Kategoria BISAC: Mathematics >> Algebra - Abstract

The author introduces the supersymmetric localization technique, a new approach for computing path integrals in quantum field theory on curved space (time) defined with interacting Lagrangian.

The author focuses on a particular quantity called the superconformal index (SCI), which is defined by considering the theories on the product space of two spheres and circles, in order to clarify the validity of so-called three-dimensional mirror symmetry, one of the famous duality proposals. In addition to a review of known results, the author presents a new definition of SCI by considering...

This book explains the group representation theory for quantum theory in the language of quantum theory. Group representation theory is a fundamental mathematical tool for quantum theory, in particular, for quantum information. Quantum theory requires so many aspects of group representation theory. There are so many books for group representation theory. Most of books based on the mathematical viewpoint focus only on a part of group representation used for quantum theory. In particular, they do not focus on the projective representation while any physical realizable symmetry is written as...

This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.

Topics presented include:

structure and representation theory of reductive algebraic monoids

monoid schemes and applications of monoids

monoids related to Lie theory

equivariant embeddings of algebraic groups

constructions and properties of monoids from algebraic combinatorics

endomorphism monoids induced from vector bundles

Hodge-Newton decompositions of reductive...

The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus.

The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and...

This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata and algebraic circuits, such as finite fields or Galois fields.

The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs...

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham s theorem on simplicial complexes. In addition, Sullivan s results on computing the rational homotopy type from forms is presented.

New to the Second Edition:

*Fully-revised appendices including an expanded discussion of the Hirsch...

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets...

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...

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field.

Then, abelian and derived categories are introduced in detail and are used to...