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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.
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The equation for the mass shell is also often written in terms of the four-momentum; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light =, as =. In the literature, one may also encounter p μ p μ = − m 0 2 {\displaystyle p^{\mu }p_{\mu }=-m_{0}^{2}} if the metric signature used is (−,+,+,+).
Mark Wahlberg and Rhea Durham's kids are home for Thanksgiving!. Durham, 46, shared a rare photo of herself, her actor husband, 53, and their four children — Ella, 21, Michael, 18, Brendan, 16 ...
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.
Expressions in the notation of the Ricci calculus may generally be interpreted as a set of simultaneous equations relating the components as functions over a manifold, usually more specifically as functions of the coordinates on the manifold. This allows intuitive manipulation of expressions with familiarity of only a limited set of rules.