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Prog. Theor. Phys. Vol. 59 No. 1 (1978) pp. 248-264
A Quantum Electrodynamics on a Lattice
Yuji Nakawaki
Faculty of Education, Setsunan University, Ikeda, Neyagawa 572
(Received May 7, 1977)
Abstract:
Aiming at incorporating the so-called “ε-separation method” into a consistent and finite formulation of quantum electrodynamics, we construct a quantum electrodynamics on a lattice. Thus we can put a reasonable interpretation on ε. The fermion field on a lattice is described by adopting the gradient operator of Drell et al. which solves the problem concerning degenerate energy levels of fermions on a lattice. An inverse operator for the gradient is defined to introduce vector potentials on a lattice. It is shown that a vector current similar to that of “ε-separation method” is thus obtained. It is shown that Ward identities of vector and axial vector currents are verified with the aid of sea gull terms and the remarkable property that we can shift origin of any loop integrals in the lattice theory. It is also shown that we cannot obtain usual local amplitudes taking the limit a →0 and that we may utilize loop integrals of the lattice theory as devices to regularize singularities of corresponding loops if we calculate loop integrals only over the region where all integral momenta are confined within their principal values.
URL :
http://ptp.ipap.jp/link?PTP/59/248/
DOI : 10.1143/PTP.59.248
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1197-1210
:
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Indication of Nonexistence of Adler Anomaly in Virture of Continuum Limit of the Lattice Theory for Fermions
-
Yuji Nakawaki
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Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1855-1857
:
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A New Choice for Two-Dimensional Dirac Equation on a Spatial Lattice
-
Yuji Nakawaki
