We discuss some recent work in which the non-minimal coupling of gravity with a self-interacting scalar field in the presence of matter can lead to a phase transition when the sign of gravitational interaction changes. It is found that gravity becomes repulsive above a critical temperature which may lie in the range 10²⁴ to 10³²K which obtains in the very early universe (10⁻³⁵ to 10⁻⁴³ sec) of the standard model. The results are intimately connected with big bang and possible removal of singularity.

Generalized theories of gravitation using the group manifold approach are outlined. It is suggested that free differential algebras should take the place of Lie algebras in current physical theory.

We give here a review of the recent developments of grand unified theories based onN=1 supergravity. We start with a brief introduction of supersymmetry and supergravity multiplets, and then discuss the construction of an invariant Lagrangian. The phenomena of gravity-induced weak symmetry breaking via the super Higgs effect at the tree level, corresponding to the conventional SU(5) gauge group, are then considered. We then extend this idea to the larger group SO(10), showing two possible breaking chains given as (i) SO(10)×susy→SU(2)_L×U(1)_R×U(1)_B-L×SU(3)_C (≡ G₂₁₁₃)×susy→U(1)_em×SU(3)_C (G_LE) predicting a secondZ-boson having mass lower than 1 TeV, and (ii) SO(10)×susy→SU(2)_L×SU(2)_R×SU(4)→(≡G₂₂₄)×susy→ SU(2)_L×U(1)_Y×SU(3)_C (≡ G₂₁₃)×susy→U(1)_em×SU(3)_C. We also consider the radiative breaking of weak symmetry via renormalisation group effects, which predicts the top quark mass. Some experimental signatures of the supersymmetric particles are investigated and possible future outlook is discussed.

Formulation of quantum first passage problem is attempted in terms of a restricted Feynman path integral that simulates an absorbing barrier as in the corresponding classical case. The positivity of the resulting probability density, however, remains to be demonstrated.

We review the recent investigations on the improved formulation of uncertainty relations which employ the information-theoretic entropy rather than variance as a measure of uncertainty. We show that this formulation also brings out clearly the relation between the overall uncertainty and the quantum mechanical interference due to measurements.

The problem of selection of preferred basis during passage from quantum to classical systems is treated with the help of a simple example of a 2-state system like the sugar molecule. A simple principle leading to this selection is stated and demonstrated in case of the chosen example. The principle, stated simply is that the preferred basis is the one in which the system environment interaction hamiltonian is diagonal.

Neutron interferometry is a unique tool for investigations in the field of particle-wave dualism because massive elementary particles behave like waves within the interferometer. The invention of perfect crystal neutron interferometers providing widely separated coherent beams stimulated a great variety of experiments with matter waves in the field of basic quantum mechanics. The phase of the spatial and spinor wave function become a measurable quantity and can be influenced individually. High degrees of coherence and high order interferences have been observed by this technique. The 4π-symmetry of a spinor wave function and the mutual modulation of nuclear and magnetic phase shifts have been measured in the past. Recent experiments dealt with polarized neutron beams, which are handled to realize the spin-superposition of two oppositionally polarized subbeams resulting in a final polarization perpendicular to both initial beam polarizations. The different actions on the coherent beams of static (DC) and dynamic (HF) flippers have been visualized.

The differences between Einstein and Bohr on the interpretation of quantum mechanics revolved around the question of completeness of the Copenhagen Interpretation. This fundamental problem is examined here in the light of recent neutron interference experiments which allow for novel experimental situations. Exploiting the possibility of neutron spin flip in these experiments, the inadequacy of the Copenhagen interpretation to fully understand the experimental results is brought out. Instead a causal interpretation of quantum mechanics is advocated, in which the neutron, as a particle, does always have a definite space time trajectory but also involves a wave which creates a potential affecting the particle neutron. The reestablishment of definite particle trajectories in the microscopic domain obliges us to reexamine the statistical treatment of ‘identical’ particles, as well as the problem of negative energies and probabilities in relativistic quantum mechanics.

The concept of spontaneous symmetry breaking arose first in the context of superconductivity, before it became important for elementary particle physics. Starting with its original discovery, a comparison of the workings of the Goldstone mechanism in relativistic quantum fixed theory on the one hand and in quantum statistical mechanics on the other is given. The roles of locality and of long range forces are traced. For condensed matter physics, an approach using functional integral methods and macroscopic order parameter fields, valid near critical points is outlined. A possibly more widely valid approach is also presented, to complete this review of the Goldstone theories in quantum statistical mechanics.

It was shown earlier that during quantum mechanical tunnelling, a microscopic particle has a distributed probability of emission about its original energy and is not constrained to be field-emitted only at its initial energy. Such an energy distribution process appears obvious on the quantum theory of observation and measurement which relates the energy of a microscopic particle with the time required for its determination through the Heisenberg’s uncertainty relation. Here, an account of the tunnelling theory based upon the latter is presented. The consequent analysis gives rise to a spectrum in the energy of the transmitted electrons and also yields a method to estimate the tunnelling time as well as the tunnelling current density across an arbitrary barrier.

Lattice field theories are described as a way to regularize continuum quantum field theories. They are obtained by replacing ordinary space time by a lattice, space time derivatives by suitable differences and Minkowski by Euclidean space. The connection between a quantum field theory isd space dimension and classical statistical mechanics in (d+1) dimensions is brought outvia elementary examples. The problem of regaining the continuum limit and of handling nonabelian gauge theories are briefly discussed.

In this short review we present the consequences of the spontaneously broken gauge theories will lead to when describing matter at high temperature and density. It appears various phase transitions should occur leading to the restoration of symmetry at high temperature of the originally broken one. Symmetry behaviour in external magnetic fields and in the early universe has been briefly mentioned.

This is a brief expositary account of Boson stochastic calculus which includes a description of quantum Ito’s formula and its application to the integration of a master equation in statistical mechanics.

We discuss some important papers that have appeared in the last twenty years on the possibility of Bose condensation in particle-antiparticle systems. Electron-hole systems in some semiconductors provide the background for a non-relativistic treatment. Bose condensation and the superfluid phase of the electron-hole fluid are strongly favoured. Next, pairing and the appearance of the superfluid vacuum state in fermion-antifermion system are considered from a relativistic viewpoint. Special attention is given to the pairs in the stateJ^P=0⁺. The pairing in the fundamental fermion-antifermion sea may provide the background subquantal level of reality of the universe.

We review the Skyrme model which treats baryons as chiral solitons.

A review of the various linear and nonlinear methods used to obtain resolution beyond natural linewidth is given.

We find that in the spin-polarized hydrogen, Bose condensation occurs for certain quantized values of the magnetic field. Once the field is fixed, sweeping of the radio-frequency results in nuclear magnetic resonance so that condensation and NMR occur simultaneously. We have found that nuclear self-induced transparency occurs. A new excitation designated by the present author as superboojum, which is a discontinuity in the hydrodynamic equations in spin-polarized hydrogen having finite nuclear as well as electronic spin is discovered.

Scalar Fourier optics is concerned with the passage of paraxial light beams through ideal optical systems. It is well known that the action of the latter on the former can be given in the framework of the two- and four-dimensional real symplectic groups. It is shown here that, based on an analysis of the Poincaré symmetry of the complete Maxwell equations in the front form, a natural representation for paraxial Maxwell beams emerges, which moreover shows the way to a generalization of scalar to vector Fourier optics preserving the group structure of ideal optical systems. Properties of generalized rays, and the usefulness of some pseudo-orthogonal groups in the treatment of Gaussian Schell-model beams, are also brought out.

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.