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Spectral Action in Noncommutative Geometry

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 27)

DOI: 10.1007/978-3-319-94788-4

ISBN: 978-3-319-94787-7

Publisher: Springer International Publishing - Springer Journals

Dec 19, 2018

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Chapter 1The Dwelling of the Spectral Action

Eckstein, Michał; Iochum, Bruno

Pages: 1 –36

[The natural habitat of the spectral action is Connes’ noncommutative geometry. Therefore, it is indispensable to lay out its rudiments encoded in the notion of a spectral triple. We will, however, exclusively focus on the aspects of the structure, which are relevant for the spectral action...
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Chapter 2The Toolkit for Computations

Eckstein, Michał; Iochum, Bruno

Pages: 37 –62

[In this chapter we introduce a number of mathematical tools, which will prove useful in the spectral action computations. Firstly, we consider the basic properties of some spectral functions via the functional calculus and general Dirichlet series. Next, we study the interplay between these...
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Chapter 3Analytic Properties of Spectral Functions

Eckstein, Michał; Iochum, Bruno

Pages: 63 –94

[In the previous chapter we have witnessed the interplay between the spectral zeta functions and the associated heat traces (cf. Proposition 2.10). We have also learned, in Sect. 2.2.2, how to exploit the Laplace transform to compute the spectral action from a given heat trace. In this chapter we...
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Chapter 4Fluctuations of the Spectral Action

Eckstein, Michał; Iochum, Bruno

Pages: 95 –112

[As we have learned in Sect. 1.6 a given spectral triple (A,H,D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 5Open Problems

Eckstein, Michał; Iochum, Bruno

Pages: 113 –119

[As a desert, we serve a number of open problems connected with the subject matter of the book. Some of them consider the general framework of spectral triples and its possible extensions, while the other are more specific and relate to the properties of the spectral action. The problems are...

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