Eckehard W. Mielke – författare

No detailed description available for "Geometrodynamics of Gauge Fields".

This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included.  By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed.Since the discovery of the Higgs boson, concepts of spontaneous  symmetry breaking in gravity have come again into focus, and, in this revised edition,  these will be exposed in geometric terms.  Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included.  By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed.Since the discovery of the Higgs boson, concepts of spontaneous  symmetry breaking in gravity have come again into focus, and, in this revised edition,  these will be exposed in geometric terms.  Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

Today, Relativity is becoming an integrated aspect of engineering fields. Its application to the Global Positioning System (GPS), extends in usage from smart watches to the navigation of cars, airplanes (drones) and even autonomous tractors. In rather expensive particle accelerators, physicists are everyday "playing" with Relativistic Billiards, common to the betatrons of cancer therapy using electrons. Computer programs, such as "ray tracing" methods, are enhanced to simulate objects in relativistic motion, which now offer us relativistic visualizations of accretion disks around compact, astrophysical objects like Black Holes.Against the backdrop of the applications explained throughout the chapters, this book takes on a practical and intuitive approach in introducing the Lorentz invariance of light propagation and space-time concepts. The book begins with simple mathematics, like the classical Pythagoras formula for energy-momentum "triangles". Later, readers will find the intuitive vector calculus reemerging in the expansion of full relativistic expressions. Prepared with instructive diagrams of recent experiments, even the layperson can grasp the essential study of Relativity and marvel at its applications within this book.