# Universal local symmetries and nonsuperposition in classical mechanics.

@article{Gozzi2010UniversalLS, title={Universal local symmetries and nonsuperposition in classical mechanics.}, author={Ennio Gozzi and Carlo D. Pagani}, journal={Physical review letters}, year={2010}, volume={105 15}, pages={ 150604 } }

In the Hilbert space formulation of classical mechanics, pioneered by Koopman and von Neumann, there are potentially more observables than in the standard approach to classical mechanics. In this Letter, we show that actually many of those extra observables 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. Because of their noninvariance, those extra observables have to…

## 15 Citations

### Hilbert space theory of classical electrodynamics

- Physics
- 2014

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics…

### Path Integrals for (Complex) Classical and Quantum Mechanics

- Physics
- 2011

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit…

### On deformations of classical mechanics due to Planck-scale physics

- Physics
- 2019

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification…

### From Koopman–von Neumann theory to quantum theory

- Physics
- 2018

Koopman and von Neumann (KvN) extended the Liouville equation by introducing a phase space function $$S^{(K)}(q,p,t)$$S(K)(q,p,t) whose physical meaning is unknown. We show that a different S(q, p,…

### Operational dynamic modeling transcending quantum and classical mechanics.

- PhysicsPhysical review letters
- 2012

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 the metric structure of time in classical and quantum mechanics

- Physics, MathematicsAnnals of Physics
- 2019

### Classical Propagation in the Quantum Inverted Oscillator

- Physics
- 2016

We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion…

## References

SHOWING 1-10 OF 17 REFERENCES

### Mardsen, Foundation of mechanics (Benjamin

- New York,
- 1978

### 315 (1931) and J. von Neumann

- Proc. Natl. Acad. Sci. U.S.A
- 1932

### Nucl. Phys. B

- Nucl. Phys. B
- 1974

### Ann. of Phys

- Ann. of Phys
- 2005

### Phys

- Rev. A 11, 2043
- 1975

### Adavanced Quantum Mechanics

- an outline of the foundamental ideas
- 1965

### Phys

- Rew. D 62, 067702 (2000), hep-th/9903136; E. Gozzi and D. Mauro, J. Math. Phys. 41, 1916
- 2000

### Phys. Rev. A

- Phys. Rev. A
- 1975

### Nucl

- Phys. B 76, 477
- 1974