ON THE STATISTICAL THEORY OF ELECTROMAGNETIC WAVES IN A FLUCTUATING MEDIUM (II). MATHEMATICAL BASIS OF THE ANALOGIES TO QUANTUM FIELD THEORY.
NATIONAL BUREAU OF STANDARDS BOULDER CO CENTRAL RADIO PROPAGATION LAB
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Many analogies to quantum field theory are inherent in the statistical theory of waves. This is due to the fact that basic equations exist in the latter theory which correspond closely to the fundamental equations of the former theory i.e., to the commutation relations and the Heisenberg equation of motion. A probability density function of waves is introduced which corresponds to the probability amplitude function in quantum mechanics. The boundary conditions at infinity for this probability density function are then found to be expressed in the same form as the vacuum boundary conditions in field theory. The theory of the statistical Greens functions and their relationships to the expectation values of the physical variables is also extensively developed, using auxiliary external sources of the wave and of the fluctuating medium. It is found that there exists a oneto-one correspondence between the formalism of Greens functions presented here and that used in field theory. The above correspondence may be important for a further development of the statistical theory of waves, just as the advanced techniques of field theory have greatly influenced the development of thermodynamics or statistical physics. Author