The Phoenix Project: master constraint programme for loop quantum gravity

By T. Thiemann. 2003

244 citations recorded by the source corpus.

The Hamiltonian constraint remains the major unsolved problem in loop quantum gravity (LQG). Some time ago, a mathematically consistent candidate Hamiltonian constraint was proposed but there are still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper, we propose a solution to this set of problems based on the so-called master constraint which combines the smeared Hamiltonian constraints for all smearing functions into a single constraint. Due to a harmonic interplay of several mathematical facts, the problems with the commutator algebra disappear and chances are good that one can control the solution space and the (quantum) Dirac observables of LQG. Even a decision on whether the theory has the correct classical limit and a connection with the path integral (or spin foam) formulation could be in reach.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8e077c3096cd053ed3574f3cb715c78ea65bf3bc

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Citations in the corpus

Scalar material reference systems and loop quantum gravity (2012, background): “[27, 28] and references therein) that reveal that some of the claims made in [24] are not tenable.”
FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY (2005, background): “In Ref.”
LQG vertex with finite Immirzi parameter (2007, methodology): “[10] T Thiemann, “The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity” Class Quant Grav 23 (2006) 2211-2248, gr-qc/0305080.”
Background independent quantum gravity: A Status report (2004, background): “these core issues, at least four diﬀerent approaches are being followed. The ﬁrst, and the closest to ideas discussed in section VIC is the ‘Master constraint program’ recently introduced by Thiemann [178]. The idea here is to avoid using an inﬁnite number of constraints C(N), each smeared by a laps”
Improved and Perfect Actions in Discrete Gravity (2009, background): “the graphs, make the implementation of the constraint algebra rather non-trivial [5, 9].”
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity (2007, unknown): “The aforementioned primary constraints are”
Loop quantum gravity: an outside view (2005, background): “• Status of the Hamiltonian constraint? In the current LQG literature, there is surprisingly little discussion of certain basic aspects concerning the Hamiltonian constraint operator, which are of central importance for the theory (recent exceptions are [25], and the socalled master constraint progr”
Algebraic quantum gravity (AQG): I. Conceptual setup (2006, background): “Given a vertex v of the algebraic graph α and two edges e, e′ incident at and outgoing from v, a loop βv,e,e′ within α starting at v along e and ending at v along (e′)−1 is said to be minimal [10] provided that there is no other loop within α satisfying the same restrictions with fewer edges travers”
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models (2004, background): “From our perspective three dimensional gravity is taken as an toy model for the application of quantization techniques that are expected to be applicable in four dimensions (see [18] for a novel proposal and an account and a discussion technical difficulties arising in four dimensions).”
Introduction to loop quantum gravity and spin foams (2004, background): “tains. An element ψγ,f ∈ Cylγ is labelled by a graph γ and a smooth function f : SU(2)Ne → C, and it is given by a functional of the connection deﬁned as ψγ,f[A] := f(he 1 [A],he 2 [A],···heN e [A]), (73) where ei for i= 1,···Ne are the edges of the corresponding graph γ. The symbol ∪ γin (72) denot”
Quantum nature of the big bang: An analytical and numerical investigation (2006, methodology): “, its dynamics is formulated using Thiemann’s master constraint program [61].”
Anomaly freedom in perturbative loop quantum gravity (2008, background): “Some rare solvable systems can be studied by exact effective equations without truncation, which in cosmology is realized for a flat isotropic model sourced by a free, massless scalar [6].”
Reduced phase space quantization and Dirac observables (2004, methodology): “nvariants. There are even obstruction theorems available in the literature [1] which state the non existence of local Dirac observables (depending on a ﬁnite number of spatial derivatives) for GR. In [2] a proposal for how to overcome the problem of structure functions for GR for the quantum theory ”
Loop Quantum Gravity (2003, background): “During the last years, Thomas Thiemann has introduced the idea of replacing the full set of quantum constraints with a single (“master”) constraint [293].”