comment: 31 pages, Latex, very minor changes, a concluding paragraph inserted, version to appear in Nucl. Phys.

Magnetic glass in Shape Memory Alloy : Ni45Co5Mn38Sn12

The first order martensitic transition in the ferromagnetic shape memory alloy Ni45Co5Mn38Sn12 is also a magnetic transition and has a large field induced effect. While cooling in the presence of field this first order magnetic martensite transition is kinetically arrested. Depending on the cooling field, a fraction of the arrested ferromagnetic austenite phase persists down to the lowest temperature as a magnetic glassy state, similar to the one observed in various intermetallic alloys and in half doped manganites. A detailed investigation of this first order ferromagnetic austenite (FM-A) to low magnetization martensite (LM-M) state transition as a function of temperature and field has been carried out by magnetization measurements. Extensive cooling and heating in unequal field (CHUF) measurements and a novel field cooled protocol for isothermal MH measurements (FC-MH) are utilized to investigate the glass like arrested states and show a reverse martensite transition. Finally, we determine a field -temperature (HT) phase diagram of Ni45Co5Mn38Sn12 from various magnetization measurements which brings out the regions where thermodynamic and metastable states co-exist in the HT space clearly depicting this system as a 'Magnetic Glass'.Comment: Magnetic field tunes kinetic arrest and CHUF shows devitrification and melting of Magnetic glas

Dual Projection and Selfduality in Three Dimensions

We discuss the notion of duality and selfduality in the context of the dual projection operation that creates an internal space of potentials. Contrary to the prevailing algebraic or group theoretical methods, this technique is applicable to both even and odd dimensions. The role of parity in the kernel of the Gauss law to determine the dimensional dependence is clarified. We derive the appropriate invariant actions, discuss the symmetry groups and their proper generators. In particular, the novel concept of duality symmetry and selfduality in Maxwell theory in (2+1) dimensions is analysed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and $Z_2$ symmetries, contrary to conventional results.Comment: 20 pages, late