Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0905.2320

Classical and Quantum Theory with a New Symmetry

Partha Ghose

Published May 14, 2009• 0 citations
arXivHTMLPDF

Abstract

A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic degrees of freedom and to be a connection in a non-flat space-time manifold, and (b) leads to a quantum theory free of the measurement problem. It is speculated that gravitomagnetism could be a possible source of the gauge field.

DOI
10.48550/arxiv.0905.2320

Related papers

The Origin of Quantum Mechanics

Ruhi Abdallah

In this paper, we derive the full quantum mechanics theory and its postulates from a totally classical field theory. We just extend the Lorentz symmetry group of space-time by adding a new simple abelian symmetry, gauge them both, and find the resultant equations of motion. Then, all the postulates of quantum mechanics, including spin and the Planck constant, are derived easily and naturally. The interpretation of quantum mechanics gets new insights. Furthermore, the speed of light constant, the number of space-time dimensions, and the Minkowskian metric are derived as collateral results. all in one piece, however ambitious it may seem, it just works. In short, Quantum mechanics is a classical field theory after all, mathematically proven.

•Sep 15, 2025•0 citations

Aspects of Gauge Quantum Mechanics on Non-Simply Connected Spaces

Asao Arai

A class of representations of the canonical commutation relations is constructed in a quantum theory of a particle moving in an external (non-Abelian) gauge field on a non-simply connected space in three space dimensions. A coupling to a Bose field of the particle is also discussed.

CRC Press eBooks•Nov 27, 2020•0 citations

Symmetries, variational principles, and quantum dynamics

J. Manjavidze, A. N. Sissakian

We describe the role of symmetries in formation of quantum dynamics. A quantum version of d′Alembert′s principle is proposed to take into account the symmetry constrains more exact. It is argued that the time reversibility of quantum process, as the quantum analogy of d′Alembert′s principle, makes the measure of the corresponding path integral δ‐like. The argument of this δ‐function is the sum of all classical forces of the problem under consideration plus the random force of quantum excitations. Such measure establishes the one‐to‐one correspondence with classical mechanics and, for this reason, allows a free choice of the useful dynamical variables. The analysis shows that choosing the action‐angle variables, one may get to the free‐from‐divergences quantum field theory. Moreover, one can try to get an independence from necessity to extract the degrees of freedom constrained by the symmetry. These properties of new quantization scheme are vitally essential for such theories as the non‐Abelian Yang‐Mills gauge theory and quantum gravity.

arXiv:hep-ph/0201182•Discrete Dynamics in Nature and Society•Jan 1, 2004•0 citations

Noncommutative Spacetime and Quantum Mechanics

Jaroslaw Wojciech Wawrzycki

In this paper we will analyze the the status of gauge freedom in quantum mechanics (QM) and quantum field theory (QFT). Along with this analysis comparison with ordinary QFT will be given. We will show how the gauge freedom problem is connected with the spacetime coordinates status - the very point at which the difficulties of QM begin. A natural solution of the above mentioned problem will be proposed in which we give a slightly more general form of QM and QFT (in comparison to the ordinary QFT) with noncommutative structure of spacetime playing fundamental role in it. We achieve it by reinterpretation of the Bohr's complementarity principle on the one hand and by incorporation of our gauge freedom analysis on the other. We will present a generalization of the Bargmann's theory of exponents of ray representations. It will be given an example involving time dependent gauge freedom describing non-relativistic quantum particle in nonrelativistic gravitational field. In this example we infer the most general Schroedinger equation and prove equality of the (passive) inertial and the gravitational masses of quantum particle.

arXiv:quant-ph/0404028•Apr 5, 2004•0 citations

Emergent quantum mechanics and emergent symmetries

Gerard ’t Hooft

Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes generated by general coordinate transformations. Thus, local gauge symmetries and general coordinate invariance could be emergent symmetries, and this might lead to new alleys towards understanding the flatness problem of the Universe. Presented at the 13th International Symposium on Particles, Strings and Cosmology, PASCOS, Imperial College, London, July 6, 2007

