Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-07-19
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, REVTEX Figure is not added. Please send e-mail to "hasimoto@newton.apphy.fukui-u.ac.jp" for request
Scientific paper
It is shown that the difficulties in formulating the quantum field theory on discrete spacetime appear already in classical dynamics of one degree of freedom on discrete time. The difference equation of motion which maintains a conserved quantity like energy has a very restricted form that is not probably derived by the least action principle. On the other hand, the classical dynamics is possible to be canonically formulated and quantized, if the equation is derived from an action. The difficulties come mainly from this incompatibility of the conserved quantity and the action principle. We formulate a quantum field theory canonically on discrete spacetime in the case where the field equation is derived from an action, though there may be no exactly conserved quantity. It may, however, be expected that a conserved quantity exists for a low "energy" region.
Hashimoto Takaaki
Hayashi Akihisa
Horibe Minoru
Yamamoto Hiroshi
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