Spectral Spaces

Author: Max Dickmann,Niels Schwartz,Marcus Tressl

Publisher: Cambridge University Press

ISBN: 1107146720

Category: Mathematics

Page: 657

View: 7522

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Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
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Motivic Homotopy Theory

Lectures at a Summer School in Nordfjordeid, Norway, August 2002

Author: Bjorn Ian Dundas,Marc Levine,P. A. Ostvaer,P.A. Østvær,Oliver Röndigs,Vladimir Voevodsky

Publisher: Springer Science & Business Media

ISBN: 3540458956

Category: Mathematics

Page: 220

View: 579

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This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work.
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Towards the Mathematics of Quantum Field Theory

Author: Frédéric Paugam

Publisher: Springer Science & Business Media

ISBN: 3319045644

Category: Science

Page: 487

View: 6674

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This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.
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