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A characteristic glimpse of the renormalization group
1.See, e.g., K. G. Wilson and J. B. Kogut, Phys. Rep. C 12, 75 (1974).
2.G. Jona‐Lasinio, Nuovo Cimento B 26, 99 (1975).
3.Although not explicitly used, one simple bound on the support of μ often applies. Assume that positive numbers and test Variables exist such that (i) equality holding only if and (ii) Then μ is supported on the space of random variables
4.G. C. Hegerfeldt and J. R. Klauder, Commun. Math. Phys. 16, 329 (1970). The arguments given therein are readily specialized to cover the present case. For simplicity, we assume that nonzero nonfunctional test variables for which for all real λ are excluded.
5.The idealized expression is probably more familiar below the critical temperature than the one in the text. But for these two choices of characteristic function the metrics are equivalent, and the spaces of allowed test variables are identical.
6.E. Brezin, J. C. LeGuillon, and J. Zinn‐Justin, “Field Theoretical Approach to Critical Phenomena,” in Phase Transitions and Critical Phenomena, Vol. 6, edited by C. Domb and M. S. Green (Academic, New York, to be published).
7.A. Aharony, “Dependence of Universal Critical Behavior on Symmetry and Range of Interaction,” in Ref. 6.
8.J. R. Klauder, Acta Physica Austr. Suppl. VIII, 227 (1971);
8.in Mathematical Methods in Theoretical Physics, Lectures in Theoretical Physics, Vol. XIVB, edited by W. E. Britten (Colorado Associated U.P., Boulder, 1974), p. 329.
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