Modern Take on Physics, a - Volume 2: Classical and Quantum Field Theory (1版)

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【簡介】 These two volumes cover the classical topics typically taught in undergraduate physics courses and beyond. However, we teach classical physics using a very different language from traditional books, influenced by the language of modern physics, in a move to encourage a positive approach towards the latter subject. Based around the unifying concept of energy, we take a distinct approach to the organisation of material, presenting physics in a cohesive manner without separating topics such as mechanics, kinematics, thermodynamics, electricity, and magnetism. Instead, physics is revealed gradually, emphasising a holistic approach to science. Despite this peculiarity, we have maintained the conventional separation between Physics I and II to assist teachers in smoothly integrating these books into their courses.These innovative volumes present valuable new perspectives. Although their approach is bold, they will certainly prompt interesting reflections on traditional teachings. A significant portion of this second volume is committed to modern physics, including an introduction to the standard model of fundamental interactions. The old quantum mechanics is largely excluded in favour of quantum field theory, which we present in a manner accessible to undergraduate students.

Brownian Motion and Potential Theory, Modern and Classical (1版)

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【簡介】 In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions. The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series. 【目錄】 Contents: Introduction Martingales and Markov Processes Brownian Motion and Ito-Calculus Semi-Groups of Operators, Potentials, and Diffusion Equations Harmonic Functions, Dynkin, and Transforms Superharmonic Functions and Riesz Measures Green Functions, Boundary Value Problems, and Kernels Potential Theory, Capacity, Boundaries, Dirichlet Spaces, and Applications Appendix: Kernels and More General Classes of Gaussian Processes

Classical Mechanics and Electrodynamics (2版)

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【簡介】 The book gives a general introduction to classical theoretical physics, in the fields of mechanics, relativity and electromagnetism. It is analytical in approach and detailed in the derivations of physical consequences from the fundamental principles in each of the fields. This second edition has a new part, namely Classical Field Theory. Highlighting a close connection between this part and earlier parts of the book, where particles, rather than fields are the center of attention. As a general introduction to classical theoretical physics, the book is different from most textbooks at this level, which focus either on classical mechanics or classical electrodynamics but not both. The book will in particular be useful as a textbook for physics courses with such a broader approach to classical physics. For a wider group of students, the book may be of interest for self study. The new inclusion on classical field theory, will give students greater understanding on previous parts of the book, such as examining the Lagrangian formulation of Maxwell's equations with Noether's theorem. This is central in the use of Lagrangian on fields, as also discussed. The text is illustrated with many figures, most of these in color. There are many useful examples and exercises which complement the derivations in the text. 【目錄】 Analytical Mechanics: Generalized Coordinates Lagrange's Equations Hamiltonian Dynamics Relativity: The Four-Dimensional Space-Time Consequences of the Lorentz Transformations Four-Vector Formalism and Covariant Equations Relativistic Kinematics Relativistic Dynamics Electrodynamics: Maxwell's Equations Electromagnetic Field Dynamics Maxwell's Equations with Stationary Sources Electromagnetic Radiation Classical Field Theory: Lagrangian and Hamiltonian Formulations Symmetry Transformations Relativistic Fields