nLab
Berezin integral

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Context

Super-Geometry

superalgebra

and

supergeometry

Formal context

Superalgebra

Supergeometry

Structures

Applications

Integration theory

integration

analytic integrationcohomological integration
measureorientation in generalized cohomology
Riemann/Lebesgue integration, of differential formspush-forward in generalized cohomology/in differential cohomology

Analytic integration

Cohomological integration

Variants

Contents

Idea

A Berezinian integral is an integral over a supermanifold that is a superpoint ℝ 0∣q.

For the infinite-dimensional version see fermionic path integral.

References

An exposition of the standard lore is here:

A general abstract discussion in terms of D-module theory is in

Revised on November 10, 2012 17:15:43 by Urs Schreiber (89.204.153.235)
Edit | Back in time (5 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: integration over supermanifolds, Lie integration, supermanifold, path integral, quantum anomaly, measure space, orientation, supergeometry - contents, (1,1)-dimensional Euclidean field theories and K-theory, supergroup, super vector space, super algebra, super Lie algebra, super vector bundle, Clifford algebra, D'Auria-Fre formulation of supergravity, supergravity, super Poincare Lie algebra, supergravity Lie 3-algebra, super Minkowski space, synthetic differential supergeometry, supergeometry, supersymmetry, Lebesgue space, supersymmetric quantum mechanics, orientation in generalized cohomology, Berezin integral, gravitino, super infinity-groupoid, Green-Schwarz action functional, Kontsevich integral, superparticle, super L-infinity algebra, smooth super infinity-groupoid, fermionic path integral, fiber integration in ordinary differential cohomology, 4-dimensional supergravity, contents of contents, elliptic Selberg integral, super-translation group, analytical index, Selberg integral, integration of differential forms, type II supergravity, integral, superdeterminant, Grothendieck-Riemann-Roch theorem, fiber integration in differential K-theory, fiber integration in differential cohomology, line integral, Freed-Witten anomaly, synthetic differential super infinity-groupoid, integration theory - contents, geometric quantization by push-forward, smooth superalgebra, super Riemann surface, Lebesgue integration, integration over infinite-dimensional manifolds, Lie differentiation, Fierz identity, supertrace, cohomological integration, 3-category of fermionic conformal nets