Infeld–van der Waerden formalism

E232967

The Infeld–van der Waerden formalism is a mathematical framework in general relativity that reformulates the theory using spinor calculus to describe gravitational and electromagnetic fields.

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Predicate Object
instanceOf framework in general relativity
mathematical formalism
spinor formalism
aimsTo simplify treatment of spinor fields in curved spacetime
unify description of gravitational and electromagnetic fields
appliesTo Lorentzian geometry
surface form: Lorentzian manifolds

curved spacetime
assumes local Lorentz invariance
metric compatibility
basedOn Lorentz group
SL(2,C)
clarifies geometric meaning of spinor fields
relationship between spinors and tensors
contrastsWith purely tensorial formulations of general relativity
describes electromagnetic fields
gravitational fields
developedInContextOf Einstein’s theory of gravitation
field general relativity
historicalPeriod 20th century theoretical physics
introducedBy Bartel Leendert van der Waerden
Leopold Infeld
language complex two-component spinors
provides spinor representation of Maxwell equations in curved spacetime
spinor representation of the Ricci tensor
spinor representation of the Weyl tensor
reformulates tensor formulation of general relativity
relatedTo Newman–Penrose formalism
Penrose spinor calculus
relates spinor quantities
tensor quantities
represents connection in spinor form
curvature in spinor form
electromagnetic field tensor in spinor form
metric tensor in spinor form
usedIn classical field theory
relativistic quantum theory of spin-1/2 fields
uses spinor calculus
usesConcept Infeld–van der Waerden formalism self-linksurface differs
surface form: Infeld–van der Waerden symbols

Pauli matrices
covariant differentiation of spinors
metric spinors
soldering forms
spin connection
spinor indices
tetrads
two-component spinors

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Full triples — surface form annotated when it differs from this entity's canonical label.

Leopold Infeld knownFor Infeld–van der Waerden formalism
Infeld–van der Waerden formalism usesConcept Infeld–van der Waerden formalism self-linksurface differs
this entity surface form: Infeld–van der Waerden symbols