# A Method for Studying Model Hamiltonians. A Minimax Principle for Problems in Statistical Physics

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## Bogoli︠u︡bov, N. N. (Nikolaĭ Nikolaevich) 1909-1992

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## A Method For Studying Model Hamiltonians A Minimax Principle For Problems In Statistical Physics

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Originally, the axiomatic approach arose from attempts to give a mathematical meaning to the quantum field theory of strong interactions of Yukawa type. The fields in such a theory are realized by operators in Hilbert space with a positive Poincare-invariant scalar product. This "classical" part of the axiomatic approach attained its modern form as far back as the sixties. In fact, from the point of view of the quark model, the theory of strong interactions of Wightman type was obtained by restricting attention to just the "physical" local operators such as hadronic fields consisting of ''fundamental'' quark fields acting in a Hilbert space of physical states.

In principle, there are enough such "physical" fields for a description of hadronic physics, although this means that one must reject the traditional local Lagrangian formalism. The connection is restored in the approximation of low-energy "phe nomenological" Lagrangians. Analytic number theory, mathematical anaylsis and their applications : collection of papers dedicated to Academician Ivan Matveevic Vinogradov on his eighty-fifth birthday by N.

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### A METHOD FOR STUDYING MODEL HAMILTONIANS: A Minimax Principle for Problems in Statistical Physics.

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