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  2. Einstein notation - Wikipedia

    en.wikipedia.org/wiki/Einstein_notation

    In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity.

  3. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.

  4. Template:Einstein summation convention - Wikipedia

    en.wikipedia.org/wiki/Template:Einstein...

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more

  5. ADM formalism - Wikipedia

    en.wikipedia.org/wiki/ADM_formalism

    The text here uses Einstein notation in which summation over repeated indices is assumed. Two types of derivatives are used: Partial derivatives are denoted either by the operator ∂ i {\displaystyle \partial _{i}} or by subscripts preceded by a comma.

  6. Classical electromagnetism and special relativity - Wikipedia

    en.wikipedia.org/wiki/Classical_electromagnetism...

    This section uses Einstein notation, including Einstein summation convention. See also Ricci calculus for a summary of tensor index notations, and raising and lowering indices for definition of superscript and subscript indices, and how to switch between them. The Minkowski metric tensor η here has metric signature (+ − − −).

  7. Covariance and contravariance of vectors - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_contra...

    In Einstein notation (implicit summation over repeated index), contravariant components are denoted with upper indices as in = A covector or cotangent vector has components that co-vary with a change of basis in the corresponding (initial) vector space. That is, the components must be transformed by the same matrix as the change of basis matrix ...

  8. Wigner's classification - Wikipedia

    en.wikipedia.org/wiki/Wigner's_classification

    The Casimir invariants of the Poincaré group are = , (Einstein notation) where P is the 4-momentum operator, and = , where W is the Pauli–Lubanski pseudovector. The eigenvalues of these operators serve to label the representations.

  9. Mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_general...

    A discrete version of the Einstein–Hilbert action is obtained by considering so-called deficit angles of these blocks, a zero deficit angle corresponding to no curvature. This novel idea finds application in approximation methods in numerical relativity and quantum gravity , the latter using a generalisation of Regge calculus.