Local Mathematics for Local Physics: From Number Scaling to Guage Theory and Cosmology

Local Mathematics for Local Physics: From Number Scaling to Guage Theory and Cosmology
Title Local Mathematics for Local Physics: From Number Scaling to Guage Theory and Cosmology PDF eBook
Author Paul Benioff
Publisher World Scientific Publishing Europe Limited
Total Pages 0
Release 2023-12
Genre Mathematics
ISBN 9781800614963

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The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.

Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology

Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology
Title Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology PDF eBook
Author Paul Benioff
Publisher World Scientific
Total Pages 296
Release 2024-01-19
Genre Mathematics
ISBN 1800614985

Download Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology Book in PDF, Epub and Kindle

The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.

Statistical Geometry and Applications to Microphysics and Cosmology

Statistical Geometry and Applications to Microphysics and Cosmology
Title Statistical Geometry and Applications to Microphysics and Cosmology PDF eBook
Author S. Roy
Publisher Springer Science & Business Media
Total Pages 262
Release 2012-12-06
Genre Science
ISBN 9401152306

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Recent results from high-energy scattering and theoretical developments of string theory require a change in our understanding of the basic structure of space-time. This book is about the advancement of ideas on the stochastic nature of space-time from the 1930s onward. In particular, the author promotes the concept of space as a set of hazy lumps, first introduced by Karl Menger, and constructs a novel framework for statistical behaviour at the microlevel. The various chapters address topics such as space-time fluctuation and random potential, non-local fields, and the origin of stochasticity. Implications in astro-particle physics and cosmology are also explored. Audience: This volume will be of interest to physicists, chemists and mathematicians involved in particle physics, astrophysics and cosmology.

Modern Mathematical Models of Time and their Applications to Physics and Cosmology

Modern Mathematical Models of Time and their Applications to Physics and Cosmology
Title Modern Mathematical Models of Time and their Applications to Physics and Cosmology PDF eBook
Author W.G. Tifft
Publisher Springer Science & Business Media
Total Pages 382
Release 2012-12-06
Genre Science
ISBN 940115628X

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The nature of time has long puzzled physicists and philosophers. Time potentially has very fundamental yet unknown properties. In 1993 a new model of multi-dimensional time was found to relate closely to properties of the cosmological redshift. An international conference was subsequently convened in April 1996 to examine past, current and new concepts of time as they relate to physics and cosmology. These proceedings incorporate 34 reviews and contributed papers from the conference. The major reviews include observational properties of the redshift, alternative cosmologies, critical problems in cosmology, alternative viewpoints and problems in gravitation theory and particle physics, and new approaches to mathematical models of time. Professionals and students with an interest in cosmology and the structure of the universe will find that this book raises critical problems and explores challenging alternatives to classical viewpoints.

Space – Time – Matter

Space – Time – Matter
Title Space – Time – Matter PDF eBook
Author Jochen Brüning
Publisher Walter de Gruyter GmbH & Co KG
Total Pages 517
Release 2018-04-09
Genre Mathematics
ISBN 3110451530

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This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

Advances in Algebraic Quantum Field Theory

Advances in Algebraic Quantum Field Theory
Title Advances in Algebraic Quantum Field Theory PDF eBook
Author Romeo Brunetti
Publisher Springer
Total Pages 460
Release 2015-09-04
Genre Science
ISBN 3319213539

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This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

New Trends in Mathematical Physics

New Trends in Mathematical Physics
Title New Trends in Mathematical Physics PDF eBook
Author Vladas Sidoravicius
Publisher Springer
Total Pages 916
Release 2016-05-01
Genre
ISBN 9789401777711

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The XV-th International Congress on Mathematical Physics took place in Rio de Janeiro, on August 5 11, 2006. I believe it was a very successful and enjoyable meeting. It is very fortunate for our community that Latin America, and especially Brazil, in decades has become the place where all ?elds of intellectual activity which are traditionally regarded as part of Mathematical Physics are developing with steady pace and remarkable quality. Another important aspect of this devel- mentis thatbesidesareaswhichalreadyhaveworldwiderecognitionandlongsta- ing tradition in Brazil such as Dynamical Systems, Statistical Mechanics, Probab- ity Theory, etc., there is intensive growth in other directions such as String Theory and Algebraic Geometry. Brazil s major universities and research institutes such as IMPA and CBPF are successfully bringing up a new generation of researchers in our ?eld. Thus it was especially pleasant to see that among more than 500 participants of the Congress, the majority was constituted by young researchers and graduate students. Given the enormous range of subjects covered during the Congress, and the - versity of scienti?c contributions, it would be pointless to summarize the contents here the quality is re?ected in these pages. Traditionally, besides its very intense scienti?c program, the Congress was the occasion for the award of the Henri Poincare Prizes of the IAMP, sponsored by the Daniel Iagolnitzer Foundation. The Laureates for the year 2006 were Ludwig Faddeev, David Ruelle and Edward Witten."