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The Philosophy of Vacuum Part 12. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | The Negative-Energy Sea 103 In summary we are led to a point of view in which the linear standard formalism appears as a quantum mechanics of charge charge dynamics represented through the normal ordering in the kinematic limit as a quantum mechanics of particles. In both cases the quantum mechanics is in canonical second quantized form. On this view there is no non-trivial particle dynamics on a fixed complex-linear space not even in Fock space40 that is there no particle Hilbert space description of the dynamics. In the kinematic case only observables that commute with J can be defined. To pursue these implications would take us too far afield and into difficult terrain. For what it is worth C -algebra theory also leads to a similar conclusion in so far as one finds that the evolution cannot be unitarily implemented within any one representation and in semi-classical quantum gravity the metric dependence of the particle interpretation of quantum fields has a natural expression in terms of inequivalent complex structures on Hilbert space.41 The almost complete failure of the constructive programme in quantum field theory in which the existence of a particle Fock space is an axiom is in itself remarkable.42 The present theory offers a new perspective which is both simple and radical. It is simple because for linear fields the standard formalism can be understood as a canonical second quantization contact with the 1-particle theory is preserved. Relativistic quantum theory is cast into a form almost identical to the non-relativistic theory. It is radical because the modification of the complex structure ramifies throughout the interpretive and mathematical framework of the theory.43 It may be that one can formulate a 40 In the present framework Fock space is defined as Vj J cannot be preserved by the evolution. 41 See Ashtekar and Magnon 1975 Woodhouse 1980 284-7 . For a self-contained introduction along more conventional lines see Birrel and Davies 1982 . 42 This .