•Jan 1, 2007•57 citations

Quantum mechanics without spacetime 1- A case for noncommutative geometry-

T. P. Singh

Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a consequence that standard linear quantum mechanics is a limiting case of an underlying non-linear quantum theory. A possible approach to the new formulation is through the use of noncommuting spacetime coordinates in noncommutative differential geometry. Here, the non-linear theory is described by a non-linear Schrodinger equation which belongs to the Doebner-Goldin class of equations, discovered some years ago. This mass-dependent non-linearity is significant when particle masses are comparable to Planck mass, and negligible otherwise. Such a nonlinearity is in principle detectable through experimental tests of quantum mechanics for mesoscopic systems, and is a valuable empirical probe of theories of quantum gravity. We also briefly remark on the possible connection our approach could have with loop quantum gravity and string theory.

•Jan 1, 2005•0 citations
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic degrees of freedom and to be a connection in a non-flat space-time manifold, and (b) leads to a quantum theory free of the measurement problem. It is speculated that gravitomagnetism could be a possible source of the gauge field.
In this paper, we derive the full quantum mechanics theory and its postulates from a totally classical field theory. We just extend the Lorentz symmetry group of space-time by adding a new simple abelian symmetry, gauge them both, and find the resultant equations of motion. Then, all the postulates of quantum mechanics, including spin and the Planck constant, are derived easily and naturally. The interpretation of quantum mechanics gets new insights. Furthermore, the speed of light constant, the number of space-time dimensions, and the Minkowskian metric are derived as collateral results. all in one piece, however ambitious it may seem, it just works. In short, Quantum mechanics is a classical field theory after all, mathematically proven.
We describe the role of symmetries in formation of quantum dynamics. A quantum version of d′Alembert′s principle is proposed to take into account the symmetry constrains more exact. It is argued that the time reversibility of quantum process, as the quantum analogy of d′Alembert′s principle, makes the measure of the corresponding path integral δ‐like. The argument of this δ‐function is the sum of all classical forces of the problem under consideration plus the random force of quantum excitations. Such measure establishes the one‐to‐one correspondence with classical mechanics and, for this reason, allows a free choice of the useful dynamical variables. The analysis shows that choosing the action‐angle variables, one may get to the free‐from‐divergences quantum field theory. Moreover, one can try to get an independence from necessity to extract the degrees of freedom constrained by the symmetry. These properties of new quantization scheme are vitally essential for such theories as the non‐Abelian Yang‐Mills gauge theory and quantum gravity.
In this paper we will analyze the the status of gauge freedom in quantum mechanics (QM) and quantum field theory (QFT). Along with this analysis comparison with ordinary QFT will be given. We will show how the gauge freedom problem is connected with the spacetime coordinates status - the very point at which the difficulties of QM begin. A natural solution of the above mentioned problem will be proposed in which we give a slightly more general form of QM and QFT (in comparison to the ordinary QFT) with noncommutative structure of spacetime playing fundamental role in it. We achieve it by reinterpretation of the Bohr's complementarity principle on the one hand and by incorporation of our gauge freedom analysis on the other. We will present a generalization of the Bargmann's theory of exponents of ray representations. It will be given an example involving time dependent gauge freedom describing non-relativistic quantum particle in nonrelativistic gravitational field. In this example we infer the most general Schroedinger equation and prove equality of the (passive) inertial and the gravitational masses of quantum particle.
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes generated by general coordinate transformations. Thus, local gauge symmetries and general coordinate invariance could be emergent symmetries, and this might lead to new alleys towards understanding the flatness problem of the Universe. Presented at the 13th International Symposium on Particles, Strings and Cosmology, PASCOS, Imperial College, London, July 6, 2007
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a consequence that standard linear quantum mechanics is a limiting case of an underlying non-linear quantum theory. A possible approach to the new formulation is through the use of noncommuting spacetime coordinates in noncommutative differential geometry. Here, the non-linear theory is described by a non-linear Schrodinger equation which belongs to the Doebner-Goldin class of equations, discovered some years ago. This mass-dependent non-linearity is significant when particle masses are comparable to Planck mass, and negligible otherwise. Such a nonlinearity is in principle detectable through experimental tests of quantum mechanics for mesoscopic systems, and is a valuable empirical probe of theories of quantum gravity. We also briefly remark on the possible connection our approach could have with loop quantum gravity and string theory.