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Author: Felix Finster
Publisher: American Mathematical Soc.
ISBN: 0821839748
Category : Mathematics
Languages : en
Pages : 314
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Book Description
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionicprojector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible toformulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective interaction which shows many similarities to the interactions of the standard model. The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material, which willbe useful to the experienced researcher.
Author: Felix Finster
Publisher: American Mathematical Soc.
ISBN: 0821839748
Category : Mathematics
Languages : en
Pages : 314
Get Book Here
Book Description
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionicprojector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible toformulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective interaction which shows many similarities to the interactions of the standard model. The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material, which willbe useful to the experienced researcher.
Author: Felix Finster
Publisher: American Mathematical Soc.
ISBN: 9780821888360
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionicprojector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible toformulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective interaction which shows many similarities to the interactions of the standard model. The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material, which willbe useful to the experienced researcher.
Author: Felix Finster
Publisher: Springer
ISBN: 3319420674
Category : Science
Languages : en
Pages : 554
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Book Description
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries". The dynamics is described by a novel variational principle, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how the causal action principle gives rise to the interactions of the standard model plus gravity on the level of second-quantized fermionic fields coupled to classical bosonic fields. The focus is on getting a mathematically sound connection between causal fermion systems and physical systems in Minkowski space. The book is intended for graduate students entering the field, and is furthermore a valuable reference work for researchers in quantum field theory and quantum gravity.
Author: Bertfried Fauser
Publisher: Springer Science & Business Media
ISBN: 3764379782
Category : Science
Languages : en
Pages : 343
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Book Description
This book provides the reader with an overview of the different mathematical attempts to quantize gravity written by leading experts in this field. Also discussed are the possible experimental bounds on quantum gravity effects. The contributions have been strictly refereed and are written in an accessible style. The present volume emerged from the 2nd Blaubeuren Workshop "Mathematical and Physical Aspects of Quantum Gravity".
Author: Bertfried Fauser
Publisher: Springer Science & Business Media
ISBN: 376438736X
Category : Science
Languages : en
Pages : 436
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Book Description
The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 354034764X
Category : Science
Languages : en
Pages : 1060
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Book Description
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
Author: Paul-Hermann Balduf
Publisher: Springer Nature
ISBN: 3031544463
Category :
Languages : en
Pages : 373
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Book Description
Author: Eric R. Sharpe
Publisher: American Mathematical Soc.
ISBN: 0821847643
Category : Mathematics
Languages : en
Pages : 259
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Book Description
"Over the past decade string theory has had an increasing impact on many areas of physics: high energy and hadronic physics, gravitation and cosmology, mathematical physics and even condensed matter physics. The impact has been through many major conceptual and methodological developments in quantum field theory in the past fifteen years. In addition, string theory has exerted a dramatic influence on developments in contemporary mathematics, including Gromov-Witten theory, mirror symmetry in complex and symplectic geometry, and important ramifications in enumerative geometry." "This volume is derived from a conference of younger leading practitioners around the common theme: "What is string theory?" The talks covered major current topics, both mathematical and physical, related to string theory. Graduate students and research mathematicians interested in string theory in mathematics and physics will be interested in this workshop."--BOOK JACKET.
Author: Lizhen Ji
Publisher: American Mathematical Soc.
ISBN: 0821875868
Category : Mathematics
Languages : en
Pages : 520
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Book Description
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
Author: Alexander Grigoryan
Publisher: American Mathematical Soc.
ISBN: 0821849352
Category : Mathematics
Languages : en
Pages : 504
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Book Description
"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and p -Laplace operators, heat kernel and spherical inversion on SL 2 (C) , random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs."--Publisher's website.
