Foundations of Mathematics and Physics One Century After Hilbert

New Perspectives

Buch | Softcover

XXI, 441 Seiten

2018
Springer International Publishing (Verlag)
978-3-030-09728-8 (ISBN)

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This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert's works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, butsheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Preface : Where we stand today, Joseph Kouneiher.- Mie's Electromagnetic Theory of Matter and the Background to Hilbert's Unified Foundations of Physics, Leo Corry.- Hilbert and Einstein, Joseph Kouneiher, John Stachel.- Grothendieck on foundations for the rebirth of geometry, Colin MacLarty.- Understanding the 6-Dimensional Sphere, Michael Aityah.- A dozen problems, questions and conjectures about positive scalar curvature, Misha Gromov.- Geometry and the Quantum, Alain Connes.- What Every Physicist Should Know About String Theory, Edward Witten.- Quanta of Space-Time and Axiomatization of Physics, Ali Chamsddine.- Twistor Theory as an Approach to Fundamental Physics, Roger Penrose.- What are we missing in our search for quantum gravity?, Lee Smolin.- A schema for duality, illustrated by bosonization, Jeremy Butterfield and Sebastian de Haro.- The dressing field method of gauge symmetry reduction, a review with examples, Thierry Masson et al.- Syntactic Phylogenetic Trees, Matilde Marcolli.

"This wonderful book is full of such insights, reflections, analyses, appraisals, and even anecdotes, and should be a smash hit: we should all seek to know more about these foundations, and we have a wonderful set of essays here, based off Hilbert's original wonderful lectures, and a lot more." (Michael Berg, MAA Reviews, July, 2018)

“This wonderful book is full of such insights, reflections, analyses, appraisals, and even anecdotes, and should be a smash hit: we should all seek to know more about these foundations, and we have a wonderful set of essays here, based off Hilbert’s original wonderful lectures, and a lot more.” (Michael Berg, MAA Reviews, July, 2018)

Erscheinungsdatum	05.03.2022
Zusatzinfo	XXI, 441 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	706 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	bosonization • Gauge Theory • Heisenberg commutation relations • Hilbert's foundations of physics • Hilbert's sixth problem • Hilbert’s sixth problem • K-homology • K-theory • massive integrable field theory • Minkowski space • Noncommutative Geometry • Pati-Salam symmetries • Penrose's quasi-local mass construction • Quantum Gravity • quantum groups • Relationship between physics and mathematics • Riemannian Geometry • String Theory • Thirring model • Twistor theory • virasoro algebra
ISBN-10	3-030-09728-5 / 3030097285
ISBN-13	978-3-030-09728-8 / 9783030097288
Zustand	Neuware