ON THE CONCEPT OF FIELD QUANTIZATION

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Abstract
Attempts by Takabayasi and Kaempffer at an entirely different method of field quantization, starting from the hydrodynamic formulation of classical field theories rather than from their formulation in terms of wave equations, are examined in the light of Ziman's recent successful approach towards the quantum hydrodynamical problem. It is pointed out that the energetic impossibility of a roton spectrum in an ideal continuum fluid, as shown by Ziman, makes it necessary to introduce into the theory a fundamental length, which acts as high frequency cut-off, and which may be interpreted as representing a substructure of the medium in which elementary particles may appear as excitations of the motion. Takabayasi's generalized hydrodynamic formulation of the nonrelativistic Schroedinger equation is treated as an example, and it is shown that the fundamental length must be of the order h/mc, if the particle corresponding to the single roton excitation of the Takabayasi field is to have the mass m.