7,100 research outputs found
The structure of classical extensions of quantum probability theory
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed
Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with
massive particles and show that we recover in this limit Feynman graph
amplitudes (with Hadamard propagator) expressed as an abelian spin foam model.
We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be
resummed. This leads to the conclusion that the dynamics of quantum particles
coupled to quantum 3d gravity can be expressed in terms of an effective new non
commutative field theory which respects the principles of doubly special
relativity. We discuss the construction of Lorentzian spin foam models
including Feynman propagatorsComment: 46 pages, the wrong file was first submitte
The Fuzzy Supersphere
We introduce the fuzzy supersphere as sequence of finite-dimensional,
noncommutative -graded algebras tending in a suitable limit to a dense
subalgebra of the -graded algebra of -functions on
the -dimensional supersphere. Noncommutative analogues of the body map
(to the (fuzzy) sphere) and the super-deRham complex are introduced. In
particular we reproduce the equality of the super-deRham cohomology of the
supersphere and the ordinary deRham cohomology of its body on the "fuzzy
level".Comment: 33 pages, LaTeX, some typos correcte
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