國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Supermathematics and its application...

SpringerLink (Online service)

Supermathematics and its applications in statistical physicsGrassmann variables and the method of supersymmetry /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Supermathematics and its applications in statistical physicsby Franz Wegner.
其他題名:	Grassmann variables and the method of supersymmetry /
作者:	Wegner, Franz.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg :2016.
面頁冊數:	xvii, 374 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mathematical physics.
電子資源:	http://dx.doi.org/10.1007/978-3-662-49170-6
ISBN:	9783662491706$q(electronic bk.)

Supermathematics and its applications in statistical physicsGrassmann variables and the method of supersymmetry /
Wegner, Franz.

Supermathematics and its applications in statistical physicsGrassmann variables and the method of supersymmetry /[electronic resource] :by Franz Wegner. - Berlin, Heidelberg :Springer Berlin Heidelberg :2016. - xvii, 374 p. :ill. (some col.), digital ;24 cm. - Lecture notes in physics,v.9200075-8450 ;. - Lecture notes in physics ;650..

Part I Grassmann Variables and Applications -- Part II Supermathematics -- Part III Supersymmetry in Statistical Physics -- Summary and Additional Remarks -- References -- Solutions -- Index.

This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.

ISBN: 9783662491706$q(electronic bk.)

Standard No.: 10.1007/978-3-662-49170-6doiSubjects--Topical Terms:

190854
Mathematical physics.

LC Class. No.: QC20

Dewey Class. No.: 530.15

Supermathematics and its applications in statistical physicsGrassmann variables and the method of supersymmetry /
LDR:03005nmm a2200325 a 4500 001 484218
003 DE-He213
005 20160923102152.0
006 m d
007 cr nn 008maaau
008 161012s2016 gw s 0 eng d
020 $a 9783662491706$q(electronic bk.)
020 $a 9783662491683$q(paper)
024 7 $a 10.1007/978-3-662-49170-6 $2 doi
035 $a 978-3-662-49170-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QC20
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
082 0 4 $a 530.15 $2 23
090 $a QC20 $b .W412 2016
100 1 $a Wegner, Franz. $3 742377
245 1 0 $a Supermathematics and its applications in statistical physics $h [electronic resource] : $b Grassmann variables and the method of supersymmetry / $c by Franz Wegner.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2016.
300 $a xvii, 374 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Lecture notes in physics, $x 0075-8450 ; $v v.920
505 0 $a Part I Grassmann Variables and Applications -- Part II Supermathematics -- Part III Supersymmetry in Statistical Physics -- Summary and Additional Remarks -- References -- Solutions -- Index.
520 $a This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.
650 0 $a Mathematical physics. $3 190854
650 0 $a Grassmann manifolds. $3 709163
650 0 $a Supersymmetry. $3 250401
650 1 4 $a Physics. $3 179414
650 2 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Statistical Physics, Dynamical Systems and Complexity. $3 376808
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 522718
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Lecture notes in physics ; $v 650. $3 451204
856 4 0 $u http://dx.doi.org/10.1007/978-3-662-49170-6
950 $a Physics and Astronomy (Springer-11651)