Feynman diagram method of treating atomic collision problems in perturbation theory is presented and matrix elements are calculated for a number of processes. The result for the resonant charge transfer in hydrogen is identical to the well known OBK value. However, in processes like collisional ionisation, the results are different from those obtained by conventional methods.

Confinement of massless particles in a suitably chosen dielectric medium is considered. Light waves of selected frequencies are shown to be confined in a medium with dielectric constantε(r)=a/r−b². A wave theoretical analysis gives equispaced frequency spectrum for the confined light, the radial dependence of its electric wave vector resembling that of hydrogen atom wave functions. In the large frequency limit an eikonal approximation of the problem gives elliptic orbits for the confined rays. Higher frequency orbits are shown to be closer to the centre of the medium than the lower frequency ones.

A model of the proton with its constituent quarks bound in a colour polarizable medium with dielectric constant varying as (a/r−b²) from a fixed centre, is presented. The Dirac equation modified by the colour polarization is solved and the analytic expression for the wavefunction of the quarks obtained shows that quarks with higher energy lie closer to the fixed centre. The energy spectrum is equispaced without any continuum. A semiclassical approximation scheme yields closed orbits for quarks which have smaller size for higher energies and no orbits with size bigger than a certain maximum, thereby rendering the quarks permanently confined. The wavefunctions of the three quarks constituting the proton are used to calculate physical parameters of the proton such as its mass, charge radius and weak coupling constant which with suitable choice of the constantsa andb appearing in the dielectric constant agree fairly well with experimental results.

A new approach to permanent confinement of non-relativistic and relativistic particles inside microscopic regions of space is presented. Motion in suitably chosen energy-dependent potentials turns out to be such that the size of orbits of particles bound in such potentials decreases when energy is supplied to them from external sources and there exists a maximum size of these orbits. The energy spectrum is purely discrete without any continuum. The dynamics of such particles requires the introduction of a space-dependent metric in the Hilbert space of states to ensure conservation of probability.

In this paper we present a review of our investigations on universal long range force between spins mediated by a massless axial vector gauge field which we name as “axial photon”. The invariance of the Lagrangian field theory of particles, possessing spin degrees of freedom, under local Lorentz transformations, necessitates the introduction of such an axial vector gauge field which interacts with spin current of the particles. Classical as well as quantum dynamics of electrons interacting with photon and axial photon are worked out. The new interaction is found to be asymptotically free. It is shown thatqed can be made finite if the coupling strengths of electron to photon and axial photon can be made equal. Experimental consequences of the existence of axial photon are discussed and the strength of the interaction is estimated by comparing predictions of the theory with experiments.