Effective Equations of Motion for Quantum Systems

@article{Bojowald2005EffectiveEO,
  title={Effective Equations of Motion for Quantum Systems},
  author={Martin Bojowald and Aureliano Skirzewski},
  journal={Reviews in Mathematical Physics},
  year={2005},
  volume={18},
  pages={713-746}
}
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in… 
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References

SHOWING 1-10 OF 33 REFERENCES
Comparison between quantum and classical dynamics in the effective action formalism
A major difficulty in comparing quantum and classical behavior resides in the structural differences between the corresponding mathematical languages. The Heisenberg equations of motion are operator
Coherent states: Theory and some Applications
In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the
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
Quantum mechanics as a statistical theory
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the
Quantum mechanics as a classical theory.
  • Heslot
  • Physics
    Physical review. D, Particles and fields
  • 1985
TLDR
Basic features of quantum mechanics follow, such as the identification of observables with self-adjoint operators, and canonical quantization rules, which gives a new insight on the geometry of quantum theory.
Geometrical Formulation of Quantum Mechanics
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a Uhler manifold. This leads to a geometrical formulation
Mathematical structure of loop quantum cosmology
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big
Isotropic loop quantum cosmology
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a
Relativistic field theories with symmetry-breaking solutions
Following some recent developments in many-body theory, we suggest a functional approach to relativistic field theories particularly suitable to treat the case of symmetry breaking solutions. The
On the Low-Energy Ramifications and a Mathematical Extension of Loop Quantum Gravity
In this thesis we address two remaining open questions in loop quantum gravity. The first deals with the low-energy limit of the theory. We illustrate some of the conceptual difficulties and their
...
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