Localizability and Space in Quantum Physics

Arthur S. Wightman

R. D. Grigore

P. A. M. Dirac

A dynamical system is called localizable if its wave functions can be expressed in terms of variables, each referring to physical conditions at only one point in space-time. These variables may be at points on any three-dimensional space-like surface in space-time.A general investigation is made of how the wave function varies when the surface is varied in any way. The variation of the wave function is given by equations of the Schr\"odinger type involving certain operators ${H}^{n}(u)$ which play the role of Hamiltonians. The commutation relations for these operators are obtained (Eqs. (50), (51)). The theory works entirely with relativistic concepts and it provides the general pattern which any relativistic quantum theory must conform to, provided the dynamical system is localizable.

Eduard Prugovečki

The concept of fuzzy phase space Gamma s , recently introduced in non-relativistic quantum mechanics, is extended to the relativistic case. The L 2 ( Gamma s ) representation of the wave packet is used as a basis for discussing localizability in Gamma s for non-zero mass particles as well as for the photon.