Reduced phase space quantization and Dirac observables
By T. Thiemann. 2004
160 citations recorded by the source corpus.
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 programme depends on the choice of the partial observables involved. The (multi-fingered) time evolution was shown to correspond to an automorphism on the set of Dirac observables, so generated and interesting representations of the latter will be those for which a suitable preferred subgroup is realized unitarily. We sketch how such a programme might look for general relativity. We also observe that the ideas by Dittrich can be used in order to generate constraints equivalent to those of the Hamiltonian constraints for general relativity such that they are spatially diffeomorphism invariant. This has the important consequence that one can now quantize the new Hamiltonian constraints on the partially reduced Hilbert space of spatially diffeomorphism invariant states, just as for the recently proposed master constraint programme.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/25c7d99d1a105211987fe43f19c6d938b7eefeef
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Citations in the corpus
- Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity (2007, background): “It is this fact which makes reduced phase space quantization feasible as observed in [4].”
- FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY (2005, background): “Given a system of constants {(τ0)r }r=1, for an observablef (Pi ,Q j) depending only onPi andQ j , the physical dynamics is given by [62][148]:”
- Scalar material reference systems and loop quantum gravity (2012, background): “However, as pointed out in [16], the Poisson algebra of these formal observables can nevertheless still be simple, thus enabling in principle a concrete reduced phase space quantization approach to quantum gravity.”
- Partial and complete observables for canonical general relativity (2005, background): “Ideas on how to use complete observables in a quantization of a gauge system and more specifically general relativity can be found in [6, 8, 9].”
- Loop quantum gravity: an outside view (2005, background): “Although there has been much discussion in the literature about these ‘relational’ aspects (see [16, 30, 31, 34] and references therein, and [105, 106] for a more recent discussion in the context of LQG), these issues are by no means conclusively settled, and we are not aware of any fully concrete r”