Ronald E. Kates

STOCHASTIC QUANTIZATION OF THE KINK SOLUTION OF ϕ4 FIELD THEORY

The method of Parisi-Wu Stochastic quantization in quantum field theory is compared to earlier work in classical field equations. The method is applied to solve for the propagator of ϕ4 field theory by perturbing the Kink solution.

Point-source idealization in classical field theories. I. Electromagnetic radiation damping of a system of two perturbed Reissner-Nordstroem singularities in the slow-motion limit

This paper calculates the leading resistive accelerations acting on a system of two slightly deformed Reissner-Nordstroem singularities due to the emission of electromagnetic radiation, using matched asymptotic expansions. The unperturbed Reissner-Nordstroem solutions are assumed to have large charge-to-mass ratios q/m and to be separated by a distance large compared to both m and q/sup 2//m. The problem is of interest primarily because of Rosenblums use of point singularities in his calculation of the mechanical work done in small-angle gravitational scattering. Classical derivations of the electromagnetic equations of motion for a charged source were faced with the choice between indeterminate equations and divergences in the stress-energy. The use of asymptotic expansions about Reissner-Nordstroem solutions makes renormalization arguments unnecessary. The following paper compares the mechanical energy loss obtained from the present matching calculation to that predicted by the Lorentz-Dirac equation; which was derived using a point-particle assumption.

Boundary conditions for zero‐rest‐mass fields in curved space‐time: A regularity theorem

This paper shows that for gravitational radiation from slow‐motion, harmonic sources, the formal power series obtained by expanding the O(e5) wave‐metric functions in inverse powers of r is a valid asymptotic expansion, provided the phase is expressed in terms of a properly strained null coordinate. The theorem proved here is useful for applying outgoing wave conditions in the neighborhood of I+.