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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Quantization of generalized mechanics

Charles F. Hayes, J. M. Jankowski

Published Dec 1, 1968• 16 citations
Publisher
DOI
10.1007/bf02712004

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We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization. 1 The neccessity of quantum mechanics (QM) was a result of experimental data for the energy spectrum of atoms which could not be explained in accord with the laws of classical mechanics. Nevertheless in the axiomatic basis of QM there are axioms which are not supported by the experimental results, since the whole system of axioms (1) is introduced only as a ”plausible generalization ” of the first axiom [1]:

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Mechanics as a general-relativistic gauge field theory, and relational quantization

Jordan François, Lucrezia Ravera

We treat the mechanics of point particles as a one-dimensional general-relativistic gauge field theory, which may be referred to as mechanical field theory (MFT), exploiting the bundle geometry of mechanical field space (MFS). The diffeomorphism covariance of MFT encodes its relational character, arising—as in all general-relativistic physics—via the conjunction of a hole and a point-coincidence argument. Any putative “boundary problem,” meaning the claim that “spacetime” boundaries break diffeomorphism and gauge symmetries, thereby dissolves. It is highlighted that the standard path integral (PI) on the MFS, the exact analog of the PI used in gauge field theory, is conceptually and technically from the standard PI of quantum mechanics. We then use the dressing field method to give a manifestly invariant and relational reformulation of MFT, which reproduces the standard textbook formulation when a clock field is chosen as a (natural) dressing field. The dressed, or basic, PI on the MFS, defining i.e., the quantization of invariant relational degree of freedom—is shown to reproduce the standard PI of quantum mechanics. This establishes the soundness of relational quantization as a general guiding principle: We outline it for general-relativistic gauge field theories.

arXiv:2510.19845•APS Open Science•Aug 19, 2026•0 citations
We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization. 1 The neccessity of quantum mechanics (QM) was a result of experimental data for the energy spectrum of atoms which could not be explained in accord with the laws of classical mechanics. Nevertheless in the axiomatic basis of QM there are axioms which are not supported by the experimental results, since the whole system of axioms (1) is introduced only as a ”plausible generalization ” of the first axiom [1]:
We treat the mechanics of point particles as a one-dimensional general-relativistic gauge field theory, which may be referred to as mechanical field theory (MFT), exploiting the bundle geometry of mechanical field space (MFS). The diffeomorphism covariance of MFT encodes its relational character, arising—as in all general-relativistic physics—via the conjunction of a hole and a point-coincidence argument. Any putative “boundary problem,” meaning the claim that “spacetime” boundaries break diffeomorphism and gauge symmetries, thereby dissolves. It is highlighted that the standard path integral (PI) on the MFS, the exact analog of the PI used in gauge field theory, is conceptually and technically from the standard PI of quantum mechanics. We then use the dressing field method to give a manifestly invariant and relational reformulation of MFT, which reproduces the standard textbook formulation when a clock field is chosen as a (natural) dressing field. The dressed, or basic, PI on the MFS, defining i.e., the quantization of invariant relational degree of freedom—is shown to reproduce the standard PI of quantum mechanics. This establishes the soundness of relational quantization as a general guiding principle: We outline it for general-relativistic gauge field theories.