It is shown how to obtain the Dirae commutator, [x,p] = ih, from the London-Weyl formalism.PACS numbers: 03.65.Ca This paper employs London's treatment of Weyl's unified field theory to deduce the Dirac commutator. 1 Although new phenomena are not necessarily implied, the work may be of interest in that it shows how quantum mechanics can be obtained from a relativistic formalism. 2 London's paper is explicit regarding its quantum mechanical implications. London derives the Bohr-Sommerfeld quantization conditions and finds a flux quantization condition which years later he applies to superconductors. 3 London's paper, however, has been largely ignored. This is unfortunate in view of the modern revival of interest in gauge theory, for it was London's paper that alerted Weyl to the importance of gauge symmetry in quantum mechanics. The paper appeared as modern quantum mechanics was displacing the Bohr-Sommerfeld formulation. London's results were apparently seen as a coincidence. Given the current view which places gauge symmetry at the heart of physical description, one might be prepared to reconsider whether London's work is not, perhaps, a signature of something deeper.The origin of quantum mechanics in the London-Weyl formalism can be attributed to the fact that Weyl's geometry is projective. 4 The "observables" of Weyl's geometry are projections, as is the case in quantum mechanics. 5 Unitary symmetry is also important, this feature having been considered by London. London did not obtain the full quantum mechanics, however, as he did not treat position and momentum variables as equally fundamental. This paper considers the possibility of formulating "phase space" with a London-Weyl geometry and finds, heuristically, that the full quantum mechanics is involved. A more searching treatment of this paper's thesis is being considered. Quantum logic, particularly Mackey's systems of imprimitives, seems to provide a fairly decisive framework with which to proceed. 6 What is peculiar and alluring about this work is its suggestion that the questions of unification, quantization, and renormalization are not independent.Consider how one goes about unfolding Weyl's
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.