Abstract
The effective action is an important tool in modern quantum field theory. In particular it can be used to probe the non-perturbative vacuum structure of a theory. Examples of this are provided by the Coleman-Weinberg1 mechanism in scalar QED, self-consistent dimensional reduction in Kaluza-Klein theory2–12, and ß-function techniques for evaluating the field equations for the target space metric in non-linear σ-models13–14. In non-perturbative applications, it is generally necessary to evaluate the effective action off-shell. It is well known, however, that the off-shell effective action as usually defined is both gauge dependent and reparametrization dependent. Reparametrization dependence means that under a field redefinition φ → φ’, the new effective action Γ’ [φ’] does not equal the original one Γ[φ] evaluated at the same phissical field φ. In terms more appropriate to the following discussion, one might say that the effective action is not a scalar function of the configuration space coordinates.
While I was walking on the stair I met a man who wasn’t there. He wasn’ there again today I wish that he would stay away. Author unknown
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© 1987 Plenum Press, New York
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Kunstatter, G. (1987). Vilkovisky’s Unique Effective Action: An Introduction and Explicit Calculation. In: Lee, H.C., Elias, V., Kunstatter, G., Mann, R.B., Viswanathan, K.S. (eds) Super Field Theories. NATO Science Series, vol 160. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0913-0_28
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DOI: https://doi.org/10.1007/978-1-4613-0913-0_28
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