# The Uncanny Precision of the Spectral Action

## Related Articles

- Quantum group covariant noncommutative geometry. Isaev, A. P. // Journal of Mathematical Physics;Dec94, Vol. 35 Issue 12, p6784
An algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the R-matrix approach to the theory of quantum groups is given. Structure groups are considered taking values in the quantum groups. The notion of noncommutative connections and curvatures is...

- Metrics on the real quantum plane. Fiore, G.; Maceda, M.; Madore, J. // Journal of Mathematical Physics;Dec2002, Vol. 43 Issue 12, p6307
Using the frame formalism we determine some possible metrics and metriccompatible connections on the noncommutative differential geometry of the real quantum plane. By definition, a metric maps the tensor product of two 1-forms into a "function" on the quantum plane. It is symmetric in a...

- Noncommutative Geometrical Structures of Multi-Qubit Entangled States. Heydari, Hoshang // International Journal of Theoretical Physics;May2011, Vol. 50 Issue 5, p1486
We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewriting the coordinate ring of a conifold or the Segre variety we can get a q-deformed relation in...

- Noncommutative geometry and fundamental physical interactions: The Lagrangian level--Historical sketch and description of the present situation. Kastler, Daniel // Journal of Mathematical Physics;Jun2000, Vol. 41 Issue 6
These notes comprise (i) a descriptive account of the history of the subject showing how physics and mathematics interwove to develop a mathematical concept of quantum manifold relevant to elementary particle theory; (ii) a detailed technical description, from scratch, of the spectral action...

- A Reconstruction Theorem for Almost-Commutative Spectral Triples. Ćaćić, Branimir // Letters in Mathematical Physics;May2012, Vol. 100 Issue 2, p181
We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner fluctuation of the metric and then prove a reconstruction theorem for almost-commutative spectral triples under this definition as a simple...

- Quantum Logic and Non-Commutative Geometry. Marchetti, P. A.; Rubele, R. // International Journal of Theoretical Physics;Jan2007, Vol. 46 Issue 1, p49
We propose a general scheme for the â€œlogicâ€ of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non-Commutative Geometry. It involves Baire*-algebras, the non-commutative version of measurable functions, arising as...

- The real quantum plane as part of 2d-minkowski space. Fiore, G.; Madore, J.; Maceda, M. // AIP Conference Proceedings;2001, Vol. 589 Issue 1, p222
Using the frame formalism we consider some possible metrics on the real quantum plane. We require that the metric be real and symmetric. In practice this means that we use the freedom of noncommutative geometry to impose a different 'Ïƒ-symmetry', which is chosen so that a complex metric is...

- Separation of noncommutative differential calculus on quantum Minkowski space. Bachmaier, Fabian; Blohmann, Christian // Journal of Mathematical Physics;Feb2006, Vol. 47 Issue 2, p023501
Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is shown that this problem can be overcome by a separation of...

- Complexified Spacetime. Sidharth, B. G. // Foundations of Physics Letters;Feb2003, Vol. 16 Issue 1, p91
It is pointed out that the Dirac position coordinates lead to an underlying non-commutative geometry, which again is symptomatic of an underlying double Weiner (Nelsonian) process.