American Mathematical Society

Book Review

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MathSciNet review: 3686327
Full text of review: PDF This review is available free of charge.
Book Information:

Author: Walter D. van Suijlekom
Title: Noncommutative geometry and particle physics
Additional book information: Mathematical Physics Studies, Springer, Dordrecht, 2015, xvi+237 pp., ISBN 978-94-017-9161-8 (hardcover), 978-94-017-9162-5 (electronic), US $69.99 (hardcover); US $54.99 (electronic)

A. Ball, M. Marcolli, Spectral action models of gravity on packed swiss cheese cosmology, Classical and Quantum Gravity, 33 (2016) no. 11, 115018

John W. Barrett, Lorentzian version of the noncommutative geometry of the Standard Model of particle physics, J. Math. Phys. 48 (2007), no. 1, 012303, 7. MR 2292605, DOI 10.1063/1.2408400

Wim Beenakker, Thijs van den Broek, and Walter D. van Suijlekom, Supersymmetry and noncommutative geometry, SpringerBriefs in Mathematical Physics, vol. 9, Springer, Cham, 2016. MR 3380781, DOI 10.1007/978-3-319-24798-4

Branimir Ćaćić, A reconstruction theorem for almost-commutative spectral triples, Lett. Math. Phys. 100 (2012), no. 2, 181–202. MR 2912480, DOI 10.1007/s11005-011-0534-5

Ali H. Chamseddine and Alain Connes, The spectral action principle, Comm. Math. Phys. 186 (1997), no. 3, 731–750. MR 1463819, DOI 10.1007/s002200050126

Ali H. Chamseddine and Alain Connes, Resilience of the spectral standard model, J. High Energy Phys. 9 (2012), 104, front matter+10. MR 3044924, DOI 10.1007/JHEP09(2012)104

Ali H. Chamseddine, Alain Connes, and Matilde Marcolli, Gravity and the standard model with neutrino mixing, Adv. Theor. Math. Phys. 11 (2007), no. 6, 991–1089. MR 2368941

Ali H. Chamseddine, Alain Connes, and Walter D. van Suijlekom, Grand unification in the spectral Pati-Salam model, J. High Energy Phys. 11 (2015), 011, front matter+12. MR 3455566, DOI 10.1007/JHEP11(2015)011

Alain Connes, Gravity coupled with matter and the foundation of non-commutative geometry, Comm. Math. Phys. 182 (1996), no. 1, 155–176. MR 1441908

Alain Connes, Noncommutative geometry and the standard model with neutrino mixing, J. High Energy Phys. 11 (2006), 081, 19. MR 2270385, DOI 10.1088/1126-6708/2006/11/081

Alain Connes and John Lott, Particle models and noncommutative geometry, Nuclear Phys. B Proc. Suppl. 18B (1990), 29–47 (1991). Recent advances in field theory (Annecy-le-Vieux, 1990). MR 1128127, DOI 10.1016/0920-5632(91)90120-4

A. Connes and H. Moscovici, The local index formula in noncommutative geometry, Geom. Funct. Anal. 5 (1995), no. 2, 174–243. MR 1334867, DOI 10.1007/BF01895667

Shane Farnsworth and Latham Boyle, Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry, New J. Phys. 17 (2015), no. February, 023021, 6. MR 3321217, DOI 10.1088/1367-2630/17/2/023021

Shane Farnsworth and Latham Boyle, Non-associative geometry and the spectral action principle, J. High Energy Phys. 7 (2015), 023, front matter+25. MR 3384192, DOI 10.1007/JHEP07(2015)023

Wentao Fan, Farzad Fathizadeh, and Matilde Marcolli, Spectral action for Bianchi type-IX cosmological models, J. High Energy Phys. 10 (2015), 085, front matter+28. MR 3435554, DOI 10.1007/JHEP10(2015)085

Nigel Higson, The local index formula in noncommutative geometry, Contemporary developments in algebraic $K$-theory, ICTP Lect. Notes, XV, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004, pp. 443–536. MR 2175637, DOI 10.1007/b94118

M. Marcolli, Noncommutative Cosmology, book in preparation.

Matilde Marcolli and Elena Pierpaoli, Early universe models from noncommutative geometry, Adv. Theor. Math. Phys. 14 (2010), no. 5, 1373–1432. MR 2826185

Matilde Marcolli, Elena Pierpaoli, and Kevin Teh, The spectral action and cosmic topology, Comm. Math. Phys. 304 (2011), no. 1, 125–174. MR 2793932, DOI 10.1007/s00220-011-1211-3

Mairi Sakellariadou, Noncommutative geometry spectral action as a framework for unification: introduction and phenomenological/cosmological consequences, Internat. J. Modern Phys. D 20 (2011), no. 5, 785–804. MR 2801512, DOI 10.1142/S021827181101913X

Walter D. van Suijlekom, Renormalizability conditions for almost-commutative manifolds, Ann. Henri Poincaré 15 (2014), no. 5, 985–1011. MR 3192656, DOI 10.1007/s00023-013-0269-1

Review Information:

Reviewer: Matilde Marcolli
Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology
Email: matilde@caltech.edu