By Lane Palmer Hughston (eds.)
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Thus, it corresponds not to a unique particle state, but rather to an entire multiplet of states--moreover, the multiplet can include states of several different 47 spins. 2) corresponds to a definite particle state only if the twistor function f(Z~) is suitably restricted. If f(Z~) is placed in a simultaneous eigenstate of a suitably complete set of commuting operators, then a unique field belonging to the multiplet vanishing. 2), only one independent combination will lead to an integral which does not vanish.
F. " Within the ring there are certain elements which are Hermitian, and therefore qualified to be regarded as observables. Our problem, then, is to de- vise a systematic way of physically interpreting these observables, which they act. it deserves Alternatively, and the states on given a physical observable taken from the milieu of elementary particle phenomenology, one may seek the appropriate differential operator with polynomial coefficients to which it corresponds. Whether the right operator has been chosen can be determined by examining its eigenvalue spectrum and its commutation relations with other known observables, to see whether these are compatible with the desired results: there is no a priori guarantee, for a given physical observable, that an appropriate twistor operator can be found--but it is implicit in the twistor particle hypothesis that this should, in fact, always be the case.
2). The Spin Operator. The momentum operator and the angular m o m e n t u m operator, squared operator, twistor terms. are all examples of observables along with the mass- which can be expressed directly It should be noticed that these observables are all differential in op- 49 erators with polynomial coefficients. All of our observables, ring of differential operators with polynomial coefficients. F. " Within the ring there are certain elements which are Hermitian, and therefore qualified to be regarded as observables.
Twistors and Particles by Lane Palmer Hughston (eds.)