A First Course on Symmetry, Special Relativity and Quantum Mechanics

A First Course on Symmetry, Special Relativity and Quantum Mechanics
Author: Gabor Kunstatter
Publisher: Springer Nature
Total Pages: 390
Release: 2020-10-19
Genre: Science
ISBN: 3030554201

This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics. Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing. Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.

A First Course on Symmetry, Special Relativity and Quantum Mechanics

A First Course on Symmetry, Special Relativity and Quantum Mechanics
Author: Gabor Kunstatter
Publisher: Springer Nature
Total Pages: 410
Release: 2022-02-18
Genre: Science
ISBN: 3030923460

This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics. Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing. Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.

Physics from Symmetry

Physics from Symmetry
Author: Jakob Schwichtenberg
Publisher: Springer
Total Pages: 294
Release: 2017-12-01
Genre: Science
ISBN: 3319666312

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.

Symmetries in Quantum Mechanics

Symmetries in Quantum Mechanics
Author: M Chaichian
Publisher: CRC Press
Total Pages: 320
Release: 2023-07-21
Genre: Science
ISBN: 1000944166

Symmetries in Quantum Mechanics: From Angular Momentum to Supersymmetry (PBK) provides a thorough, didactic exposition of the role of symmetry, particularly rotational symmetry, in quantum mechanics. The bulk of the book covers the description of rotations (geometrically and group-theoretically) and their representations, and the quantum theory of angular momentum. Later chapters introduce more advanced topics such as relativistic theory, supersymmetry, anyons, fractional spin, and statistics. With clear, in-depth explanations, the book is ideal for use as a course text for postgraduate and advanced undergraduate students in physics and those specializing in theoretical physics. It is also useful for researchers looking for an accessible introduction to this important area of quantum theory.

Non-relativistic Quantum Theory: Dynamics, Symmetry And Geometry

Non-relativistic Quantum Theory: Dynamics, Symmetry And Geometry
Author: Kai S Lam
Publisher: World Scientific Publishing Company
Total Pages: 458
Release: 2009-08-24
Genre: Science
ISBN: 9813107480

This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern-Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

Symmetry and Quantum Mechanics

Symmetry and Quantum Mechanics
Author: Scott Corry
Publisher: CRC Press
Total Pages: 246
Release: 2016-11-25
Genre: Mathematics
ISBN: 1315354608

Structured as a dialogue between a mathematician and a physicist, Symmetry and Quantum Mechanics unites the mathematical topics of this field into a compelling and physically-motivated narrative that focuses on the central role of symmetry. Aimed at advanced undergraduate and beginning graduate students in mathematics with only a minimal background in physics, this title is also useful to physicists seeking a mathematical introduction to the subject. Part I focuses on spin, and covers such topics as Lie groups and algebras, while part II offers an account of position and momentum in the context of the representation theory of the Heisenberg group, along the way providing an informal discussion of fundamental concepts from analysis such as self-adjoint operators on Hilbert space and the Stone-von Neumann Theorem. Mathematical theory is applied to physical examples such as spin-precession in a magnetic field, the harmonic oscillator, the infinite spherical well, and the hydrogen atom.

Seven Fundamental Concepts in Spacetime Physics

Seven Fundamental Concepts in Spacetime Physics
Author: Vesselin Petkov
Publisher: Springer Nature
Total Pages: 115
Release: 2024-01-12
Genre: Science
ISBN: 3031497309

The book presents seven fundamental concepts in spacetime physics mostly by following Hermann Minkowski’s revolutionary ideas summarized in his 1908 lecture "Space and Time." These concepts are: spacetime, inertial and accelerated motion in spacetime physics, the origin and nature of inertia in spacetime physics, relativistic mass, gravitation, gravitational waves, and black holes. They have been selected because they appear to be causing most misconceptions and confusion in spacetime physics. This second edition has been revised to include additional clarifications, more detailed elaboration of the arguments and also new material published in the interim.

An Invitation to Quantum Field Theory

An Invitation to Quantum Field Theory
Author: Luis Alvarez-Gaumé
Publisher: Springer Science & Business Media
Total Pages: 299
Release: 2011-11-26
Genre: Science
ISBN: 3642237274

This book provides an introduction to Quantum Field Theory (QFT) at an elementary level—with only special relativity, electromagnetism and quantum mechanics as prerequisites. For this fresh approach to teaching QFT, based on numerous lectures and courses given by the authors, a representative sample of topics has been selected containing some of the more innovative, challenging or subtle concepts. They are presented with a minimum of technical details, the discussion of the main ideas being more important than the presentation of the typically very technical mathematical details necessary to obtain the final results. Special attention is given to the realization of symmetries in particle physics: global and local symmetries, explicit, spontaneously broken, and anomalous continuous symmetries, as well as discrete symmetries. Beyond providing an overview of the standard model of the strong, weak and electromagnetic interactions and the current understanding of the origin of mass, the text enumerates the general features of renormalization theory as well as providing a cursory description of effective field theories and the problem of naturalness in physics. Among the more advanced topics the reader will find are an outline of the first principles derivation of the CPT theorem and the spin-statistics connection. As indicated by the title, the main aim of this text is to motivate the reader to study QFT by providing a self-contained and approachable introduction to the most exciting and challenging aspects of this successful theoretical framework.

Symmetry and the Standard Model

Symmetry and the Standard Model
Author: Matthew Robinson
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2011-08-17
Genre: Science
ISBN: 1441982671

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.