國立虎尾科技大學 |

Tensor Categories and Endomorphisms of von Neumann Algebras = with Applications to Quantum Field Theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Tensor Categories and Endomorphisms of von Neumann Algebras/ by Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren.
其他題名:	with Applications to Quantum Field Theory /
作者:	Bischoff, Marcel.
其他作者:	Kawahigashi, Yasuyuki.
面頁冊數:	X, 94 p. 138 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Quantum field theory. -
電子資源:	https://doi.org/10.1007/978-3-319-14301-9
ISBN:	9783319143019

Tensor Categories and Endomorphisms of von Neumann Algebras = with Applications to Quantum Field Theory /
Bischoff, Marcel.

Tensor Categories and Endomorphisms of von Neumann Algebraswith Applications to Quantum Field Theory /[electronic resource] :by Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren. - 1st ed. 2015. - X, 94 p. 138 illus.online resource. - SpringerBriefs in Mathematical Physics,32197-1757 ;. - SpringerBriefs in Mathematical Physics,8.

Introduction -- Homomorphisms of von Neumann algebras -- Endomorphisms of infinite factors -- Homomorphisms and subfactors -- Non-factorial extensions -- Frobenius algebras, Q-systems and modules -- C* Frobenius algebras -- Q-systems and extensions -- The canonical Q-system -- Modules of Q-systems -- Induced Q-systems and Morita equivalence -- Bimodules -- Tensor product of bimodules -- Q-system calculus -- Reduced Q-systems -- Central decomposition of Q-systems -- Irreducible decomposition of Q-systems -- Intermediate Q-systems -- Q-systems in braided tensor categories -- a-induction -- Mirror Q-systems -- Centre of Q-systems -- Braided product of Q-systems -- The full centre -- Modular tensor categories -- The braided product of two full centres -- Applications in QFT -- Basics of algebraic quantum field theory -- Hard boundaries -- Transparent boundaries -- Further directions -- Conclusions.

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

ISBN: 9783319143019

Standard No.: 10.1007/978-3-319-14301-9doiSubjects--Topical Terms:

579915
Quantum field theory.

LC Class. No.: QC174.45-174.52

Dewey Class. No.: 530.14

Tensor Categories and Endomorphisms of von Neumann Algebras = with Applications to Quantum Field Theory /
LDR:03315nam a22003975i 4500 001 968578
003 DE-He213
005 20200703134947.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319143019 $9 978-3-319-14301-9
024 7 $a 10.1007/978-3-319-14301-9 $2 doi
035 $a 978-3-319-14301-9
050 4 $a QC174.45-174.52
072 7 $a PHQ $2 bicssc
072 7 $a SCI057000 $2 bisacsh
072 7 $a PHS $2 thema
082 0 4 $a 530.14 $2 23
100 1 $a Bischoff, Marcel. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1066090
245 1 0 $a Tensor Categories and Endomorphisms of von Neumann Algebras $h [electronic resource] : $b with Applications to Quantum Field Theory / $c by Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a X, 94 p. 138 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Mathematical Physics, $x 2197-1757 ; $v 3
505 0 $a Introduction -- Homomorphisms of von Neumann algebras -- Endomorphisms of infinite factors -- Homomorphisms and subfactors -- Non-factorial extensions -- Frobenius algebras, Q-systems and modules -- C* Frobenius algebras -- Q-systems and extensions -- The canonical Q-system -- Modules of Q-systems -- Induced Q-systems and Morita equivalence -- Bimodules -- Tensor product of bimodules -- Q-system calculus -- Reduced Q-systems -- Central decomposition of Q-systems -- Irreducible decomposition of Q-systems -- Intermediate Q-systems -- Q-systems in braided tensor categories -- a-induction -- Mirror Q-systems -- Centre of Q-systems -- Braided product of Q-systems -- The full centre -- Modular tensor categories -- The braided product of two full centres -- Applications in QFT -- Basics of algebraic quantum field theory -- Hard boundaries -- Transparent boundaries -- Further directions -- Conclusions.
520 $a C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
650 0 $a Quantum field theory. $3 579915
650 0 $a String theory. $3 1254756
650 0 $a Mathematical physics. $3 527831
650 0 $a Algebra. $2 gtt $3 579870
650 1 4 $a Quantum Field Theories, String Theory. $3 768973
650 2 4 $a Mathematical Physics. $3 786661
700 1 $a Kawahigashi, Yasuyuki. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1264185
700 1 $a Longo, Roberto. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1264186
700 1 $a Rehren, Karl-Henning. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1264187
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319143026
776 0 8 $i Printed edition: $z 9783319143002
830 0 $a SpringerBriefs in Mathematical Physics, $x 2197-1757 ; $v 8 $3 1263793
856 4 0 $u https://doi.org/10.1007/978-3-319-14301-9
912 $a ZDB-2-PHA
912 $a ZDB-2-SXP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Physics and Astronomy (R0) (SpringerNature-43715)