Weyl's theory applied to some quantum-mechanical problems

The traditional Standard Quantum Mechanics (SQM) theory is unable to solve the Spin-s problem, i.e., to justify the utterly important "Pauli Exclusion Principle". A complete and straightforward solution of the Spin-Statistics problem is presented based on the "Weyl Integrable Quantum Mechanics" (WIQM) theory. This theory provides a Weyl-gauge invariant formulation of the Standard Quantum Mechanics and reproduces successfully, with no restrictions, the full set of the quantum mechanical processes, including the formulation of Dirac's or Schrödinger's equation, of Heisenberg's uncertainty relations, and of the nonlocal EPR correlations. etc. When the Weyl Integrable Quantum Mechanics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the "intrinsic helicity", or the "intrinsic angular - momentum". This additional particle property, not considered by Standard Quantum Mechanics, determines the correct Spin-Statistics Connection (SSC) observed in Nature. All this leads to the consideration of a novel, most complete (in the EPR sense) quantum mechanical theory.The traditional Standard Quantum Mechanics (SQM) theory is unable to solve the Spin-s problem, i.e., to justify the utterly important "Pauli Exclusion Principle". A complete and straightforward solution of the Spin-Statistics problem is presented based on the "Weyl Integrable Quantum Mechanics" (WIQM) theory. This theory provides a Weyl-gauge invariant formulation of the Standard Quantum Mechanics and reproduces successfully, with no restrictions, the full set of the quantum mechanical processes, including the formulation of Dirac's or Schrödinger's equation, of Heisenberg's uncertainty relations, and of the nonlocal EPR correlations. etc. When the Weyl Integrable Quantum Mechanics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the "intrinsic helicity", or the "intrinsic angular - momentum". This additional particle property, not considered by Standard Quantum Mechanics, determines the correct Spin-Statistics Connection (SSC) observed in Nature. All this leads to the consideration of a novel, most complete (in the EPR sense) quantum mechanical theory.

quant-pharXiv:2511.13360Nov 18, 20250 citations

The Weyl representation in classical and quantum mechanics

Alfredo M. Ozorio de Almeida

Physics ReportsMar 1, 1998212 citations

Solving the Quantum Nonlocality Enigma by Weyl's Conformal Geometrodynamics

Enrico Santamato, F. De Martini

Since the 1935 proposal by Einstein Podolsky and Rosen the riddle of nonlocality, today demonstrated by innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a non relativistic approach based on the Weyl's conformal differential geometry applied to the Hamilton-Jacobi solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the nonlocality rests on the entanglement of the spin internal variables, playing the role of "hidden variables". At the end, the violation of the Bell inequalities is demonstrated without recourse to the common nonlocality paradigm. A discussion over the role of the "% \textit{internal space"} of any entangled dynamical system involves deep conceptual issues, such the \textit{indeterminism} of quantum mechanics and explores the in principle limitations to any exact dynamical theory when truly "hidden variables" are present. Because of the underlying geometrical foundations linking necessarily gravitation and quantum mechanics, the theory presented in this work may be considered to belong to the unifying "quantum gravity" scenario.Since the 1935 proposal by Einstein Podolsky and Rosen the riddle of nonlocality, today demonstrated by innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a non relativistic approach based on the Weyl's conformal differential geometry applied to the Hamilton-Jacobi solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the nonlocality rests on the entanglement of the spin internal variables, playing the role of "hidden variables". At the end, the violation of the Bell inequalities is demonstrated without recourse to the common nonlocality paradigm. A discussion over the role of the "% \textit{internal space"} of any entangled dynamical system involves deep conceptual issues, such the \textit{indeterminism} of quantum mechanics and explores the in principle limitations to any exact dynamical theory when truly "hidden variables" are present. Because of the underlying geometrical foundations linking necessarily gravitation and quantum mechanics, the theory presented in this work may be considered to belong to the unifying "quantum gravity" scenario.

arXiv:1203.0033Feb 29, 20126 citations

The Principle of Uncertainty in Weyl's System

GREGORY A. BREIT

Using Weyl's geometrical interpretation of quantum mechanics the fundamental relations of the transformation theory can be treated without making use of Dirac's $\ensuremath{\delta}$ function. The principle of uncertainty is particularly clear in this system. It is shown that in the discrete representation for a definite axis of the coordinate $q$ all Eigenwerte of the conjugate momentum $p$ are equally probable. It is also shown how in the limit of very fine subdivision the results of Heisenberg and Bohr are obtained. The whole treatment receives an easy interpretation by applying it to the problem of the diffraction of waves by a grating. Weyl's method of discussing quantities with continuous ranges of values is found to be equivalent to investigating diffraction phenomena in the limiting case of an infinitesimal grating space. The quantum condition $i(PQ\ensuremath{-}QP)=1$ is shown to be correct in a purely operational sense in spite of the fact that as a matrix equation it is untrue.Using Weyl's geometrical interpretation of quantum mechanics the fundamental relations of the transformation theory can be treated without making use of Dirac's $\ensuremath{\delta}$ function. The principle of uncertainty is particularly clear in this system. It is shown that in the discrete representation for a definite axis of the coordinate $q$ all Eigenwerte of the conjugate momentum $p$ are equally probable. It is also shown how in the limit of very fine subdivision the results of Heisenberg and Bohr are obtained. The whole treatment receives an easy interpretation by applying it to the problem of the diffraction of waves by a grating. Weyl's method of discussing quantities with continuous ranges of values is found to be equivalent to investigating diffraction phenomena in the limiting case of an infinitesimal grating space. The quantum condition $i(PQ\ensuremath{-}QP)=1$ is shown to be correct in a purely operational sense in spite of the fact that as a matrix equation it is untrue.

Physical ReviewOct 1, 192813 citations

A deficiency of Weinberg's quantum mechanics

Debendranath Sahoo

Letters in Mathematical PhysicsJun 1, 19940 citations

q

all Eigenwerte of the conjugate momentum

p

are equally probable. It is also shown how in the limit of very fine subdivision the results of Heisenberg and Bohr are obtained. The whole treatment receives an easy interpretation by applying it to the problem of the diffraction of waves by a grating. Weyl's method of discussing quantities with continuous ranges of values is found to be equivalent to investigating diffraction phenomena in the limiting case of an infinitesimal grating space. The quantum condition $i(PQ\ensuremath{-}QP)=1$ is shown to be correct in a purely operational sense in spite of the fact that as a matrix equation it is untrue.