Vilkovisky-DeWitt Effective Action Research Articles

Stability of plasma oscillations in hot gluonic matter.

It is argued that the high-temperature gluon-plasma damping constants previously calculated by use of the background-field method and the Vilkovisky-DeWitt effective action do not have a physical interpretation since they are not derived from correlation functions relevant to linear-response theory. A correct application of the gauge- and parametrization-independent formalism does not affect the plasmon frequency, but yields the following modified results for the longitudinal and transverse damping constants: ..gamma../sub L/ = ..gamma../sub T/ = -(9/32..pi..)g/sup 2/NT. .AE

The Vilkovisky-DeWitt effective action for quantum gravity

The Vilkovisky-DeWitt effective action for gauge theories is reviewed and then discussed in the context of N-dimensional quantum gravity and quantum Kaluza-Klein theory. The formalism gives an effective action which is gauge-independent and gauge and field-parametrization invariant. These features are illustrated for the vacuum energy of N-dimensional gravity. The Bunch-Parker local momentum space approach is used to calculate also the induced Ricci scalar term in the expansion of the effective action in powers of the curvature. The effective field equations are applied to the self-consistent dimensional reduction of five-dimensional Kaluza-Klein theory. A solution exists, but is found to be physically unacceptable.

The Vilkovisky-DeWitt effective action and its application to Yang-Mills theories

In gauge theories both gauge invariance and gauge independence can be achieved by the reparametrization invariant definition of effective actions due to Vilkovisky and its amendment by DeWitt. In Yang-Mills theories we establish the precise connection to the conventional definition to all orders of perturbation theory. An explicit calculation in 2-loop order verifies the necessity of DeWitt's modification in order to preserve renormalization. Some of the new Feynman rules following from the Vilkovisky-DeWitt effective action are made explicit, and gauge independence of the new off-shell vertex functions is checked in the example of the non-abelian gauge field self energy evaluated in 1-loop order in various gauges. The novel definition of the effective action is then applied to spontaneously broken Yang-Mills theories to obtain a gauge independent renormalization group equation. The decoupling threshold of the running gauge coupling constant which is a crucial quantity in grand unified theories is computed to 1-loop accuracy.