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Blatter H: Radical Relativity

Radical Relativity

An Uncommon Way to Spacetime

This book is devoted to description of different geometric structures, including the classical structures of differential geometry like de Rham complex, Dolbeaux complex and Dirac complex and also some structures that have not attracted yet an attention of mathematicians in the language of supersymmetric quantum mechanics. The book is addressed both to physicists and mathematicians.The first part is addressed mainly to physicists and describes basic properties of smooth manifolds of different type: real, complex, Kaehler, hyperkaehler and HKT. The second part is addressed to mathematicians and describes basic properties of classical and quantum mechanical systems, including supersymmetric systems with Grassmann dynamic variables. The third part is called Synthesis: we show how the physical methods allow one to describe in a simple way and understand many nontrivial geometric facts. For example, the famous Atiyah-Singer theorem admits a rather natural and simple supersymmetric interpretation.This book is an updated and expanded version of the book Differential geometry through supersymmetric glasses published in 2020 by World Scientific. New material on hyperkaehler geometry and its supersymmetric description and on the gauge fields in CPn manifolds is added.

Geometry Meets Supersymmetry

Series in Computational Biophysics

Multiscale methods are ideally suited to simulate the processes at work in many biomolecular systems, which often span a large range of time and length scales. Multiscale Methods in Molecular Biophysics highlights the advantages of these methods for integrating different levels of detail in a single simulation setting. It covers the practical methodology and successful applications in areas such as enzyme catalysis, protein folding, and ligand binding. The book is divided into three main sections: combination quantum and classical (atomistic) descriptions, approaches that combine atomistic and coarse-grained level of details, and multiscale methods where the resolution coupling is between global collective coordinates and local details.

Multiscale methods are ideally suited to simulate the processes at work in many biomolecular systems, which often span a large range of time and length scales. Multiscale Methods in Molecular Biophysics highlights the advantages of these methods for integrating different levels of detail in a single simulation setting. It covers the practical methodology and successful applications in areas such as enzyme catalysis, protein folding, and ligand binding. The book is divided into three main sections: combination quantum and classical (atomistic) descriptions, approaches that combine atomistic and coarse-grained level of details, and multiscale methods where the resolution coupling is between global collective coordinates and local details.

Multiscale Methods in Molecular Biophysics

Introduction To Statistics And Data Analysis For Physicists (Fourth Edition)

Springer Proceedings in Physics

This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems - 2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023. It offers readers an array of captivating connections between fractal theory and nonlinear dynamics across various physics sub-domains and mathematical modeling. Fractal geometry has been developed to describe irregular natural objects that defy characterization using Euclidean geometry. Fractal techniques, such as fractal dimension and fractal functions, prove effective in mathematically modeling real-world phenomena and forecasting future consequences. The impact of fractal theory on physical sciences is widely recognized, as natural phenomena frequently exhibit fractal structures. These new concepts revolutionize our understanding of the large-scale properties of matter distribution in the universe. 
The book aims to familiarize readers with recent developments in common fractal patterns found in statistical physics, quantum physics, and plasma physics. Furthermore, it highlights the relationship between fractals and nonlinear dynamics through innovative approaches in mathematical modeling. This publication caters to professionals in mathematics, physics, and computer science, and also serves as a helpful resource for non-specialists seeking to comprehend fractal and nonlinear dynamics concepts. It offers valuable applications for researchers in both pure and applied backgrounds of physics and engineering.

This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems—2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023. It offers readers an array of captivating connections between fractal theory and nonlinear dynamics across various physics sub-domains and mathematical modeling. Fractal geometry has been developed to describe irregular natural objects that defy characterization using Euclidean geometry. Fractal techniques, such as fractal dimension and fractal functions, prove effective in mathematically modeling real-world phenomena and forecasting future consequences. The impact of fractal theory on physical sciences is widely recognized, as natural phenomena frequently exhibit fractal structures. These new concepts revolutionize our understanding of the large-scale properties of matter distribution in the universe.The book aims to familiarize readers with recent developments in common fractal patterns found in statistical physics, quantum physics, and plasma physics. Furthermore, it highlights the relationship between fractals and nonlinear dynamics through innovative approaches in mathematical modeling. This publication caters to professionals in mathematics, physics, and computer science, and also serves as a helpful resource for non-specialists seeking to comprehend fractal and nonlinear dynamics concepts. It offers valuable applications for researchers in both pure and applied backgrounds of physics and engineering.

