By using Kikkawa’s method the equivalence of the nonrenormalizable pair interaction$$\bar \psi \psi \phi ^2 $$ to a renormalizable theory is proved. Equivalence relationships between a few other nonrenormalizable and renormalizable interactions are also indicated.

We study a model of quark confinement defined by the vanishing of colour currents. The model is shown to be equivalent to quantum chromodynamics and this equivalence is interpreted as due to the compositeness of the colour gluons. The Green’s functions of the theory are found to contain nontrivial structure only for colour singlet composites which can be identified with hadrons.

We find the classical solutions of a model of quark confinement defined by the vanishing of colour currents. Both plane-wave type of solutions extending all over space as well as string-type of solutions confined to restricted regions of space are found.

The Raman spectra of mixed crystals of [(NH₄)_1−x K_x]₂ SO₄ in the region 50–3400 cm⁻¹ at 293 K and below 223 K have been reported. At room temperature 293 K, as the concentration of K⁺ ion increases in the crystal up to 50%, the frequencies of the totally symmetric vibrations of SO₄²⁻ and NH₄⁺ ions increase and thereafter the frequency of SO₄²⁻ vibration decreases and attains the value in K₂SO₄. This change in frequency up to 50% of potassium concentration is due to the breaking of hydrogen bonds of the type N-H...O. The behaviour of Raman intensities of A_g(v₁) mode of SO₄²⁻ for various concentrations (x=0, 0·03, 0·11, 0·5, 0·85) suggest that the phase transition changes from first order type to one of second order. The phase transition in mixed crystals of [(NH₄)_1−x K_x]₂ SO₄ can be a cooperative phenomenon arising from a coupling between (NH₄)⁺ ions through hydrogen bonds with the distorted SO₄²⁻ ions in the low temperature phase.

We consider spinor, scalar and vector fields with colour degrees of freedom and find the classical solutions when the constraint of vanishing colour currents is imposed. We find that there are no non-trivialc-number solutions for spinor fields transforming as a triplet under SU(3), although solutions exist for scalar and vector fields. We also show that the colour current of spinor fields coupled to an instanton is zero.

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.

Using the Ward-Takahashi identities from the hidden supersymmetry in Langevin equation we present a very simple proof of the equivalence of stochastic quantization to field theories.