Prog. Theor. Phys. Vol. 52 No. 2 (1974) pp. 688-706
On Quantum Field Theory. I
— Quantum Field Theory as Quantum Mechanics
Department of Physics, Kwansei Gakuin University, Nishinomiya 662
(Received December 26, 1973)
A new approach to finding a steady foundation of quantum field theory is investigated with the help of the so-called non-standard mathematics. We construct a model of the quantum field theory as quantum mechanical system with very much degrees of freedom. The importance of the notion of the models incidental to the formally given quantum field theory and the notion of their physical equivalence are strongly emphasized.
DOI : 10.1143/PTP.52.688
- G. Takeuchi, Proc. Jap. Acad. 38 (1962).
A. Robinson, Non-Standard Analysis (North-Holland, 1965).
See also, P. J. Kelemen and A. Robinson, J. Math. Phys. 13 (1972), 1870[CrossRef].
R. Kambe, Talk at the Research Institute for Mathematical Sciences, Kyoto (1973).
- R. Jost, (ed.) `Local Quantum Theory' in the Proceedings of International School of Physics, “Enrico Fermi”, August, 1968 (Academic Press, New York, 1969).
R. Jost, The General Theory of Quantized Fields (Am. Math. Soc. Publications, Providence, 1963).
R. F. Streater and A. S. Wightman, PCT, Spin & Statistics, and All That (Benjamin, New York, 1964).
N. N. Bogoliubov, A. A. Logunov and I. T. Todorov, Axiomatic Quantum Field Theory (Benjamin, 1973).
- See, for example, R. Courant and D. Hilbert, Method of Mathematical Physics (Interscience, 1943).
P. Kristensen, L. Mejlbo and E. T. Poulsen, Commun. Math. Phys. 1 (1965), 175[CrossRef].
There, \hatΩ stand is denoted as \mathfrakS.