Titlebook: Quantum Physics; A Functional Integra James Glimm,Arthur Jaffe Textbook 19811st edition Springer-Verlag New York Inc. 1981 Finite.Identity.

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Phase Transitions 6.1, . can be decomposed into irreducible components ., called ., each of which satisfies the axioms OS0-4. The pure phases are characterized by the property OS4 of a unique vacuum, and . is itself a pure phase if and only if its vacuum state is unique.

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s, quantum mechanics, and quantum fields. The unity of mathemati- cal structure for problems of diverse origin in physics should be no surprise. For classical physics it is provided, for example, by a common mathematical formalism based on the wave equation and Laplace‘s equation. The unity transcen

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Phase Transitions and Critical Pointsstrongly correlated to a finite number of ξ., j ≠ .. The weak coupling situations are handled by expansions, as in Chapter 2, and should be regarded as perturbations of an infinite tensor product, zero interaction model.

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Estimates Independent of Dimensionhe bounds of this chapter do not depend on the lattice spacing. This is in contrast to the ultraviolet bounds of Chapter 8, which depend strongly on dimension. Section 12.2, i.e. integration by parts, is similarly independent of dimension.

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Regularity and Axiomsparts identities generate the perturbation expansion of Sections 8.4, 9.4 as well as the high and low temperature expansions studied in Part III and in the literature. These tools allow a detailed investigation of the local (ultraviolet) singularities of the models on the one hand and the large distance (infrared) decoupling on the other.