The process μ⁻+¹²C→¹²B+v_μ is studied using the modified Hartree Fock wavefunction obtained with the unitary-model-operator-approach starting from the realistic hardcore nucleon-nucleon interaction, with the aim of testing the wavefunctions and obtaining a numerical value for the induced pseudoscalar coupling constant (g_P). These observables, namely, the partial capture rate to the¹²B(1⁺; g.s), its recoil nuclear polarisation and the total capture rate, which exhaust the available experimental data in the above process have been calculated and compared with the other theoretical and experimental results.

As far as the partial capture rate is concerned the use of the unitary-model operator approach wave functions for¹²C withb=2.09 fm and Cohen-Kurath wave function for¹²B(1⁺; g.s) reduces the pure shell model capture rate by about 30%. The effect of strong configuration mixing in the ground state of¹²C in taken into account by introducing a scale factor ξ similar to the ‘amplitude reduction factor’ of Donnelly and Walecka. With this ξ the agreement with the experiment both for the partial capture rate and the beta decay ‘ft’ value is found to be satisfactory.

The¹²B(1⁺; g.s) recoil polarisation is found to be insensitive to the use of the unitary-model-operator-approach wave functions. When compared with the experimental data, we obtaing_P=(14.9±1.9)g_A.

The total capture rate is found to be sensitive to the use of the unitary-modeloperator-approach wave functions which contain the effect of nucleon-nucleon short range correlations and we obtain a satisfactory agreement with the experiment for¹⁶O and¹²C, thereby revealing the importance of the effect of such correlations in the total capture rate studies.

The partial capture rates for the process,μ⁻ +¹⁶O (g·s) →¹⁶N (2⁻, 1⁻, 0⁻, 3⁻) +v_μ have been calculated using the particle-hole wavefunctions obtained using self-consistent procedure. In deriving these wavefunctions, the effectiveN-N interaction has been constructed from the bare Hamada-Johnston interaction. The terms in the muon capture Hamiltonian that depend on the momentum of the capturing proton have been included and their importance in 0⁺ → 0⁻ transition is exhibited. The agreement with the available experimental data is good. The need to incorporate meson exchange effects in 0⁺ → 0⁻ transition is pointed out.

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.

It is shown that the fermion number in a five-dimensional Kaluza-Klein theory (M⁴×S¹) in which the fermion is interacting with a monopole field, is quantized in units of (ϕR)² where the scalar ϕ is asymptotically constant andR is the radius of S¹.

Gribov ambiguity in gauge field theories is discussed and it is shown that such an ambiguity exists even for Abelian theories in covariant gauge at finite temperature. Both geometric and algebraic proofs are presented. In view of the importance of non-perturbative methods, some special gauges are given in which such ambiguities do not exist or are not relevant. The significance of these in the study of confinement in QCD is pointed out.