Propagating spin modes in canonical quantum gravity

Abstract

One of the main results in canonical quantum gravity is the introduction of spin network states as a basis on the space of kinematical states. To arrive at the physical state space of the theory though we need to understand the dynamics of the quantum gravitational states. To this aim we study a model in which we allow for the spins, labeling the edges of spin networks, to change according to simple rules. The gauge invariance of the theory, restricting the possible values for the spins, induces propagating modes of spin changes. We investigate these modes under various assumptions about the parameters of the model.Comment: 11 pages, 7 figures included using epsfi

Self-Organized Critical Behavior: The Evolution of Frozen Spin Networks Model in Quantum Gravity

“…The spin network evolves from one gauge invariance state to another one by adding or subtracting a loop flux. The evolving rules fall into two main classes [4,5]: One is the random vertex class, which involves choosing a random vertex and simultaneously changing the colors of its three incident edges by an even integer △c. The other one is the random edge class in which one edge is chosen randomly and its color is changed by an even number △c.…”

“…Rovelli and Smolin [6] pointed out that the space has discrete structure at Plank scale in canonical quantum gravity [7,8,9], and then it was proposed by Markopoulou et al [3] that the discrete space should be a SOC system for the lack of an external fine tuning to the universe's parameters. The proposal was studied further by Borissov and Gupta [4], and then by Ansari and Smolin [5] more recently. For other researches on critical phenomenon in quantum gravity see refs.…”

“…Furthermore, the identities of the gauge invariance imposed at vertices is not chosen as the conditions on states, but a dynamical process in which the system evolves to gauge invariance state. The evolution rules adopted by Borissov and Gupta [4] did not lead to the SOC. Then Ansari and Smolin [5] developed a new set of evolution rules and observed the SOC.…”

“…Recently, the self-organized criticality (SOC) also became an attractive problem in quantum gravity [3,4,5]. Rovelli and Smolin [6] pointed out that the space has discrete structure at Plank scale in canonical quantum gravity [7,8,9], and then it was proposed by Markopoulou et al [3] that the discrete space should be a SOC system for the lack of an external fine tuning to the universe's parameters.…”

“…The research on the SOC in quantum gravity [4,5] was based on the frozen spin network, a simplified case of loop quantum gravity, in which the embedding graph is fixed and the spin that labels the edge evolves. Furthermore, the identities of the gauge invariance imposed at vertices is not chosen as the conditions on states, but a dynamical process in which the system evolves to gauge invariance state.…”