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Canonical static concept record

Slater determinant

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Summary

The determinant or exterior product of one-particle spin-orbitals representing a single antisymmetric fermion configuration.

Record metadata

Canonical name: Slater determinant
Concept ID: slater_determinant
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Algebra
Domains: Algebra
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Antisymmetric tensor construction

Carrier(s)

one-particle orbitals $\phi_1,\ldots,\phi_N$

Data

antisymmetrized tensor product or determinant

Axioms / constraints

changes sign under odd particle permutations
vanishes when two orbitals coincide

Canonically induces

one-body density matrix for the determinant
fermionic exchange structure

Notes

A single Slater determinant captures antisymmetry and exchange but not general many-body correlation.

Concept sources

Wikipedia — Slater determinant — Slater determinant · encyclopedic reference · source ID wp-slater_determinant
nLab — Slater determinant — Slater determinant · mathematical reference · source ID nlab-slater_determinant
NIST — Atomic Spectroscopy: An Introduction — Atomic Spectroscopy: An Introduction · NIST technical reference · source ID nist-atomic-spectroscopy

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Exterior algebra Slater determinant

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: slater_from_exterior
Relation type: Canonical construction canonical-construction
Direction: source → target
Endpoint roles: source: Canonically constructs; target: Canonically constructed from
Authored annotation: antisymmetric exterior product

Authored explanation

A Slater determinant is the exterior product of occupied one-particle spin-orbitals.

How to interpret this relation type

Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.

Relation sources

Wikipedia — Exterior algebra — Exterior algebra · encyclopedic reference · source ID wp-exterior_algebra
nLab — exterior algebra — exterior algebra · mathematical reference · source ID nlab-exterior_algebra
Wikipedia — Slater determinant — Slater determinant · encyclopedic reference · source ID wp-slater_determinant
nLab — Slater determinant — Slater determinant · mathematical reference · source ID nlab-slater_determinant
NIST — Atomic Spectroscopy: An Introduction — Atomic Spectroscopy: An Introduction · NIST technical reference · source ID nist-atomic-spectroscopy

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.