Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-02-18
Int.J.Mod.Phys. A13 (1998) 2047-2074
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX
Scientific paper
10.1142/S0217751X98000901
Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical parameters of the theory. The relevant finiteness conditions resulting from this requirement relate all dimensionless couplings in the theory. At first sight, Yukawa couplings which are equivalent to the generators of some Clifford algebra with identity element represent a very promising type of solutions of the condition for one-loop finiteness of the Yukawa couplings. However, under few reasonable and simplifying assumptions about their particular structure, these Clifford-like Yukawa couplings prove to be in conflict with the requirements of one- and two-loop finiteness of the gauge coupling and of the absence of gauge anomalies, at least for all simple gauge groups up to and including rank 8.
Lucha Wolfgang
Moser Michael
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