Geometry of the Standard Model of Elementary Particles PDF Download
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Author: Andrzej Derdzinski
Publisher: Springer Science & Business Media
ISBN: 3642503101
Category : Science
Languages : en
Pages : 205
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Book Description
The book gives an exposition of the standard model of elementary particles based on coordinate-free differential geometric foundations. It addresses students in physics and mathematics.
Author: Andrzej Derdzinski
Publisher: Springer Science & Business Media
ISBN: 3642503101
Category : Science
Languages : en
Pages : 205
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Book Description
The book gives an exposition of the standard model of elementary particles based on coordinate-free differential geometric foundations. It addresses students in physics and mathematics.
Author: Florian Scheck
Publisher: Springer Science & Business Media
ISBN: 3540440712
Category : Science
Languages : en
Pages : 352
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Book Description
The outcome of a close collaboration between mathematicians and mathematical physicists, these Lecture Notes present the foundations of A. Connes noncommutative geometry, as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.
Author: Walter D. van Suijlekom
Publisher: Springer
ISBN: 9401791627
Category : Science
Languages : en
Pages : 246
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Book Description
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
Author: Matthew Robinson
Publisher: Springer Science & Business Media
ISBN: 1441982671
Category : Science
Languages : en
Pages : 343
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Book Description
While theoretical particle physics is an extraordinarily fascinating field, the incredibly fast pace at which it moves along, combined with the huge amount of background information necessary to perform cutting edge research, poses a formidable challenge for graduate students. This book represents the first in a series designed to assist students in the process of transitioning from coursework to research in particle physics. Rather than reading literally dozens of physics and mathematics texts, trying to assimilate the countless ideas, translate notations and perspectives, and see how it all fits together to get a holistic understanding, this series provides a detailed overview of the major mathematical and physical ideas in theoretical particle physics. Ultimately the ideas will be presented in a unified, consistent, holistic picture, where each topic is built firmly on what has come before, and all topics are related in a clear and intuitive way. This introductory text on quantum field theory and particle physics provides both a self-contained and complete introduction to not only the necessary physical ideas, but also a complete introduction to the necessary mathematical tools. Assuming minimal knowledge of undergraduate physics and mathematics, this book lays both the mathematical and physical groundwork with clear, intuitive explanations and plenty of examples. The book then continues with an exposition of the Standard Model of Particle Physics, the theory that currently seems to explain the universe apart from gravity. Furthermore, this book was written as a primer for the more advanced mathematical and physical ideas to come later in this series.
Author: Mark J.D. Hamilton
Publisher: Springer
ISBN: 3319684396
Category : Mathematics
Languages : en
Pages : 667
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Book Description
The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.
Author: Bjørn Felsager
Publisher:
ISBN:
Category : Electromagnetism
Languages : en
Pages : 668
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Book Description
Teil 1: Basic properties of particles and fields. Teil 2: Basic principles and applications of differential geometry
Author: Chong-sa Lim
Publisher: World Scientific
ISBN: 9814491411
Category : Science
Languages : en
Pages : 314
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Book Description
This book provides a unified description of elementary particle interactions and the underlying theories, namely the Standard Model and beyond. The authors have aimed at a concise presentation but have taken care that all the basic concepts are clearly described. Written primarily for graduate students in theoretical and experimental particle physics, The Physics of the Standard Model and Beyond conveys the excitement of particle physics, centering upon experimental observations (new and old) and a variety of ideas for their interpretation.
Author: John Iliopoulos
Publisher: Oxford University Press
ISBN: 0192658166
Category : Science
Languages : en
Pages : 522
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Book Description
Since the development of natural philosophy in Ancient Greece, scientists have been concerned with determining the nature of matter's smallest constituents and the interactions among them. This textbook examines the question of the microscopic composition of matter through an accessible introduction to what is now called 'The Physics of Elementary Particles'. In the last few decades, elementary particle physics has undergone a period of transition, culminating in the formulation of a new theoretical scheme, known as 'The Standard Model', which has profoundly changed our understanding of nature's fundamental forces. Rooted in the experimental tradition, this new vision is based on geometry and sees the composition of matter in terms of its accordance with certain geometrical principles. This textbook presents and explains this modern viewpoint to a readership of well-motivated undergraduate students, by guiding the reader from the basics to the more advanced concepts of Gauge Symmetry, Quantum Field Theory and the phenomenon of spontaneous symmetry breaking through concrete physical examples. This engaging introduction to the theoretical advances and experimental discoveries of the last decades makes this fascinating subject accessible to undergraduate students and aims at motivating them to study it further.
Author: Alain Connes
Publisher: American Mathematical Soc.
ISBN: 1470450453
Category : Mathematics
Languages : en
Pages : 810
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Book Description
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. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. 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. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. 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.
Author: Gordon McCabe
Publisher: Elsevier
ISBN: 0080498302
Category : Science
Languages : en
Pages : 265
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Book Description
This book provides a philosophically informed and mathematically rigorous introduction to the 'standard model' of particle physics. The standard model is the currently accepted and experimentally verified model of all the particles and interactions in our universe. All the elementary particles in our universe, and all the non-gravitational interactions -the strong nuclear force, the weak nuclear force, and the electromagnetic force - are collected together and, in the case of the weak and electromagnetic forces, unified in the standard model. Rather than presenting the calculational recipes favored in most treatments of the standard model, this text focuses upon the elegant mathematical structures and the foundational concepts of the standard model.· Combines an exposition of the philosophical foundations and rigorous mathematical structure of particle physics· Demonstrates the standard model with elegant mathematics, rather than a medley of computational recipes· Promotes a group-theoretical and fibre-bundle approach to the standard model, rather than the Lagrangian approach favoured by calculationalists· Explains the different approaches to particle physics and the standard model which can be found within the literature
