Proceedings of the Royal Society of London A Mathematical and Physical Sciences

On Schwinger’s variational principle

T. W. B. Kibble, John Charlton Polkinghorne

Published Dec 24, 1957• 21 citations

Abstract

Abstract The classical and quantum theories of dynamical systems whose Lagrangians are linear in the co-ordinate derivatives are studied, with a view to clarifying a number of points in relation to Schwinger’s quantum-mechanical variational principle. In particular, linear variations of the dynamical variables are considered, and it is shown that they may be consistently included in Schwinger’s formalism. It is also found to be possible to obtain Green’s generalized commutation rules by excluding c number variations from the theory, for a suitably restricted class of Lagrangian.

DOI: 10.1098/rspa.1957.0218

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