عنوان

Noncommutative geometry, quantum fields and motives /

شابک

0821842102

شابک

9780821842102

شماره

b770807

عنوان اصلي

Noncommutative geometry, quantum fields and motives /

نام عام مواد

[Book]

نام نخستين پديدآور

Alain Connes, Matilde Marcolli.

محل نشرو پخش و غیره

Providence, R.I. :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

©2008.

نام خاص و کميت اثر

xxii, 785 pages :

ساير جزييات

illustrations ;

ابعاد

26 cm.

عنوان فروست

American Mathematical Society colloquium publications,

مشخصه جلد

vol. 55

شاپا ي ISSN فروست

0065-9258 ;

متن يادداشت

Published under license from Hindustan Book Agency--T.p. verso.

متن يادداشت

Includes bibliographical references (pages 749-761) and index.

متن يادداشت

Quantum fields, noncommutative spaces, and motives -- Basics of perturbative QFT -- Feynman diagrams -- Dimensional regularization --The graph by graph method of Bogoliubov-Parasiuk-Hepp-Zimmermann -- The Connes-Kreimer theory of perturbative renormalization -- Renormalization and the Riemann-Hilbert correspondence -- Motives in a nutshell -- The Standard Model of elementary particles -- The framework of (metric) noncommutative geometry -- The spectral action principle -- Noncommutative geometry and the Standard Model -- The finite noncommutative geometry -- The product geometry -- Bosons as inner fluctuations -- The spectral action and the Standard Model Lagrangian -- Standard Model Lagrangian from the spectral action -- Functional integral -- Dimensional regularization and noncommutative geometry -- Riemann zeta function and noncommutative geometry -- Counting primes and the zeta function -- Classical and quantum mechanics of zeta -- Principal values from the local trace formula -- Quantum states of the scaling flow -- The map [actual symbol not reproducible] -- The adele class space: finitely many degrees of freedom -- Weil's formulation of the explicit formulas -- Spectral realization of critical zeros of L-functions -- Lefschetz formula for Archimedean local factors -- Quantum statistical mechanics and Galois symmetries -- Overview: three systems -- Quantum statistical mechanics -- Q-lattices and commensurability -- 1-dimensional Q-lattices -- 2-dimensional Q-lattices -- The modular field -- Arithmetic of the GL[subscript 2] system -- KMS states and complex multiplication -- Quantum statistical mechanics of Shimura varieties -- Endomotives, thermodynamics, and the Weil explicit formula -- Morphisms and categories of noncommutative spaces -- Endomotives -- Motives and noncommutative spaces: higher dimensional perspectives -- A thermodynamic "Frobenius" in characteristic zero -- A cohomological Lefschetz trace formula -- Weil proof for function fields -- A noncommutative geometry perspective -- The analogy between QG and RH -- Appendix 1. Operator algebras -- Appendix 1.1. C*-algebras -- Appendix 1.2. Von Neumann algebras -- Appendix 1.3. The passing of time -- Appendix 2. Galois theory.

متن يادداشت

Quantum fields, noncommutative spaces, and motives -- The Riemann zeta function and noncommutative geometry -- Quantum statistical mechanics and Galois symmetries -- Endomotives, thermodynamics, and the Weil explicit formula -- Appendix.

بدون عنوان

0

بدون عنوان

0

متن يادداشت

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

موضوع مستند نشده

Noncommutative differential geometry.

موضوع مستند نشده

Quantum field theory.

موضوع مستند نشده

31.81 mathematical physiscs.

موضوع مستند نشده

Álgebra.

موضوع مستند نشده

Análise global.

موضوع مستند نشده

Corpos globais.

موضوع مستند نشده

Geometria algébrica.

موضوع مستند نشده

Mecânica quântica.

موضوع مستند نشده

Motiv

موضوع مستند نشده

Motives (Mathematics)

موضوع مستند نشده

Nichtkommutative Differentialgeometrie

موضوع مستند نشده

Noncommutative differential geometry.

موضوع مستند نشده

Noncommutative differential geometry.

موضوع مستند نشده

Quantenfeldtheorie

موضوع مستند نشده

Quantum field theory-- Mathematics.

موضوع مستند نشده

Quantum field theory.

موضوع مستند نشده

Teoria analítica dos números.

موضوع مستند نشده

Teoria dos números.

شماره

ويراست

شماره رده

شماره رده

نشانه اثر

نشانه اثر

شماره رده

شماره رده

کد سيستم

کد سيستم

مستند نام اشخاص تاييد نشده

Connes, Alain.

مستند نام اشخاص تاييد نشده

Marcolli, Matilde

تاريخ عمليات

20201206165446.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y