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Mappingclass groups of 3manifolds in canonical quantum gravity
"... Abstract. Mappingclass groups of 3manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries, their inequivalent unitary irreducible representations ..."
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Abstract. Mappingclass groups of 3manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries, their inequivalent unitary irreducible representations should give rise to a complex superselection structure. This highlights certain aspects of spatial diffeomorphism invariance that to some degree seem physically meaningful and which persist in all approaches based on smooth 3manifolds, like geometrodynamics and loop quantum gravity. We also attempt to give a flavor of the mathematical ideas involved.
What Price Determinism? A Hole Other Story!∗
, 2005
"... In their modern classic “What Price Substantivalism? The Hole Story ” Earman and Norton argued that substantivalism about spacetime points implies that general relativity is indeterministic and, for that reason, must be rejected as a candidate ontology for the theory. More recently, Earman has cott ..."
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In their modern classic “What Price Substantivalism? The Hole Story ” Earman and Norton argued that substantivalism about spacetime points implies that general relativity is indeterministic and, for that reason, must be rejected as a candidate ontology for the theory. More recently, Earman has cottoned on to a related argument (in fact, related to a response to the hole argument) that arises in the context of canonical general relativity, according to which the enforcing of determinism along standard lines—using the machinery of gauge theory— leads to a ‘frozen universe ’ picture (grounded in an absence of changes in values of general relativity’s observables). Prima facie this would seem to land the antisubstantivalist in waters at least as deep as those that Earman and Norton argued troubled substantivalism. In this paper I introduce the argument in what I think are clearer terms than Earman’s, and assess his treatment of the problem. For the most part I agree with Earman about the nature of the problem, but I find aspects of his discussion wanting, especially as regards his proposed ontology. I argue that ontological sense can be made of the changelessness if a structuralist stance is adopted with respect to a natural class of observables.
Star Products and Geometric Algebra
, 2008
"... The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficient part of superanalysis one obta ..."
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The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficient part of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner. 1