The Representation of Canonical Variables as the Limit of Infinite Space Volume: The Case of the BCS Model

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Abstract
We examine the possibility of obtaining the representation suitable for a given Hamiltonian through a limiting procedure. The model employed is that of the Bardeen‐Cooper‐Schrieffer's superconductivity theory, for which the infinite‐volume limit of the Wightman functions gives the right representation. This method is found to be helpful in analyzing the so‐called symmetry breaking solutions. In particular, it serves for throwing some light to the Haag's work on the gauge property of the BCS model as well as to the Nambu's dynamical model of elementary particles. What is meant by the limit of infinite volume is studied with regard to the convergence of the Hamiltonian operator.