## 27 Citations

### Classical and Quantum Mechanics via Supermetrics in Time

- Physics
- 2010

Koopman-von Neumann in the 30’s gave an operatorial formulation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this…

### Variational approach to dequantization

- Physics
- 2005

We present a dequantization procedure based on a variational approach whereby quantum fluctuations latent in the quantum momentum are suppressed. This is done by adding generic local deformations to…

### 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…

### 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,…

### 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…

### Geometric Dequantization of Spin

- Physics
- 2004

In this Letter we propose two path integral approaches to describe the classical mechanics of spinning particles. We show how these formulations can be derived from the associated quantum ones via a…

### 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.

### Projective representation of the Galilei group for classical and quantum–classical systems

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman–von Neumann formulation of classical mechanics. This classical representation…

## References

SHOWING 1-10 OF 26 REFERENCES

### Introduction to Supersymmetry and Supergravity

- Physics, Geology
- 1983

Over the past years, we have witnessed a dramatic increase in “public interest” in supersymmetry and super gravity. This interest cannot as yet be based on any solid experimental facts, but it has…

### Path Integrals in Quantum Mechanics Statistics and Polymer Physics

- Physics
- 1990

Elementary properties and simple solutions external sources, correlation function and perturbation theory semiclassical time displacement amplitude Feynman-Kleinert variational approach and…

### Field Theory: A Path Integral Approach

- Physics
- 1993

Path Integrals and Quantum Mechanics Harmonic Oscillator Generating Functional Path Integrals for Fermions Supersymmetry Semi-Classical Methods Path Integral for the Double Well Path Integral for…

### Quantum theory of many-variable systems and fields

- Physics
- 1985

These lecture notes are based on special courses on Field Theory and Statistical Mechanics given for graduate students at the City College of New York. It is an ideal text for a one-semester course…

### For a review of geometric quantization see for example: N. Woodhouse, " Geometric Quantization

- For a review of geometric quantization see for example: N. Woodhouse, " Geometric Quantization
- 1980

### ) we have a commutator and not an anticommutator

- Comparing (F.6) and (F.7) we obtain that the non-zero graded commutators are: [q, λ q ] = i

### Phys. Rev D

- Phys. Rev D
- 1989

### Topics in KvN Theory

- Ph.D. thesis, Trieste 2003 [quant-ph/0301172]; D. Mauro, Int. J. Mod. Phys. A 17 (2002), 1301 [quant-ph/0105112]; E. Gozzi and D. Mauro, Ann. Phys. 296 (2002) 152 [quant-ph/0105113]; E. Gozzi and D. Mauro, Int. J. Mod. Phys. A 19 (2004), 1475 [quant-ph/0306029]; E. Deotto, D. Mauro and E. Gozzi, J.
- 2003

### THE FOUNDATIONS OF MECHANICS.

- EducationScience
- 1918

Find the secret to improve the quality of life by reading this foundations of mechanics, which can be your favorite book to read after having this book.