A straightforward derivation of the Dirac-Schwinger covariance condition is given within the framework of classical field theory. The crucial role of the energy continuity equation in the derivation is pointed out. The origin of higher order derivatives of delta function is traced to the presence of higher order derivatives of canonical coordinates and momenta in the energy density functional.

An investigation of the newly discovered charmed mesonsD 0 andD +, particularly their non-leptonic decay modes, is carried out in the framework of the MIT bag model. The amplitude for a number of two-body final state decays are explicitly evaluated and compared with other available estimates.

Two cases of forced harmonic oscillators with time dependent mass for which exact propagators can be evaluated are presented. From the exact propagators, normalized solutions of the corresponding Schrödinger equations are arrived at. Time-dependent invariants are also found.

Time-dependent spherically symmetricSU(2) Yang-Mills-Higgs system is shown to be chaotic near the ’t Hooft-Polyakov monopole solution by calculating the maximal Lyapunov exponents. A phase transition like behaviour from order to chaos is observed as a parameter depending on the self interaction constant of scalar fields increases.

Chaotic behaviour of a quartic oscillator system given byH l/2(p₁²+p₂²)+ (1/12)(1 -α) (q₁⁴+q₂⁴)+1/2q₁²q₂² is studied. Though the Riemannian curvature is positive the system is nonintegrable except when S/B α = 0. Calculation of maximal Lyapunov exponents indicates a direct correlation between chaos and negative curvature of the potential boundary.

In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of the original drive system with appropriate scaling factors with a response hyperchaotic system is considered. A self-combination system is constructed from hyperchaotic Lorenz system by combining state variables of the Lorenz system with appropriate scaling factors. Modified function projective synchronization between the newly constructed combination hyperchaotic Lorenz system and hyperchaotic Lu system is investigated using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function projective synchronized. Numerical simulations are done to show the validity and effectiveness of the proposed synchronization scheme.