Selected Proceedings of the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems—2023 (ISMAFDS-2023)

Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns

The purpose of the book is a mathematical and experimental study of extreme, multivalued waves based on scalar field equations. It is known that Einstein tried to build a unified (interdisciplinary) field theory that would unite all interactions in Nature into a single system. The book uses this idea, supplemented by the idea that all fundamental interactions have a wave, resonant, nonlinear nature. The theoretical foundation of the book also consists of the results of Leonard Euler.

Fundamental questions about the polysemy of Nature are considered. On this basis, various highly nonlinear wave processes are modeled, ranging from waves in resonators and ocean waves to descriptions of particle-waves, the origin of the Universe and data from double-slit experiments. Gravitational and inertial effects are associated with solutions of relativistic wave equations. According to the book, the unsolved nature of some fundamental problems in physics is explained by the nonlinear and resonant nature of the world around us, which exists in a non-smooth and inhomogeneous space-time.

We do not know how strong the influence of multivalued wave processes on the Universe is. This book is the first attempt to assess this influence. At the same time, the extreme waves considered in this book may be applied to different technologies and systems ranging from the atomic scale to the cosmos.

With this book, the author celebrates the 100th anniversary of the beginning of the development of quantum mechanics and modern cosmology.

From Euler Figures to Faraday Waves, Particle-Waves and Universes

Extreme Multivalued Waves as a Model of Everything

Theory, Observations, and Applications

An Introduction to General Relativity and Cosmology

Dynamics and Astrophysics of Galaxies

Leuchte und entdecke

Wieso? Weshalb? Warum?

Wieso? Weshalb? Warum? Leuchte und entdecke - Weltraum

Radon Series on Computational and Applied Mathematics

Hilbert Space Methods for the Theory of Electromagnetism

Maxwell’s Equations

This will be the 7th book in the author's 'Lectures on ...' book series, and the first aimed at graduate-level readers(two additional graduate texts are in preparation). Primarily intended for physics graduate students, the book is accessible to advanced undergraduates and will appeal to students with a background in statistics and a keen interest in quantum physics. By the end of this book, readers will be well-prepared for working on research projects that require the drawing of inference from the noisy data collected in quantum experiments, as epitomized by quantum state estimation.The book begins with chapters on the basics of estimation theory and the basics of quantum theory. This includes, in particular, the roles played by the frequentist methods of statistics, which are crucial when planning an experiment, and the Bayesian methods, which are the tools for drawing inference from the actual data gathered. A central concept is that of optimal error regions that supplement the point estimators ('best guesses') with the analogs of error bars in the high-dimensional parameter space; there is, in particular, the plausible region which comprises all point estimators supported by the data.Practical applications require the evaluation of high-dimensional integrals with the aid of Monte Carlo integration. For that, one needs to draw samples of quantum states from the relevant distributions, namely the priors and posteriors of Bayesian methodology. The book discusses the algorithms well-suited for this kind of sampling, which is central to the processing of real-life data.The book illustrates all concepts with pertinent examples and offers numerous exerciseswhich the readers can practice and perfect their skills with. The presentation is detailed and does not skip technical steps, which makes the book particularly valuable for self-studying readers and as textbook adopted by lecturers teaching courses on this or related topics. While the book is based on lecture notes developed for the author's courses on quantum state estimation at NUS and BIT, this book also offers a comprehensive account of the concepts and methods developed in the author's group at CQT and presents this material in textbook form for the first time.

Lectures On Quantum State Estimation

Fractional Calculus presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and contribute to the development of this exciting research area. It is especially devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights.This new, extended edition includes additional chapters about the optical model in view of fractional calculus, using machine learning to detect anti-causal sound samples, remarks on covariance in non-local field theories and a completely new section on numerical algorithms for fractional calculus. Motivated by positive responses, new exercises with elaborated solutions are added, significantly supporting a deeper understanding of the general aspects of the theory.Besides students and researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject.

Fractional Calculus: An Introduction For Physicists (Fourth Edition)

Many-Body Green's Functions for Time-Dependent Problems

Radical Relativity

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