Prog. Theor. Phys. Vol. 94 No. 2 (1995) pp. 249-261
How to Quantize Fields Canonically on Discrete Space-Time
Department of Applied Physics, Fukui University, Fukui 910
*Department of Physics, Faculty of Education, Fukui University, Fukui 910
(Received November 16, 1994)
We propose a canonical procedure to quantize fields with interaction on discrete space-time. The time evolution operator that reproduces the field equation is represented by using canonical variables. The generator of the operator is a conserved quantity, but its existence is not obvious. It is possible to calculate the S-matrix perturbatively. Our quantization gives the same results as those given by the path integral quantization.
DOI : 10.1143/PTP.94.249
H. Yamamoto, Phys. Rev. D30 (1984), 1727[APS]; D32 (1985), 2659;
Nucl. Phys. B (Proc. Suppl.) 6 (1989), 154[CrossRef].
- H. Yamamoto, A. Hayashi, T. Hashimoto and M. Horibe, Prog. Theor. Phys. 93 (1995), 173[PTP].
- H. Yoshida, Conserved Quantities of Symplectic Integrators for Hamiltonian Systems (National Astronomical Observatory, Japan, Preprint, 1990).
- A. R. Hibbs and R. P. Feynman, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
- K. Osterwalder and R. Schrader, Comm. Math. Phys. 31 (1973), 83; 42 (1975), 281.
R. Haag and D. Kastler, J. Math. Phys. 5 (1964), 848[CrossRef].
A. Wightman and L. G\aarding, Ark. Fys. 28 (1965), 129.