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Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifo

Field theory (Physics) --- Lagrange equations. --- Mathematics.

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Cambray contextualizes the work of C. G. Jung in relation to contemporary scientific advancements such as relativity and quantum theory and explores how Jung's theories, practices, and clinical methods iinfluenced the current field of complexity theory.

Coincidence. --- Field theory (Physics) --- System theory. --- Complexity (Philosophy) --- Empathy. --- Democracy --- Psychological aspects. --- Jung, C. G.

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The Transparent Becoming of World undertakes a penetrating inquiry into the quotidian world we take for granted and the brain that silently hoists our bubbles of world-thrownness. After critiquing the traditional views of direct realism, indirect realism and idealism, the continual becoming of world is explained by a novel integration of process dynamics, as formulated by Whitehead, Heidegger and Bohm, with the burgeoning field of quantum neurophilosophy. A rich ontological duality newly opened by quantum brain theory is exploited: the "between-two" of dual quantum modes. Existence as world-thrownness is between-two in waking and dreaming alike. This highly original interdisciplinary book may be of interest to philosophers, psychologists, neuroscientists, consciousness researchers, indeed anyone attracted to the enigma of their own lived existence. (Series A).

Mind and reality. --- Process philosophy. --- Quantum field theory. --- Neuropsychology --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Change --- Philosophy --- Reality and mind --- Reality --- Philosophy.

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Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. Some of its consequences (e.g., the Chebotarev density theorem) apply even to nonabelian extensions. This book is an accessible introduction to class field theory. It takes a traditional approach in that it presents the global material first, using some of the original techniques of proof, but in a fashion that is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included exercises throughout the text. Professor Nancy Childress is a member of the Mathematics Faculty at Arizona State University.

Mathematics. --- Field Theory and Polynomials. --- Number Theory. --- Field theory (Physics). --- Number theory. --- Mathématiques --- Champs, Théorie des (Physique) --- Théorie des nombres --- Class field theory. --- Nombres, Théorie des --- Corps de classe

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This book has resulted from a course in the general theory of relativity at the University of Oslo where the author has lectured for more than twenty years. Although the text is designed for master students, it is rather self-contained. Since mathematics courses on differential geometry and tensor calculus usually employ a rather abstract notation different from the component notation used in physical applications, the book introduces not only an introduction to the physical principles of the theory and physical applications of the theory, but also introduces the mathematics which is needed, in particular the calculus of differential forms. Detailed calculations are given of the bending of light, the perihelion precession of Mercury and the predictions for the Hafele-Keating experiment. The Tolman-Oppenheimer-Volkoff equation is deduced and solved for an incompressible fluid to give the internal Schwarzschild solution. Rotating black holes are discussed. The Friedmann-Robertson-Walker universe models are deduced. Also the reader will become familiar with the Universe model which is now considered as the standard model of the universe; a flat model filled with vacuum energy and cold matter. The inflationary era at the first moment of the history of our universe is also discussed.

Relativity (Physics) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Physics. --- Natural philosophy --- Philosophy, Natural --- Gravitation. --- Astronomy. --- Astrophysics. --- Cosmology. --- Classical and Quantum Gravitation, Relativity Theory. --- Mathematical Methods in Physics. --- Astronomy, Astrophysics and Cosmology. --- Physical sciences --- Dynamics --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Mathematical physics. --- Physical mathematics --- Mathematics --- Astronomical physics --- Astronomy --- Cosmic physics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties