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Mathematics of quantization and quan...

Derezinski, Jan, (1957-)

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Mathematics of quantization and quantum fields /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematics of quantization and quantum fields // Jan Derezinski, Christian Gérard.
作者:	Derezinski, Jan,
其他作者:	Gérard, Christian,
出版者:	Cambridge :Cambridge University Press, : 2013.,
面頁冊數:	xii, 674 p. :ill ;26 cm.
標題:	Geometric quantization. -
ISBN:	9781107011113 (hbk.) :

Mathematics of quantization and quantum fields /
Derezinski, Jan,1957-

Mathematics of quantization and quantum fields /Jan Derezinski, Christian Gérard. - Cambridge :Cambridge University Press,2013. - xii, 674 p. :ill ;26 cm. - Cambridge monographs on mathematical physics.. - Cambridge monographs on mathematical physics.

Includes bibliographical references (pages 661-667) and indexes.

Introduction --

Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, such as tensors, algebras, Fock spaces and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in -depth coverage, this text is essential reading for graduate students and researchers in departments of mathematics and physics--

ISBN: 9781107011113 (hbk.) :US280.00 (2 vol.)

LCCN: 2012032862Subjects--Topical Terms:

579202
Geometric quantization.

LC Class. No.: QC174.17.G46 / D47 2013

Dewey Class. No.: 530.120151

Mathematics of quantization and quantum fields /
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100 1 $a Derezinski, Jan, $d 1957- $e author. $3 1982340
245 1 0 $a Mathematics of quantization and quantum fields / $c Jan Derezinski, Christian Gérard.
260 # $a Cambridge : $b Cambridge University Press, $c 2013.
300 $a xii, 674 p. : $b ill ; $c 26 cm.
490 1 0 $a Cambridge monographs on mathematical physics.
504 $a Includes bibliographical references (pages 661-667) and indexes.
505 0 # $t Introduction -- $t Vector spaces -- $t Operators in Hilbert spaces -- $t Tensor algebras -- $t Analysis in L2(Rd) -- $t Measures -- $t Algebras -- $t Anti-symmetric calculus -- $t Canonical commutation relations -- $t CCR on Fock spaces -- $t Symplectic invariance of CCR in finite dimensions -- $t Symplectic invariance of the CCR on Fock spaces -- $t Canonical anti-commutation relations -- $t CAR on Fock spaces -- $t Orthogonal invariance of CAR algebras -- $t Clifford relations -- $t Orthogonal invariance of the CAR on Fock spaces -- $t Quasi-free states -- $t Dynamics of quantum fields -- $t Quantum fields on space-time -- $t Diagrammatics -- $t Euclidean approach for bosons -- $t Interacting bosonic fields.
520 # $a Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, such as tensors, algebras, Fock spaces and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in -depth coverage, this text is essential reading for graduate students and researchers in departments of mathematics and physics-- $c Provided by publisher.
650 # 0 $a Geometric quantization. $3 579202
650 # 0 $a Quantum theory $x Mathematics. $3 705044
700 1 # $a Gérard, Christian, $d 1960- $e author. $3 1982341
830 0 $a Cambridge monographs on mathematical physics $3 1969313