Alladi Ramakrishnan

On the scattering of pions by deuterons

The scattering of pions by deuterons has been studied under the impulse approximation and explicit expressions for the cross-sections for the elastic, inelastic and charge exchange scatterings have been obtained using the Chew-Low amplitude for the pion-nucleon scattering. Numerical calculations have been carried out at various energies and comparison has been made with the available experimental results.

CXVII. A stochastic problem relating to counters

Summary The probability distribution function π(n, t) of the number of registered events n in a time interval t for a counter in the case when the registered and unregistered events are followed by different dead times, is derived by using the method of product densities formulated recently by one of us (R.).

Stochastic processes associated with random divisions of a line

A class of stochastic processes associated with points randomly distributed in a line of finite extension L, is considered. A general integral equation for the function representing the probability distribution of the stochastic variable under consideration is derived and solved by using the Laplace transform technique. Examples of the above class of processes are cited. In particular, the problem of the fluctuations in brightness of the Milky Way is discussed in detail. The results of Chandrasekhar and Munch in regard to this astrophysical problem are derived in a simple and direct manner.

Elastic photoproduction of neutral pions from deuterium

Abstract The elastic photoproduction of neutral pion from deuterium has been studied under the impulse approximation using the Chew-Low amplitude for the photoproduction of π 6 from nucleons. The differential cross-sections have been obtained at various photon energies (1.5, 2.0 and 2.5 in units of pion mass and they are in good agreement with the available experimental values. Studies of the final spin state of the deuteron have also been made.

Studies on the Stochastic Problem of Electron-photon Cascades

A bPjef review of the well known fluctuation problem of cosmic radiation is given in a proper historical setting. We also present our latest numerical calculations for the second moments of the electron distribution as a sequel to those of Bhabha and <:hakrabarthy for the mean number. velopment of techniques to deal ·with the very diffic~lt mathematical problem relating to the stochastic variable representing the number of particles distributed in a continuous infinity of states characterised by the energy parameter. This problem has attracted the attention ,of many workers and many p~werful math,ematical techniques have been devised. More tha~ forty papers have been published but unfortunately in many of them, inadequate references hav_e been made to earlier or contemporary work. Out of the large number of papers on this subject, only two deal in detail with numerical results relating to the electron-photon cascade~that of Scott and Uhlenbeck (B. 6) and of Janossy and Messel (D. 4). Th~stl1e object of the present paper is twofold: 1. To give a. brief summary of the developments of the mathematical techniques in their proper historical setting; . 2. To p~~sent our latest numerical results** based upon the paper of Bhabha and

CXVI. Counters with random dead time

Summary The problem of determining the probability distribution function π(n, t) of the number of registered events n in a time interval t when the dead times following the registered and unregistered events are themselves stochastic variates is solved using a method developed recently by the author and P. M. Mathews (Ramakrishnan and Mathews 1953).

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.

The physical basis of quantum field theory

Abstract Notation. Throughout this paper we shall use the following notation: x denotes the space-time point with space coordinates x1, x2, x3 and time component x4; p represents similarly the four momentum. When p4 is actually the energy corresponding to p1, p2, p3 we write it also as Ep. p · x denotes the Feynman scalar product p4x4 − p · x where p · x is the scalar product of the vectors p and x with components p1, p2, p3 and x1, x2, x3 respectively. p implies p4γ4 − p · γ. In space-time integration (k) denotes a typical space-time vertex. We assume c = ℏ = 1. We also neglect numerical factors when they are not relevant for the discussion.

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: