Noncommutative Geometry, Quantum Fields and Motives

By Alain Connes, Matilde Marcolli. 2007

644 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8e28de8521823ec89e25cc26ccf494d895fc24f1

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars (2014, methodology): “The fermionic terms in the action functional for gravity coupled to matter come from an additional term not included in the spectral action, which accounts for the kinetic terms of the fermions and the boson-fermion interaction terms, see [11, 19].”
On p-adic mathematical physics (2006, background): “Motives, algebraic and noncommutative geometry are explored in [34, 35, 36, 37, 38].”
KMS states on the C∗-algebras of finite graphs (2012, positive): “As in [3], we distinguish between KMS∞ states, which are weak* limits of sequences of KMSβn states as βn → ∞, and ground states, which are states φ such that the functions φa,b : z 7→ φ(aγz(b)) are bounded on the upper-half plane for a, b ∈ {sμs ∗ ν : μ, ν ∈ E }.”
Euler's constant: Euler's work and modern developments (2013, methodology): “There is a statistical mechanics interpretation of the Riemann zeta function as a partition function given in Bost and Connes [40], with subsequent developments described in Connes and Marcolli [64].”
Scalar Curvature for Noncommutative Four-Tori (2013, background): “s well, and show that its extremum is attained if and only if the Weyl factor is a constant, which is equivalent to having a metric with constant curvature. 5.1. Scalar curvature for T4 . Following [9, 11, 14] and the above discussion, we dene the scalar curvature of T4 equipped with the perturbed”
From polygons and symbols to polylogarithmic functions (2011, background): “One should also mention work of Connes and Marcolli [88] in this direction.”