Tantalising asymmetries in special relativity

We watch as asymmetric tries to slow regu Vth by the study compares vectors timelike and spacelike

Decomposition of intervals in special relativity

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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

Some new mathematical features in cascade theory

AbstractThe fluctuation problem in cascade theory is viewed from the standpoint of the invariant imbedding method of Bellman et al. [1]. The correlation functions that are used in the description of the electromagnetic cascades are shown to obey a simple system of two component vector differential equations. The advantage of the present method over the conventional approach of writing down Kolmogorov forward equations for these functions lies in that we encounter 2 × 2 matrices of a particular type only. In view of the simplicity of the structure it is possible to generalize the equations to correlation functions of arbitrary order. The reduction in dimension from 2n × 2n matrices to only 2 × 2 matrices which may, at first sight, appear perplexing is due to the fact that each of the 2n elements that appear in the single system of differential equations, corresponding to the two different initial conditions, can be obtained by considering 2n disjoint systems of two component vector equations. The imbedding technique is also used to arrive at the independent differential equations satisfied by sequent product densities that are encountered in more comprehensive description of electromagnetic cascades

Stochastic processes associated with a symmetric oscillatory poisson process

A symmetric oscillatory Poisson process is defined and its stochastic features studied. The process represented by the symbolic integral of this oscillatory Poisson process is then discussed in detail. The results obtained are applied to the well-known stochastic problem of multiple scattering of charged particles in their passage through matter

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 "non-relativistic approximation" it is only the negative energy intermediate state that contributes to the matrix element