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Genuine covariant description of Hamiltonian dynamics

Merced Montesinos

After reviewing the covariant description of Hamiltonian dynamics, some applications are done to the non-relativistic isotropic three-dimensional harmonic oscillator, Rovelli's model, and SO (3, 1) BF theories.

arXiv:gr-qc/0602072Journal of Physics Conference SeriesJan 1, 20055 citations

Covariance systems

Jan Naudts, Maciej Kuna

We introduce new definitions of states and representations of covariance systems. The GNS-construction is generalized in this context. It associates a representation with each state of the covariance system. Next, the states are extended to the states of an appropriate covariance algebra. Two applications are given. We describe a non-relativistic quantum particle and give a simple description of the quantum spacetime model introduced by Doplicher et al (Doplicher et al 1994 Phys. Lett. B 331 39, Doplicher et al 1995 Commun. Math. Phys. 172 187).We introduce new definitions of states and representations of covariance systems. The GNS-construction is generalized in this context. It associates a representation with each state of the covariance system. Next, the states are extended to the states of an appropriate covariance algebra. Two applications are given. We describe a non-relativistic quantum particle and give a simple description of the quantum spacetime model introduced by Doplicher et al (Doplicher et al 1994 Phys. Lett. B 331 39, Doplicher et al 1995 Commun. Math. Phys. 172 187).

arXiv:math-ph/0009031Journal of Physics A Mathematical and GeneralOct 19, 20018 citations

The G-dynamics of the QCPB theory

Gen Wang

In this paper, we further study the G-dynamics newly emerged in the covariant dynamics defined by the quantum covariant Poisson bracket (QCPB) theory. We propose three new operators based on the G-dynamics, we find that the non-Hermitian operators are inevitable to appear in the framework of the QCPB. Then we seek the precise formulations of the G-dynamics to calculate the practical quantum problems, the G-dynamics of three types in terms of different Hamiltonian are discovered. The geometrinetic energy operator for quantum harmonic oscillator as an application is further calculated.In this paper, we further study the G-dynamics newly emerged in the covariant dynamics defined by the quantum covariant Poisson bracket (QCPB) theory. We propose three new operators based on the G-dynamics, we find that the non-Hermitian operators are inevitable to appear in the framework of the QCPB. Then we seek the precise formulations of the G-dynamics to calculate the practical quantum problems, the G-dynamics of three types in terms of different Hamiltonian are discovered. The geometrinetic energy operator for quantum harmonic oscillator as an application is further calculated.

arXiv:2004.01001Mar 31, 20200 citations

On the non-relativistic motion equations in the hamiltonian form

В. И. Фущич, A. G. Nikitin, V. A. Salogub

Reports on Mathematical PhysicsApr 1, 19786 citations

A manifestly covariant hamiltonian formalism of relativistic quantum mechanics

Wanda Hanus

Reports on Mathematical PhysicsJan 1, 19710 citations

Relativistic Ladder Operators for the Three-Dimensional Harmonic Oscillator

Ducharme, Robert J.

The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillator. Correspondence to the Schrödinger equation for the harmonic oscillator in the non-relativistic limit is demonstrated.The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillator. Correspondence to the Schrödinger equation for the harmonic oscillator in the non-relativistic limit is demonstrated.

arXiv:0905.1750May 12, 20090 citations

Genuine covariant description of Hamiltonian dynamics

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Genuine covariant description of Hamiltonian dynamics

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