CRITICAL EXPONENTS, SCALING LAW, UNIVERSALITY AND RENORMALIZATION GROUP FLOW IN STRONG COUPLING QED

The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

THE BOUND ON THE RENORMALIZED CHARGE IN QUANTUM ELECTRODYNAMICS AND IN THE WESS-ZUMINO MODEL

An upper bound on the renormalized coupling constant α≤3πε+O(ε2) is found in quantum electrodynamics in n=4–2ε space-time. Analogous bound is obtained for a la Speer regularized Wess-Zumino model. The obtained bound means the triviality of QED and the Wess-Zumino model in the limit of the regularization removing.