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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.
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.
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 (+ − − −).
For compactness and convenience, the Ricci calculus incorporates Einstein notation, which implies summation over indices repeated within a term and universal quantification over free indices. Expressions in the notation of the Ricci calculus may generally be interpreted as a set of simultaneous equations relating the components as functions ...
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.
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.
The Year Without a Santa Claus, a Christmas special from Jules Bass and Arthur Rankin, Jr., turns 50 this December. The beloved special was adapted from the book of the same name by Phyllis ...
In a light-cone coordinate system, two of the coordinates are null vectors and all the other coordinates are spatial. The former can be denoted + and and the latter .. Assume we are working with a (d,1) Lorentzian signature.