The Continuum Limit Of Causal Fermion Systems

Author : Felix Finster
Publisher : Springer
Page : 548 pages
File Size : 49,5 Mb
Release : 2016-08-19
Category : Science
ISBN : 9783319420677

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The Continuum Limit of Causal Fermion Systems by Felix Finster Pdf

This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries". The dynamics is described by a novel variational principle, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how the causal action principle gives rise to the interactions of the standard model plus gravity on the level of second-quantized fermionic fields coupled to classical bosonic fields. The focus is on getting a mathematically sound connection between causal fermion systems and physical systems in Minkowski space. The book is intended for graduate students entering the field, and is furthermore a valuable reference work for researchers in quantum field theory and quantum gravity.

Author : Felix Finster,Niky Kamran
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 51,9 Mb
Release : 2019-06-10
Category : Electronic
ISBN : 9781470436216

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Spinors on Singular Spaces and the Topology of Causal Fermion Systems by Felix Finster,Niky Kamran Pdf

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

Author : Felix Finster,Domenico Giulini,Johannes Kleiner,Jürgen Tolksdorf
Publisher : Springer Nature
Page : 302 pages
File Size : 42,6 Mb
Release : 2020-04-09
Category : Science
ISBN : 9783030389413

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Progress and Visions in Quantum Theory in View of Gravity by Felix Finster,Domenico Giulini,Johannes Kleiner,Jürgen Tolksdorf Pdf

This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Author : Remo Ruffini,Gregory Vereshchagin
Publisher : World Scientific
Page : 4880 pages
File Size : 51,7 Mb
Release : 2022-12-15
Category : Science
ISBN : 9789811269783

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Sixteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg16 Meeting On General Relativity (In 4 Volumes) by Remo Ruffini,Gregory Vereshchagin Pdf

The proceedings of MG16 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 46 plenary presentations, 3 public lectures, 5 round tables and 81 parallel sessions arranged during the intense six-day online meeting. All talks were recorded and are available on the ICRANet YouTube channel at the following link: www.icranet.org/video_mg16.These proceedings are a representative sample of the very many contributions made at the meeting. They contain 383 papers, among which 14 come from the plenary sessions.The material represented in these proceedings cover the following topics: accretion, active galactic nuclei, alternative theories of gravity, black holes (theory, observations and experiments), binaries, boson stars, cosmic microwave background, cosmic strings, dark energy and large scale structure, dark matter, education, exact solutions, early universe, fundamental interactions and stellar evolution, fast transients, gravitational waves, high energy physics, history of relativity, neutron stars, precision tests, quantum gravity, strong fields, and white dwarf; all of them represented by a large number of contributions.The online e-proceedings are published in an open access format.

Author : Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf
Publisher : Birkhäuser
Page : 518 pages
File Size : 45,8 Mb
Release : 2016-02-24
Category : Science
ISBN : 9783319269023

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Quantum Mathematical Physics by Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf Pdf

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Author : Giacomo Mauro D’Ariano,Paolo Perinotti
Publisher : MDPI
Page : 508 pages
File Size : 52,6 Mb
Release : 2020-03-23
Category : Mathematics
ISBN : 9783039283804

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Quantum Information and Foundations by Giacomo Mauro D’Ariano,Paolo Perinotti Pdf

Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.

Author : Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 41,9 Mb
Release : 2012-02-08
Category : Mathematics
ISBN : 9783034800433

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Quantum Field Theory and Gravity by Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler Pdf

One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Author : Sergio Cacciatori,Batu Güneysu,Stefano Pigola
Publisher : Springer Nature
Page : 359 pages
File Size : 50,8 Mb
Release : 2019-11-23
Category : Science
ISBN : 9783030180614

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Einstein Equations: Physical and Mathematical Aspects of General Relativity by Sergio Cacciatori,Batu Güneysu,Stefano Pigola Pdf

This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.

Author : Bertfried Fauser,Jürgen Tolksdorf,Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 51,5 Mb
Release : 2009-06-02
Category : Science
ISBN : 9783764387365

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Quantum Field Theory by Bertfried Fauser,Jürgen Tolksdorf,Eberhard Zeidler Pdf

The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.

