Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-01-25
Phys.Rev.D80:105001,2009
Physics
High Energy Physics
High Energy Physics - Theory
11 pages
Scientific paper
10.1103/PhysRevD.80.105001
There exists a paradox in quantum field theory: substituting a field configuration which solves a subset of the field equations into the action and varying it is not necessarily equivalent to substituting that configuration into the remaining field equations. We take the $S^4$ and Freund-Rubin-like instantons as two examples to clarify the paradox. One must match the specialized configuration field variables with the corresponding boundary conditions by adding appropriate Legendre terms to the action. Some comments are made regarding exceptional degenerate cases.
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