In a recent interesting note by Kfilnay (1975), he argued that the nonlinear scalar field operator, (b, for elementary particles, obeying the proportionalityis a more fundamental starting point in a quantum field theory of elementary particles than Heisenberg's nonlinear spinor field relationThe reason given was (as he showed earlier) that "quantum Fermi fields can be entirely described in terms of c numbers and of Bose fields acting on Bose states." I should like to point out a very basic reason for starting with a spinor formalism rather than the scalar formalism, in a theory of elementary particles according to Heisenberg's view. It is the requirement of maintaining full compatibility with the most general symmetry requirements of the theory of special relativity. If the most fundamental description of elementary particles is to be in terms of a quantum (or c-number) field theory, satisfying the covariance requirements of the theory of special relativity, then the field operators (or c-number field solutions) for these fundamental particles are the basis/'unctions for the irreducible representations of the Poincar~ group. This result is strictly a consequence of the symmetry imposed by the theory of special relativity-it is independent of whether the underlying symmetry group is to relate to the covariance of a quantum or a c-number field theory! © 1976 Plenum Publishing Corporation. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.
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