# Path-integral approach to 't Hooft's derivation of quantum physics from classical physics

@article{Blasone2004PathintegralAT, title={Path-integral approach to 't Hooft's derivation of quantum physics from classical physics}, author={Massimo Blasone and Petr Jizba and Hagen Kleinert}, journal={Physical Review A}, year={2004}, volume={71}, pages={052507} }

We present a path-integral formulation of 't Hooft's derivation of quantum physics from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.

## 28 Citations

### THE GAUGE SYMMETRY OF THE THIRD KIND AND QUANTUM MECHANICS AS AN INFRARED LIMIT

- Physics
- 2007

We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thus, quantum mechanical systems are dissipatively embedded into a nonlinear classical…

### 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…

### General linear dynamics – quantum, classical or hybrid

- Physics
- 2011

We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of…

### A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

- Physics
- 2008

Abstract
A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger…

### 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.

### Quantum Fields, Cosmological Constant and Symmetry Doubling

- Physics
- 2007

We explore how energy-parity, a protective symmetry for the cosmological constant [Kaplan and Sundrum, 2005], arises naturally in the classical phase space dynamics of matter.We derive and generalize…

### Reconsidering Born's Postulate and Collapse Theory

- Physics
- 2013

We investigate the possibility that the amplitude of quantum wave can have a deeper physical meaning other than the probabilistic interpretation base on Born’s postulate. We find that the…

## References

SHOWING 1-10 OF 161 REFERENCES

### Path Integrals in Quantum Mechanics

- Physics
- 2007

We present the path integral formulation of quantum mechanics and demonstrate its equivalence to the Schrödinger picture. We apply the method to the free particle and quantum harmonic oscillator,…

### A NOVEL APPROACH TO NONCOMMUTATIVITY IN PLANAR QUANTUM MECHANICS

- Physics
- 2001

Noncommutative algebra in planar quantum mechanics is shown to follow from 't Hooft's recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a…

### Path integrals in quantum mechanics

- Physics
- 2005

1. Gaussian integrals 2. Path integral in quantum mechanics 3. Partition function and spectrum 4. Classical and quantum statistical physics 5. Path integrals and quantization 6. Path integral and…

### Constrained Dynamics: With Applications to Yang-Mills Theory, General Relativity, Classical Spin, Dual String Model

- Physics
- 1982

Classical regular systems.- Classical singular systems.- The reduced phase-space.- Quantization of constrained systems.- The electromagmetic field.- Yang-Mills theory.- The relativistic particle.-…

### Quantization of the relativistic particle

- Physics
- 2000

We revise the problem of quantizing the relativistic particle. We present the modified canonical scheme, which allows us to construct the consistent relativistic quantum mechanics as well as to…

### Quantum Dissipation and Quantum Noise

- Physics
- 1995

Abstract We derive the exact action for a damped mechanical system (and the special case of the linear oscillator) from the path integral formulation of the quantum Brownian motion problem developed…

### A canonical approach to the quantization of the damped harmonic oscillator

- Physics
- 2001

We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the…