T. K. Radha

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.

Correlation problems in evolutionary stochastic processess

In a previous contribution to these Proceedings (Ramakrishnan(1)) the concept of product density was introduced to describe the statistical distribution of a discrete number of particles in a continuous space E, corresponding to a single point t, where t is the parameter with respect to which the stochastic process evolves. This is extended to densities corresponding to n points on the t axis and correlation problems associated with these density functions are studied with particular reference to electron-photon cascades.

On the concept of virtual states

The technique of the decomposed Feynman propagator is used to establish the equivalence between the Feynman and field theoretic formalisms. It is shown that for an nth order process, each of the 2n−1 decomposed Feynman diagrams is equivalent to a certain group in the n! field theoretic diagrams. This is demonstrated for the fourth order Compton scattering of an electron by identifying the energy denominators in the two formalisms.

ON THE DECOMPOSITION OF THE FEYNMAN PROPAGATOR

The Feynman propagator, in momentum representation, is a four-dimensional transform over space and time variables. If the space and time integrations are performed separately, the propagator can be decomposed into two parts, one corresponding to positive and the other to negative energy intermediate state. By the use of this decomposed propagator, the relative contributions of the positive and negative energy intermediate states to the matrix element can be estimated. For example in Compton scattering it leads to the apparently paradoxical result that in the “nonrelativistic approximation” it is only the negative energy intermediate state that contributes to the matrix element.

Dispersion analysis of Ξ production in KN collisions

Abstract An analysis by dispersion theory for the production process K + N → Ξ + K is given for different combinations of the relative parties of the strange particles involved. Solutions are given for partial wave amplitudes under reasonable approximations. Graphs for differential cross-sections for P(ΞN) = +1 and P(YN) = −1 are presented.

On the Y*-resonances

SummaryOn the assumption that the recently observed A-π and Σ-π resonances are in theS-wave,J=1/2 state, effective range formulae are derived for the Λ-π and Σ-π scattering amplitudes in this state using a static approximation.RiassuntoIn base all’ipotesi che le risonanze Λ-π e Σ-π, osservate di recente, siano nello statoJ = 1/2 dell’ondaS, si deducono, facendo uso di un’approssimazione statica, le formule del range effettivo per le ampiezze di scattering Λ-π e Σ-π in questo stato.

Possible resonances in Ξp reactions

Cross-sections and angular distributions of ΞN interactions are investigated to determine the possibilities of Y*, YY and YN resonances.

Pion production in hyperon-nucleon collisions

SummaryThe process Σ−+p→Σ0+π− is analysed by the Chew-Low extrapolation method. The final state interactions due to the possible π-p and Yπ resonances have also been incorporated.RiassuntoSi analizza col metodo di estrapolazione di Chew-Low il processo Σ−+p→Σ0+π− Si sono incluse anclie le interazioni nello stato finale dovute a possibili risonanze π-p e Yπ.

Some consequences of spin 3/2 for Ξ

SummaryConsequences of the assignment of spin 3/2 for the cascade are investigated. The Ξ-p and Ξ-p interactions are analysed for both even and odd Ξ-N parity. The binding energies of double hyperfragments by the capture of Ξ by nuclei are also calculated. The decay systematics of the Ξ is also given.RiassuntoSi studiano le conseguenze dell’assegnazione dello spin 2/3 alla cascata. Si analizzano le interazioni Ξ-p e Ξ-p per parità X-N sia pari che dispari. Si calcolano pure le energie di legami dei doppi iperframmenti per cattura di Ξ nei nuclei. Si dà anche la sistematica di decadimento del Ξ.