Author : Felix Finster,Niky Kamran
Publisher : Unknown
Page : 128 pages
File Size : 49,9 Mb
Release : 2019
Category : Electronic
ISBN : 147045257X

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Spinors on Singular Spaces and the Topology of Causal Fermion Systems by Felix Finster,Niky Kamran Pdf

Author : Felix Finster
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 48,5 Mb
Release : 2006
Category : Dirac equation
ISBN : 9780821839744

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The Principle of the Fermionic Projector by Felix Finster Pdf

The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionicprojector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible toformulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective interaction which shows many similarities to the interactions of the standard model. The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material, which willbe useful to the experienced researcher.

Author : Henrik Bruus,Karsten Flensberg,ØRsted Laboratory Niels Bohr Institute Karsten Flensberg
Publisher : Oxford University Press
Page : 458 pages
File Size : 41,7 Mb
Release : 2004-09-02
Category : Science
ISBN : 9780198566335

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Many-Body Quantum Theory in Condensed Matter Physics by Henrik Bruus,Karsten Flensberg,ØRsted Laboratory Niels Bohr Institute Karsten Flensberg Pdf

The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.

Author : John W Fowler
Publisher : World Scientific
Page : 536 pages
File Size : 46,9 Mb
Release : 2021-07-08
Category : Science
ISBN : 9789811243486

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Randomness And Realism: Encounters With Randomness In The Scientific Search For Physical Reality by John W Fowler Pdf

Randomness is an active element relevant to all scientific activities. The book explores the way in which randomness suffuses the human experience, starting with everyday chance events, followed by developments into modern probability theory, statistical mechanics, scientific data analysis, quantum mechanics, and quantum gravity. An accessible introduction to these theories is provided as a basis for going into deeper topics.Fowler unveils the influence of randomness in the two pillars of science, measurement and theory. Some emphasis is placed on the need and methods for optimal characterization of uncertainty. An example of the cost of neglecting this is the St. Petersburg Paradox, a theoretical game of chance with an infinite expected payoff value. The role of randomness in quantum mechanics reveals another particularly interesting finding: that in order for the physical universe to function as it does and permit conscious beings within it to enjoy sanity, irreducible randomness is necessary at the quantum level.The book employs a certain level of mathematics to describe physical reality in a more precise way that avoids the tendency of nonmathematical descriptions to be occasionally misleading. Thus, it is most readily digested by young students who have taken at least a class in introductory calculus, or professional scientists and engineers curious about the book's topics as a result of hearing about them in popular media. Readers not inclined to savor equations should be able to skip certain technical sections without losing the general flow of ideas. Still, it is hoped that even readers who usually avoid equations will give those within these pages a chance, as they may be surprised at how potentially foreboding concepts fall into line when one makes a legitimate attempt to follow a succession of mathematical implications.

Author : Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein
Publisher : Springer Nature
Page : 160 pages
File Size : 42,7 Mb
Release : 2020-01-27
Category : Science
ISBN : 9783030344894

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Tensor Network Contractions by Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein Pdf

Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Author : Vladimir Z. Kresin
Publisher : Springer
Page : 296 pages
File Size : 46,9 Mb
Release : 2013-06-05
Category : Science
ISBN : 1489915575

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Pair Correlations in Many-Fermion Systems by Vladimir Z. Kresin Pdf

At first glance, the articles in this book may appear to have nothing in common. They cover such seemingly disparate subjects as the properties of small metallic clusters and the behavior of superfluid He3, nuclear physics and organic materials, copper oxides and mag netic resonance. Why have they been brought together, particUlarly in our time of narrow spe cialization? In fact, the properties and effects described in this book touch upon one and the same fundamental phenomenon: pair correlation. Introduced in the theory of superconductivity by J. Bardeen, L. Cooper, and J. Schrieffer (BCS), this effect plays a key role in various Fermi systems. The book consists of several sections. The first chapter is concerned with conven tional and high Tc superconductors. The second chapter describes two relatively young fami lies of superconductors: organics and fullerenes. Chapter III addresses the superfluidity of 3 He • The discovery of this phenomenon in 1971 was a big event in physics and last year was acknowledged by a Nobel prize. This book contains the text of the Nobel lecture. Chapters IV and V are devoted to correlations in finite Fermi systems such as small metallic clusters, C 60 anions, and atomic nuclei. The book thus covers a broad range of problems, illuminating the close ties between various areas of physics.