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Grassmann number

In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra of a complex vector space. The special case of a 1-dimensional algebra is known as a dual number. Grassmann numbers saw an early use in physics to express a path integral representation for…

Informal discussion, General description and properties & Formal definition

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Overview

Informal discussion

General description and properties

Formal definition

Properties

Involution, choice of field

Analysis

Integration

Matrix representations

Generalisations

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Map overview Semantic statistics

Grassmann number

Nodes72
Edges71
Triples59
Avg. degree1.97
Density0.027778
Components1

How this topic connects Entity context

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Grassmann number

Top relations

related to Informal discussion · 12
Grassmann number → Differential, Each, Euclidean, Exterior, Grassmann, Having, Lie, More, One, Such, The, The Grassmann
related to Analysis · 9
Grassmann number → By, Grassmann, Lambda, Note, Products, Some, That, The, This
related to General description and properties · 8
Grassmann number → Euclidean, Grassmann, Grassmann-valued, Noether's, Similarly, The, The Grassmann, They
related to Matrix representations · 8
Grassmann number → Consider, Grassmann, Hilbert, In, Mathematically, Physically, Since, These Grassmann
related to Formal definition · 6
Grassmann number → Formally, Grassmann, It, Lambda, The, The Grassmann
related to Conventions and complex integration · 5
Grassmann number → An, Grassmann, Hermitian, Some, The
related to Integration · 5
Grassmann number → Berezin, Fermi, Grassmann, In, Integrals
related to Generalisations · 3
Grassmann number → Grassmann, There, These
related to Involution, choice of field · 3
Grassmann number → Grassmann, It, The

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Important terminology

grassmann numbers algebra number displaystyle field one space complex theta generators variables called case fermions definition exterior general superspace defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Grassmann numberrelated to AnalysisProducts0.60section
Grassmann numberrelated to AnalysisGrassmann0.60section
Grassmann numberrelated to AnalysisBy0.60section
Grassmann numberrelated to AnalysisThis0.60section
Grassmann numberrelated to AnalysisNote0.60section
Grassmann numberrelated to AnalysisLambda0.60section
Grassmann numberrelated to AnalysisThe0.60section
Grassmann numberrelated to AnalysisThat0.60section
Grassmann numberrelated to AnalysisSome0.60section
Grassmann numberrelated to Conventions and complex integrationAn0.60section
Grassmann numberrelated to Conventions and complex integrationGrassmann0.60section
Grassmann numberrelated to Conventions and complex integrationThe0.60section

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