MODULAR VARIABLES IN QUANTUM THEORY.
Final rept. 1 Jun 65-31 May 67,
YESHIVA UNIV NEW YORK BELFER GRADUATE SCHOOL OF SCIENCE
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The non-local aspects of interaction between quantum systems are investigated. These aspects are particularly conspicuous in quantum phenomena without a classical analog, such as the quantum effects of electromagnetic potentials. The study of the potential effect leads to the introduction of a new type of dynamical variables, modular variables, which are suitable to express the physical features of the quantum mechanical non-locality. The potential effect is reviewed and the question of whether the effect can be described as an exchange of otherwise conserved dynamical quantities is discussed. It is shown that this can be done in terms of modular momentum. Some fundamental properties of modular variables are investigated. In particular it is demonstrated that for these variables the quantum equations of motion are essentially different from the classical ones, and that modular momentum may commute with modular position. It is shown how the peculiar properties of modular momentum enable us to predict new quantum effects with no classical analog, such as radiationless acceleration of charged particles. The concept of modular energy is introduced and its usefulness is shown by suggesting new interesting quantum effects. The two-slit electron interference experiment is discussed in terms of modular momentum. Some further applications of modular variables are outlined, and the difference between classical and quantum mechanical non-locality is considered.
- Quantum Theory and Relativity