2,693 research outputs found
Remarks on Alain Connes' approach to the standard model
Our 1992 remarks about Alain Connes' interpretation of the standard model
within his theory of non-commutative riemannian spin manifolds.Comment: 9 pages TeX, dedicated to the memory of E. M. Polivano
Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
In analogy with conventional quantum mechanics, non-commutative quantum
mechanics is formulated as a quantum system on the Hilbert space of
Hilbert-Schmidt operators acting on non-commutative configuration space. It is
argued that the standard quantum mechanical interpretation based on Positive
Operator Valued Measures, provides a sufficient framework for the consistent
interpretation of this quantum system. The implications of this formalism for
rotational and time reversal symmetry are discussed. The formalism is applied
to the free particle and harmonic oscillator in two dimensions and the physical
signatures of non commutativity are identified.Comment: 11 page
T-duality with H-flux: non-commutativity, T-folds and G x G structure
Various approaches to T-duality with NSNS three-form flux are reconciled.
Non-commutative torus fibrations are shown to be the open-string version of
T-folds. The non-geometric T-dual of a three-torus with uniform flux is
embedded into a generalized complex six-torus, and the non-geometry is probed
by D0-branes regarded as generalized complex submanifolds. The
non-commutativity scale, which is present in these compactifications, is given
by a holomorphic Poisson bivector that also encodes the variation of the
dimension of the world-volume of D-branes under monodromy. This bivector is
shown to exist in SU(3) x SU(3) structure compactifications, which have been
proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors
are generically not parallel, thereby giving rise to a non-trivial Poisson
bivector. Furthermore we show that for non-geometric T-duals, the Poisson
bivector may not be decomposable into the tensor product of vectors.Comment: 25 pages, LaTeX; v2: typos corrected, references adde
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