- Access by Xinjiang University
The Second-Quantized Theory of Spin-½ Particles in the Nonrelativistic Limit
Phys. Rev. 86, 340 – Published 1 May, 1952
DOI: https://doi.org/10.1103/PhysRev.86.340
Abstract
The second-quantized Dirac Hamiltonian for free electrons is transformed by a canonical transformation to a representation in which the positive and negative energy wave operators are separately represented by two-component operators. The transformation employed is the second-quantized analog of the one derived by Foldy and Wouthuysen in their discussion of the one-particle Dirac theory and its nonrelativistic limit. This transformation is then applied to the wave operators and the Hamiltonian in the second-quantized, charge-conjugate formalism for Dirac particles. The wave operators for positrons and electrons become linearly-independent two-component operators, and the Hamiltonian separates into an electron and a positron part, each of which contains only the corresponding two-component wave operators.
It is also shown that by means of an appropriate, readily determinable sequence of canonical transformations, Hamiltonians for fields of spin-½ particles interacting via intermediary fields can also be reduced to nonrelativistic form. This is accomplished by transforming the Hamiltonian to a representation in which it is exhibited effectively as a series expansion in powers of the Compton wavelength of the spin-½ particle. Illustration of the method is provided by detailed examination of the case of nucleons interacting via the pseudoscalar meson field.
References (6)
- L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950) Foldy and Wouthuysen in unpublished
- L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Company, Inc., New York, 1949), p. 351
- W. Heitler, The Quantum Theory of Radiation (Oxford University Press, London, 1949), second edition, p. 86
- K. M. Case, Phys. Rev. 76, 14 (1949)
- M. Sugarawara and Y. Ono, Prog. Theoret. Phys. 5, 901 (1950)
- S. Tani, Prog. Theoret. Phys. 6, 267 (1951)