Classical dynamics from a unitary representation of the Galilei group

@article{BermdezManjarres2020ClassicalDF,
  title={Classical dynamics from a unitary representation of the Galilei group},
  author={A. D. Berm{\'u}dez Manjarres and M. Nowakowski and David Batic},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
4 Citations
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References

SHOWING 1-10 OF 65 REFERENCES
Geometrization of quantum mechanics
Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional
A new quantization map
Universal local symmetries and nonsuperposition in classical mechanics.
TLDR
It is shown that actually many of those extra observables in the Hilbert space formulation of classical mechanics are not invariant under a set of universal local symmetries which appear once the Koopman and von Neumann formulation is extended to include the evolution of differential forms.
The Galilean covariance of quantum mechanics in the case of external fields
Textbook treatments of the Galilean covariance of the time-dependent Schrodinger equation for a spinless particle seem invariably to cover the case of a free particle or one in the presence of a
Operational dynamic modeling transcending quantum and classical mechanics.
TLDR
It is shown that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory, and should provide a basis for formulating novel theories.
On Koopman-von Neumann Waves II
In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the
Minimal Coupling in Koopman–von Neumann Theory
Abstract Classical mechanics (CM), like quantum mechanics (QM), can have an operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in the 1930s. They basically formalized, via
Canonical Realizations of the Galilei Group
The general theory of the realizations of finite Lie groups by means of canonical transformations in classical mechanics, which has been developed in a preceding paper and already applied to the
ON KOOPMAN–VON NEUMANN WAVES II
In this paper, we continue the study started in Ref. 1, of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the 1930s. In particular, we show that the
Galilei Group and Nonrelativistic Quantum Mechanics
This paper is devoted to the study of the Galilei group and its representations. The Galilei group presents a certain number of essential differences with respect to the Poincare group. As Bargmann
...
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