Reduced phase space quantization and Dirac observables

@article{Thiemann2006ReducedPS,
  title={Reduced phase space quantization and Dirac observables},
  author={Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={2006},
  volume={23},
  pages={1163 - 1180}
}
  • T. Thiemann
  • Published 6 November 2004
  • Mathematics
  • Classical and Quantum Gravity
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than structure constants. Here we use this framework and propose how to implement explicitly a reduced phase space quantization of a given system, at least in principle, without the need to compute the gauge equivalence classes. The degree of practicality of this… 
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References

SHOWING 1-10 OF 29 REFERENCES
Partial and complete observables for Hamiltonian constrained systems
We will pick up the concepts of partial and complete observables introduced by Rovelli in Conceptional Problems in Quantum Gravity, Birkhäuser, Boston (1991); Class Quant Grav, 8:1895 (1991); Phys
QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed
EXTENDED OBSERVABLES IN HAMILTONIAN THEORIES WITH CONSTRAINTS
In a classical Hamiltonian theory with second-class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are
Modern Canonical Quantum General Relativity
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the
Quantization of Gauge Systems
This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical
A complete set of observables for cylindrically symmetric gravitational fields
The author constructs a complete set of observables on the infinite-dimensional phase space of cylindrically symmetric gravitational fields. These observables have vanishing Poisson brackets with all
Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity
The quantization of Lorentzian or Euclidean 2 + 1 gravity by canonical methods is a well studied problem. However, the constraints of 2 + 1 gravity are those of a topological field theory and
Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories
It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague
Testing the master constraint programme for loop quantum gravity: I. General framework
TLDR
It is shown that the master constraint programme has a wide range of applicability but that there are many, physically interesting subtleties that must be taken care of in doing so.
Quantum spin dynamics (QSD): VI. Quantum Poincaré algebra and a quantum positivity of energy theorem for canonical quantum gravity
We quantize the generators of the little subgroup of the asymptotic Poincare group of Lorentzian four-dimensional canonical quantum gravity in the continuum. In particular, the resulting ADM energy
...
...