Feynman's propagator in Schwinger's picture of Quantum Mechanics Articles uri icon

publication date

  • August 2021

start page

  • 1

end page

  • 17


  • 26


  • 36

International Standard Serial Number (ISSN)

  • 0217-7323

Electronic International Standard Serial Number (EISSN)

  • 1793-6632


  • A novel derivation of Feynman's sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics ispresented. It is shown that such construction corresponds to the GNS representation ofa natural family of states called Dirac-Feynman-Schwinger (DFS) states. Such statesare obtained from aq-Lagrangian function l on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and theq-Lagrangian l allows us to define a DFS state on the algebra of the groupoid. The particular instanceof the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman's original derivation of the propagator for a point particle described by a classical Lagrangian L.


  • Mathematics


  • feynman's propagator; groupoid algebras; groupoids; q -lagrangian; states