The Structure of representations of the canonical commutation relations
Author : John S. Lew
Publisher :
Page : 596 pages
File Size : 33,69 MB
Release : 1960
Category : Quantum field theory
ISBN :
Author : John S. Lew
Publisher :
Page : 596 pages
File Size : 33,69 MB
Release : 1960
Category : Quantum field theory
ISBN :
Author : John S. Lew
Publisher :
Page : 306 pages
File Size : 35,77 MB
Release : 1960
Category :
ISBN :
Author : John S. Lew
Publisher :
Page : pages
File Size : 14,76 MB
Release : 1960
Category :
ISBN :
Author : Dénes Petz
Publisher :
Page : 120 pages
File Size : 49,13 MB
Release : 1990
Category : Mathematics
ISBN :
Author : Asao Arai
Publisher : Springer Nature
Page : 505 pages
File Size : 24,49 MB
Release : 2020-02-04
Category : Science
ISBN : 9811521808
Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation–theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov–Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics.
Author : Lars Hellstrm
Publisher : World Scientific
Page : 280 pages
File Size : 34,4 MB
Release : 2000
Category : Mathematics
ISBN : 9789810244033
Noncommutative algebras, rings and other noncommutative objects, along with their more classical commutative counterparts, have become a key part of modern mathematics, physics and many other fields. The q-deformed Heisenberg algebras defined by deformed Heisenberg canonical commutation relations of quantum mechanics play a distinguished role as important objects in pure mathematics and in many applications in physics. The structure of commuting elements in an algebra is of fundamental importance for its structure and representation theory as well as for its applications. The main objects studied in this monograph are q-deformed Heisenberg algebras -- more specifically, commuting elements in q-deformed Heisenberg algebras. In this book the structure of commuting elements in q-deformed Heisenberg algebras is studied in a systematic way. Many new results are presented with complete proofs. Several appendices with some general theory used in other parts of the book include material on the Diamond lemma for ring theory, a theory of degree functions in arbitrary associative algebras, and some basic facts about q-combinatorial functions over an arbitrary field. The bibliography contains, in addition to references on q-deformed Heisenberg algebras, some selected references on related subjects and on existing and potential applications. The book is self-contained, as far as proofs and the background material are concerned. In addition to research and reference purposes, it can be used in a special course or a series of lectures on the subject or as complementary material to a general course on algebra. Specialists as well as doctoral and advanced undergraduate students in mathematics andphysics will find this book useful in their research and study.
Author : Gordon McCabe
Publisher : Elsevier
Page : 265 pages
File Size : 33,77 MB
Release : 2011-08-30
Category : Science
ISBN : 0080498302
This book provides a philosophically informed and mathematically rigorous introduction to the 'standard model' of particle physics. The standard model is the currently accepted and experimentally verified model of all the particles and interactions in our universe. All the elementary particles in our universe, and all the non-gravitational interactions -the strong nuclear force, the weak nuclear force, and the electromagnetic force - are collected together and, in the case of the weak and electromagnetic forces, unified in the standard model. Rather than presenting the calculational recipes favored in most treatments of the standard model, this text focuses upon the elegant mathematical structures and the foundational concepts of the standard model. · Combines an exposition of the philosophical foundations and rigorous mathematical structure of particle physics· Demonstrates the standard model with elegant mathematics, rather than a medley of computational recipes· Promotes a group-theoretical and fibre-bundle approach to the standard model, rather than the Lagrangian approach favoured by calculationalists· Explains the different approaches to particle physics and the standard model which can be found within the literature
Author : Hideyasu Yamashita
Publisher :
Page : 18 pages
File Size : 37,28 MB
Release : 1999
Category : Commutation relations (Quantum mechanics)
ISBN :
Author : Palle E.T. Jorgensen
Publisher : Courier Dover Publications
Page : 307 pages
File Size : 44,92 MB
Release : 2017-05-22
Category : Science
ISBN : 0486822575
Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.
Author : K.-D. Bierstedt
Publisher : Elsevier
Page : 355 pages
File Size : 20,13 MB
Release : 1980-01-01
Category : Mathematics
ISBN : 0080871496
Functional Analysis: Surveys and Recent Results II