The Rearrangement of Symmetries in Dynamical Maps

概要

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An attempt to describe symmetries and broken symmetries simultaneously in field theory leads to a formulation in which the Heisenberg, Schrodinger and interaction representations, as well as the Hamiltonian and unphysical particles, are not called upon. The key idea is to start from the formal structure of interacting field equations for basic fields, which define the symmetries and specify the dynamics, and to obtain the possible consistent expressions, called dynamical maps, of the basic fields in terms of incoming fields of observable particles. General principles for the construction of dynamical maps are indicated. The dynamical map determines the commutation properties of the basic fields. The Goldstone theorem is examined for various cases of canonical dynamical maps, and in these cases symmetries of the basic fields appear to be rearranged to the gauge invariance of Goldstone fields. Three examples corroborating the general conclusions are cited of the construction of dynamical maps in the pair approximation.
理論物理学刊行会の論文
1965-09-00