Schwinger J. Quantum kinematics and dynamics 2000

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Early in 1955 I began to write an article on the Quantum Theory of Fields. The introduction contained this description of its plan. "In part A of this article a general scheme of quantum kinematics and dynamics is developed within the nonrelativistic framework appropriate to systems with a finite number of dynamical variables. Apart from specific physical consequences of the rclativistic invariance requirement, the extension to fields in part B introduces relatively little that is novel, which permits the major mathematical features of the theory of fields to be discussed in the context of more elementary physical systems."
A preliminary and incomplete version of part A was used as the basis of lectures delivered in July, 1955 at the Les Houches Summer School of Theoretical Physics. Work on part A ceased later that year and part B was never begun. Several years after, I usedsome of the material in a series of notes published in the Proceedings of the National Academy of Sciences. And there the matter rested until, quite recently, Robert Kohler (State University College at Buffalo) reminded me of the continuing utility of the Les Houches notes and suggested their publication. He also volunteered to assist in this process. Here is the result. The main text is the original and still incomplete 1955 manuscript, modified only by the addition of subheadings. To it is appended excerpts from the Proc. Nat. Acad. of Sciences articles that supplement the text, together with two papers that illustrate and further develop its methods.
The Algebra of Measurement
The Geometry of States
The Dynamical Principle
The Special Canonical Group
Canonical Transformations
Groups of Transformations
Canonical Transformation Functions
Green's Functions
Some Applications And Further Developments