Nielsen, Torben T.
Bose Algebras: The Complex and Real Wave Representations [electronic resource] / by Torben T. Nielsen. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1991. - VI, 138 p. online resource. - Lecture Notes in Mathematics, 1472 0075-8434 ; . - Lecture Notes in Mathematics, 1472 .
The Bose algebra ?0?,?,? -- Lifting operators to ?? -- The coherent vectors in ?? -- The Wick ordering and the Weyl relations -- Some special operators -- The complex wave representation -- The real wave representation -- Bose algebras of operators -- Wave representations of ?(?+?*).
The mathematics of Bose-Fock spaces is built on the notion of a commutative algebra and this algebraic structure makes the theory appealing both to mathematicians with no background in physics and to theorectical and mathematical physicists who will at once recognize that the familiar set-up does not obscure the direct relevance to theoretical physics. The well-known complex and real wave representations appear here as natural consequences of the basic mathematical structure - a mathematician familiar with category theory will regard these representations as functors. Operators generated by creations and annihilations in a given Bose algebra are shown to give rise to a new Bose algebra of operators yielding the Weyl calculus of pseudo-differential operators. The book will be useful to mathematicians interested in analysis in infinitely many dimensions or in the mathematics of quantum fields and to theoretical physicists who can profit from the use of an effective and rigrous Bose formalism.
9783540473671
10.1007/BFb0098303 doi
Mathematics.
Global analysis (Mathematics).
Mathematical physics.
Mathematics.
Analysis.
Mathematical and Computational Physics.
QA299.6-433
515
Bose Algebras: The Complex and Real Wave Representations [electronic resource] / by Torben T. Nielsen. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1991. - VI, 138 p. online resource. - Lecture Notes in Mathematics, 1472 0075-8434 ; . - Lecture Notes in Mathematics, 1472 .
The Bose algebra ?0?,?,? -- Lifting operators to ?? -- The coherent vectors in ?? -- The Wick ordering and the Weyl relations -- Some special operators -- The complex wave representation -- The real wave representation -- Bose algebras of operators -- Wave representations of ?(?+?*).
The mathematics of Bose-Fock spaces is built on the notion of a commutative algebra and this algebraic structure makes the theory appealing both to mathematicians with no background in physics and to theorectical and mathematical physicists who will at once recognize that the familiar set-up does not obscure the direct relevance to theoretical physics. The well-known complex and real wave representations appear here as natural consequences of the basic mathematical structure - a mathematician familiar with category theory will regard these representations as functors. Operators generated by creations and annihilations in a given Bose algebra are shown to give rise to a new Bose algebra of operators yielding the Weyl calculus of pseudo-differential operators. The book will be useful to mathematicians interested in analysis in infinitely many dimensions or in the mathematics of quantum fields and to theoretical physicists who can profit from the use of an effective and rigrous Bose formalism.
9783540473671
10.1007/BFb0098303 doi
Mathematics.
Global analysis (Mathematics).
Mathematical physics.
Mathematics.
Analysis.
Mathematical and Computational Physics.
QA299.6-433
515