Supermanifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1992
|
| Edition: | 2. ed. |
| Series: | Cambridge monographs on mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 407 S. |
| ISBN: | 0521413206 0521423775 |
Staff View
MARC
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| 100 | 1 | |a De Witt, Bryce S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Supermanifolds |c Bryce DeWitt |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1992 | |
| 300 | |a XVIII, 407 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge monographs on mathematical physics | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 4 | |a Supervariétés (Mathématiques) | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Supermanifolds (Mathematics) | |
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Record in the Search Index
| _version_ | 1804120388104355840 |
|---|---|
| adam_text | Contents
Preface
XVII
Preface to the second edition
xviii
1
1
1.1
1
Grassmann
1
Supernumbers
1
c-numbers and a-numbers
2
Superanalytic functions of supernumbers
3
Integration of superanalytic functions of supernumbers
5
1.2
their integrals
5
Complex conjugation
5
Functions, distributions and integrals over Rc
6
Fourier transforms over Re
8
1.3
8
Basic definitions
8
Fourier transforms over R.
10
IntegraL· over RJ
12
1.4
14
Definition
14
Bases
16
Pure bases
17
Pure real bases
20
Standard bases
24
l.S Linear transformations,
spaces
24
Change of basis
24
Shifting indices. The
25
Extensions of the
27
Dual supervector spaces
28
Dual bases
30
Further index-shifting conventions
31
1.6
33
The
33
The SHperdetermmant
34
VII
viii Contents
The superdeterminant in special cases
The superdeterminant in the general case
1.7
Notation
Integration
Homogeneous linear transformations of the
Homogeneous linear transformations of all the coordinates
Nonlinear transformations
Gaussian integrals over
Exercises
Comments on chapter
2
2.1
Topology
Supermanifolds, charts and atlases
Scalar fields and supercurves
Diffeomorphisms and embeddings
Ordinary manifolds. Skeleton and body of a supermanifold
Projectively Hausdorff, compact, paracompact and
manifolds. Realizations of the body
2.2
Scalar fields as supervectors
Contravariant
Alternative presentation of
Components
Tangent spaces
Tangents to supercurves
2.3
Supercommutators and antisupercommutators
Λ
The super Lie bracket
Local frames
Super Lie brackets of local frame fields
Covariant vector fields
Differentials
2.4
Tensors at a point
The supervector space T ,(p)
Tensor products
Tensor and multitensor fields
Index-shifting conventions. Contractions
The
2.5
Contents ix
Definition 78
Explicit
Lie derivations as supervectors
The derivative mapping
Integral supercurves. Congruences
Dragging of tensor fields
2.6
Definition
The exterior product
Bases for forms
Derivations of forms
Гйе
Tfte
2.7
Definition
7Άβ
Explicit forms
Multiple covariant derivatives. The torsion
Гйе
7%e it//»«·
Parallel transport. Supergeodesics
Distant parallelism
2.8
77ie metric tensor field
Canonical form of the metric tensor at a point
Canonical or orthosymplectic bases
Riemannian connections
37»
Tfe
F
Conformally related
Confomudly flat Riemannian supermanifolds
Killing vector fields
Conformai
7йе
2.9
Integration over Rf
Locally finite atlases and partitions of unity
Integration over paracompact
Integration over Riemannian supermanifolds
Integrals of total divergences
7йе
An example
Contents
Exercises
Comments on chapter
3
3.1
Definition
Canonical diffeomorphisms
Left- and right-invariant vector fields
Left- and right-invariant local frame fields
Left- and right-invariant congruences
One-parameter Abelian subgroups
The exponential mapping. Canonical coordinates
The super Lie algebra
The structure constants
The right and left auxiliary functions
Identities satisfied by the auxiliary functions
Construction of a super Lie group from its super Lie algebra
3.2
Definition
Orbits
Transitive realizations
Isotropy subgroups
Coset spaces
Killingflows
Properties of the coordinate components of the Qa
A special canonical coordinate system
Coordinates for the coset spaces
Classification of transitive realizations
Matrix representations of super Lie groups
Contragredient representations
Inner automorphisms. The adjoint representation
Matrix representations of the super Lie algebra
3.3
Invariant tensor fields
Differential equations for geometrical structures
Integrability of the differential equations
A special coordinate system
Condition for the existence of a group-invariant measure function
Condition for the existence of a group-invariant metric tensor field
Condition for the existence of a group-invariant connection
Solutions of the differential equations
Geometry of the group supermanifold
Identity of the left- and right-invariant connections
Parallelism at a distance in the group supermanifold
Contents xi
Integration
A special class of super Lie groups
Exercises
Comments on chapter
4
4.1
Properties of the structure constants
Conventional super Lie groups, Zt-graded algebras
Unconventional super Lie groups
Structure of conventional super Lie Groups. The extending repre¬
sentation
Construction of a class of super Lie algebras
Notation
4.2
The group GL (m, n)
The group SL (m, n)
The group SL (m, w)/GL
The orthosymplectic group OSp
The
The group P(m)
The group Q(m)
The group Q(m)
4.3
The groups D(2,
The group F(4)
The structure of F(4)
Pseudorepresentation of F(4)
The group G(3)
The structure ofGt
The structure of G{3)
Pseudorepresentation of G(3)
4.4
The super
The super
The coset space: super
Killing flows and invariant connections
Riemannian geometry of the coset space
The super
4.5
The diffeomorphism group IM(M)
The group SDifip/./i)
The canonical transformation group Can(Af,
The group of contact transformations
xii Contents
The
The group W(n)
The groups S{ri) and §(n)
The groups
Exercises
Comments on chapter
5
5.1
Configuration spaces
Supermanifolds as configuration spaces
Space of histories
The action functional and the dynamical equations
Infinitesimal disturbances and Green s functions
Reciprocity relations
The Peierls bracket
Peierls bracket identities
