N.R. Ranganathan

Kemmer algebra from generalized Clifford elements

Our earlier studies [l, 2, 31 on the generalised Clifford algebra (G.C.il.) formulated by K. Yamazaki [4] 1 e d us to a surprising connection between the generalised Clifford algebra and the unitary groups which describe the internal symmetry of elementary particles. We shall now show that it is possible to obtain the matrices of the Duffin-Kemmer-Petiau [5] (D.K.P.) algebra which enter the space-time description of particles having spin zero or one through a wave equation, known in literature as the D.K.P. equation. Such a derivation of D.K.P. algebra from the generalised Clifford algebra leads us automatically to a method of constructing the elements of the algebra of the orthogonal groups also.

Stochastic methods in quantum mechanics

Relations to quantum mechanics of the superposition principle, the concepts of realization and inverse probability, product densities of many- particle systems, the method of regeneration points, and ambigenous stochastic processes are discussed. An alternative interpretation of the Feynman formalism and direct proof of equivalence of the Feynman and field-theoretic formalisms are presented. Possibilities of developing a nonperturbative approach using Feynman formalism by adopting study methods for ambigenous processes evolving both forward and backward, with respect to a one-dimensional, parameter are discussed. Results in the theory of linear matrix equation solutions are presented. (L.N.N.)

The generalized Clifford algebra and the unitary group

During the past two years following the first formulation of L-matrix theory [I] the Matscience group has been concerned with the generalised Clifford algebra of matrices which are the mth roots of unity. The generalised algebra was discovered by Yamazaki [2] in 1964 and the matrix representations in the lowest dimension were first given by Morris in 1967 [3]. We shall now present some new results on the subject and point out a surprising and unexpected connection with the generators of the special unitary group. It has been established that there are (2n + 1) matrices L, , L, ,..., L2n+l of dimension mn x mn obeying the two generalised Clifford conditions:

On an isobaric spin scheme for leptons and the leptonic decays of strange particles

Abstract An isobaric spin scheme for leptons is discussed using the concept of missing components. A phenomenological set of rules is also suggested to explain the low rates of most of the | ΔS | = 1 decays.

SOME REMARKS ON THE STRUCTURE OF ELEMENTARY PARTICLE INTERACTIONS

6. SummaryThe existence of symmetries which can lead to minimal electromagnetic interactions have been investigated and three specific invariances to obtain this minimal character have been proposed. Applications of these principles to strong and weak interactions are seen to lead to certain suggestive results. A model of strong interactions arising out of these considerations is also discussed.

A NOTE ON DISPERSION RELATIONS

Dispersion theory is examined on the basis of a reciprocal relationship between the real and imaginary part of the scattering amplitude and it is shown that the knowledge of the absorptive part over the unphysical region leads to a linear integral equation for the dispersive part.

A note on scattering and production amplitudes

Abstract A relation between scattering and production amplitudes to processes involving an arbitrary number of final channels has been arrived at following a method due to Sucher and Day. Possible applictions of this equation toπ−π,K−Kandπ+π →K+K scatterings are pointed out. Also simple and exact expression for the γ−γ scattering amplitude in terms of the amplitude for the processγ+γ → e − +e + has been obtained.

A note on the interaction between nucleon and anti-nucleon

The interaction potential between nucleon and anti-nucleon is derived by using the new Tamm-Dancoff formalism.

Photo-mesons from polarized nucleons

SummaryIt is shown that the angular distribution of photo-mesons obtained from polarized nucleons behaves differently for left and right circularly polarized beams.

Meson production in nucleon-nucleon collisions

A calculation of the amplitude for meson production in a nucleon-nucleon collision is presented using the method of Low. By making a suitable Tamm-Dancoff approximation, the matrix element for the process is expressed in terms of the two nucleon potential, pion nucleon scattering matrix element and nucleon vertex operator.