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VII.—Quantum Mechanics of Fields. I. Pure Fields
Published online by Cambridge University Press: 14 February 2012
Extract
The difficulties met in the usual treatment of quantised field theories seem to us somewhat similar to those which occurred in Bohr's semi-classical quantum mechanics of particles. In this theory the orbits were described by Fourier series in the time; there was no exact correspondence between the periodic terms of this series and quantum transitions, but only an approximate one for terms of high order. Matrix mechanics considers not the Fourier series, but the single terms which are generalised into matrix elements having not one but two indices. This generalisation is founded on Ritz's combination principle.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 1 , 1944 , pp. 40 - 57
- Copyright
- Copyright © Royal Society of Edinburgh 1944
References
page 41 note † The order of the factors in (1.4) and later equations, although so far arbitrary, is chosen with regard to later application to non-commuting quantities.
page 45 note † Helv. Phys. Acla, VII. 1934, 709.Google Scholar
page 46 note † The reciprocals of the field components can be admitted also. Then in counting the number of factors with and without the asterisk the reciprocals are to be subtracted.
page 47 note † Zeits.f. Phys., XLIX, 1928, 339Google Scholar ; Phys. Zeits. Sowjet., VI, 1934. 425Google Scholar.
page 52 note † The commutation laws in this form for Fourier coefficients have been already obtained in the case of Maxwell's electromagnetic field by Novobatzki, Zeits.f. Physik, CXI, 1938, 293Google Scholar.
page 53 note † Cf. Pauli, W., Rev. Mod. Phys., XIII, 1941, 204.Google Scholar