Utilizing one-particle one-hole variations of ATDHF states by invoking commutators obtained from generators of complete set of coordinates and of momenta, the ATDHF equations were shown in an earlier work to yield the valley condition. In principle, variations of ATDHF states should also be exploited by using anticommutators involving the said generators. It is demonstrated here that owing to the canonicity condition relating the generators of coordinates and of momenta, use of anticommutators gives rise to exactly the same valley condition on the ATDHF path.

An introductory review of BRST hamiltonian formalism is presented. The method of quantization of gauge and string theories is discussed. A few simple examples are presented to illustrate the BRST techniques.

CP-violating rate asymmetry can be generated in a process only if its amplitude possesses an absorptive part. It is pointed out that such an absorptive part can be provided ine⁺e⁻ annihilation by the presence of aZ(Z′) resonance of non-zero width. The CP asymmetry in the process$$e^ + e^ - \to l_i \bar l\left( {l_i \bar l_j } \right)$$, wherel_i are charged leptons, is discussed in several models. In a specific two-Z model, large and observable CP asymmetry ine⁺e⁻ →τ⁺e⁻ (τ⁻e⁺) is shown to be possible at LEP/SLC energies.

A careful analysis of$$B_d^0 - \bar B_d^0 $$ mixing data, incorporating the most recent QCD corrections to the parameterx_d, as well as the recent data regarding the matrix elements |V_ub| and |V_cb| leads to a reliable lower limit on mass oft-quark, for examplem_t ⩾ 115 GeV.

Approximate solutions of Altarelli-Parisi equations are obtained in low-x limit and have tested them in EMC low-x and low-Q² data. The results are compared with the phenomenological non-perturbative evolutions. Data conform to perturbative as well as non-perturbative evolutions but do not conform to the predictions of non-linear evolution.

We solve analytically the problem of a biased random walk on a finite chain of ‘sites’ (1,2,…,N) in discrete time, with ‘myopic boundary conditions’—a walker at 1 (orN) at timen moves to 2 (orN − 1) with probability one at time (n + 1). The Markov chain has period two; there is no unique stationary distribution, and the moments of the displacement of the walker oscillate about certain mean values asn → ∞, with amplitudes proportional to 1/N. In the continuous-time limit, the oscillating behaviour of the probability distribution disappears, but the stationary distribution is depleted at the terminal sites owing to the boundary conditions. In the limit of continuous space as well, the problem becomes identical to that of diffusion on a line segment with the standard reflecting boundary conditions. The first passage time problem is also solved, and the differences between the walks with myopic and reflecting boundaries are brought out.

The problem of calculating the equilibrium properties ofv-dimensional fluid mixture of hardv-spheres is studied. High temperature expansion for the density independent radial distribution function is derived for a hardv-sphere mixture. The ‘excess’ quantum corrections to the second virial coefficient and the excess free energy are also studied. Significant features are the large increase in ‘excess’ quantum correction with increasing dimensionality.

Several examples of the application of the minimax technique to relativistic calculations on one-electron atoms are given here. Normalizable eigenfunctions corresponding to the ground states of one-electron atoms with various angular momenta are derived analytically.