5.2
Definition
Linear operators
Physical
5.3
Transition to the quantum theory
The
External sources
Chronologically ordered form of the operator dynamical equations
The Feynman functional integral
5.4
A ction functional and Green s functions
Eigenvectors ofx
The energy
A pure basis
An alternative representation
The functional integral representation of
Evaluation of the functional integral
The average superelassical trajectory
Propagator for xmv{<)
5.5
Action functional and Green s functions
Mode functions and Hamiltonian
Basic supervectors
Eigenvectors ofxx and xv Choice of pure basis
Coherent states
The functional integral representation of iff*,
Contents xiii
Direct
The importance of endpoint contributions
The stationary trajectory as a matrix element
The Feynman propagator
5.6
A c tion
Mode functions and Hamiltonian
Energy eigenvectors
Coherent states
Hamilton-Jacobi theory
The amplitude
The functional-integral representation of
The stationary path between coherent states
The Feynman propagator
Energy eigenfunctions
5.7
The simplest model
New conserved quantities
The Bose-Fermi supersymmetry group
Eigenvectors of
The supersymmetry group as a transformation group
Auxiliary variable
Nonlinear Bose-Fermi supersymmetry
The supersymmetry group
A pure basis
Tfte energy spectrum
Spontaneously broken supersymmetry
Exercises
Comments on chapter
б
6.1 Nontrivial
Standard canonical systems
Green s functions
Equivalence ofPeierls and
6.2
Problems with the naive quantization rule
Operator-valued forms. The projection m-form
The position operator
Vector operators
The momentum operator
Restriction to a local chart
Lack of uniqueness of the momentum operator
Overlapping charts. Transformation of coordinates
xiv Contents
The position representation
The momentum operator in the position representation
The
The position representation of the projection m-form
6.3
A special class of systems
Covariant variation
Covariant differentiation with respect to
The dynamical equations
Covariant functional differentiation
6.4
Formal computation of
The functional integral
Normalization
Ambiguity in the functional integral
Homotopy
Homotopy mesh
The total amplitude
Change of homotopy mesh
The role ofhontology
The universal covering space
The total amplitude revisited
6.5
Integration over phase space
The
Evaluation of the chronologically ordered Hamiltonian
6.6
Brief review of Hamilton-
The Van Vleck-Morette determinant
Jacobi fields and the Green s function for the trajectory xc
Determinanta!
The loop expansion
The WKB approximation
The heat kernel expansion
Role of the two-loop term in the independent verification of
New variables
Computation of the two-loop term
6.7
Inclusion ofa-type dynamical variables
Green s functions and Peierls brackets
Energy and supersymmetry group
Quantization
Basis supervectors
Contents xv
Differential
Coherent states
Energy eigenfunctions
The
Functional integral for the coherent-state transition amplitude
The Chern-Gauss-Bonnet formula
Exercises
Comments on chapter
References
Index
|
| any_adam_object | 1 |
| author | De Witt, Bryce S. |
| author_facet | De Witt, Bryce S. |
| author_role | aut |
| author_sort | De Witt, Bryce S. |
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| callnumber-first | Q - Science |
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| callnumber-raw | QC20.7.M24 |
| callnumber-search | QC20.7.M24 |
| callnumber-sort | QC 220.7 M24 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 350 |
| classification_tum | MAT 537f MAT 580f PHY 417f PHY 411f |
| ctrlnum | (OCoLC)23356149 (DE-599)BVBBV006158516 |
| dewey-full | 530.1/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/5 |
| dewey-search | 530.1/5 |
| dewey-sort | 3530.1 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T16:41:17Z |
| institution | BVB |
| isbn | 0521413206 0521423775 |
| language | English |
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| physical | XVIII, 407 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Cambridge Univ. Pr. |
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| series2 | Cambridge monographs on mathematical physics |
| spelling | De Witt, Bryce S. Verfasser aut Supermanifolds Bryce DeWitt 2. ed. Cambridge u.a. Cambridge Univ. Pr. 1992 XVIII, 407 S. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Manifolds gtt Physique mathématique Supervariétés (Mathématiques) Mathematische Physik Mathematical physics Supermanifolds (Mathematics) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Supermannigfaltigkeit (DE-588)4289285-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Supermannigfaltigkeit (DE-588)4289285-5 s DE-604 Topologische Mannigfaltigkeit (DE-588)4185712-4 s Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003895885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | De Witt, Bryce S. Supermanifolds Manifolds gtt Physique mathématique Supervariétés (Mathématiques) Mathematische Physik Mathematical physics Supermanifolds (Mathematics) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Supermannigfaltigkeit (DE-588)4289285-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4185712-4 (DE-588)4289285-5 (DE-588)4037379-4 |
| title | Supermanifolds |
| title_auth | Supermanifolds |
| title_exact_search | Supermanifolds |
| title_full | Supermanifolds Bryce DeWitt |
| title_fullStr | Supermanifolds Bryce DeWitt |
| title_full_unstemmed | Supermanifolds Bryce DeWitt |
| title_short | Supermanifolds |
| title_sort | supermanifolds |
| topic | Manifolds gtt Physique mathématique Supervariétés (Mathématiques) Mathematische Physik Mathematical physics Supermanifolds (Mathematics) Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Supermannigfaltigkeit (DE-588)4289285-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Manifolds Physique mathématique Supervariétés (Mathématiques) Mathematische Physik Mathematical physics Supermanifolds (Mathematics) Topologische Mannigfaltigkeit Supermannigfaltigkeit Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003895885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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