Partial and complete observables for Hamiltonian constrained systems
By B. Dittrich. 2004
290 citations recorded by the source corpus.
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 Rev, D65:124013 (2002); Quantum Gravity, Cambridge University Press, Cambridge (2007) in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kuchař’s Bubble-Time Formalism (J Math Phys, 13:768, 1972). Moreover one can define a non-trivial gauge action on the space of complete observables and also state the Poisson brackets of these functions. Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9183000800cf804e14f3a7958210d735c7205c21
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Citations in the corpus
- From black holes to white holes: a quantum gravitational, symmetric bounce (2017, unknown): “In this context, further developments have been carried out in order to identify classical (partial) Dirac observables [51, 52] and various applications have been studied [53–56].”
- Loop Quantum Gravity (2003, unknown): “[86] B.”
- Loop Quantum Cosmology (2005, background): “iant physical meaning in general relativity, and conceptually an internal time is more appropriate. Evolution is then measured in a relational manner of some degrees of freedom with respect to others [184, 185, 186]. In quantum cosmology, as we have seen, this concept is even more general since inte”
- Scalar material reference systems and loop quantum gravity (2012, background): “ manifestly gauge invariant form has been considered, to the best of our knowledge, for the first time in [11, 12]. Aspects of this have been rediscovered in different language by several authors, e.g. [13, 14, 15]. In these works, a complicated formula appears that “projects” a non gauge invariant fu”
- Partial and complete observables for canonical general relativity (2005, methodology): “as how to use complete observables in a quantization of a gauge system and more specifically general relativity can be found in [6],[8] and in [9]. In this work we will apply the methods developed in [7] to general relativity. One central result of this work is a variation of the method to calculate”
- Loop quantum gravity: an outside view (2005, background): “ter fields (which then would commute with the constraints). Although there has been much discussion in the literature about these ‘relational’ aspects (see [19, 16, 18, 34] and references therein, and [97, 98] for a more recent discussion in the context of LQG), these issues are by no means conclusiv”
- Improved and Perfect Actions in Discrete Gravity (2009, background): “(2.6) The dynamics of this discretized system is obtained by looking for stationary variations of (2.5) w.r.t the tn, qn.”
- Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity (2007, background): “lowing facts: 1. The functions Of(τ) are weak Dirac observables with respect to the CI, that is {CI,Of(τ)} ≈ 0 (2.13) This remarkable property is due to the key observation that the XI weakly commute [3, 4]. 2. The multi parameter family ofmaps Oτ : f→ O f(τ)is ahomomorphism fromthe commutative alge”