Some Notes on Nonrenormalizable Field Theory
- 1 October 1955
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 100 (1), 362-370
- https://doi.org/10.1103/physrev.100.362
Abstract
Some nonrecoil, derivative coupling theories, which are exactly soluble, are analyzed in order to discover what it is that produces the nonrenormalizable behavior typical of derivative coupling. This behavior is found to arise as the result of an essential singularity which the operators of the derivative theories possess at the origin in coordinate space and the resulting branch point the Fourier transforms of these operators possess at the origin in the complex coupling constant domain. This branch point causes the breakdown of the expansion of the Fourier transform of the operators in powers of the coupling constant and introduces the nonrenormalizable infinities. It is shown that a coordinate space coupling constant expansion is possible, and that a Fourier transform of the operators of the derivative theories may be defined by analytic continuations and made finite by renormalization.Keywords
This publication has 5 references indexed in Scilit:
- Renormalization of Derivative Coupling TheoriesPhysical Review B, 1955
- Propagators of quantized fieldIl Nuovo Cimento (1869-1876), 1955
- Some Special Examples in Renormalizable Field TheoryPhysical Review B, 1954
- Field equations in functional formProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1954
- Space-Time Approach to Non-Relativistic Quantum MechanicsReviews of Modern Physics, 1948