D'Alembert operator

In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates (t, x, y, z), it has the form Here is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with , , for . (Some authors alternatively use the negative metric signature of (− + + +), with .)

Comment
enIn special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates (t, x, y, z), it has the form Here is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with , , for . (Some authors alternatively use the negative metric signature of (− + + +), with .)
DifferentFrom
D'Alembert's equation
D'Alembert's principle
Has abstract
enIn special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates (t, x, y, z), it has the form Here is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with , , for . Note that the μ and ν summation indices range from 0 to 3: see Einstein notation. We have assumed units such that the speed of light c = 1. (Some authors alternatively use the negative metric signature of (− + + +), with .) Lorentz transformations leave the Minkowski metric invariant, so the d'Alembertian yields a Lorentz scalar. The above coordinate expressions remain valid for the standard coordinates in every inertial frame.
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D'Alembert operator
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Category:Differential operators
Category:Hyperbolic partial differential equations
Coordinate chart
Covariant derivative
D'Alembert's formula
Dirac delta function
Einstein notation
Electromagnetic four-potential
Electromagnetism
Four-gradient
Green's function
Heaviside step function
Jean le Rond d'Alembert
Klein–Gordon equation
Laplace operator
Laplacian
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Metric signature
Minkowski metric
Minkowski space
Nabla symbol
One-way wave equation
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Quantum field theory
Relativistic heat conduction
Rendiconti del Circolo Matematico di Palermo
Ricci calculus
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Wave equation
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5457H
D'Alembertiaan
D'Alembertiano
D'alembertien
D'Alembert işleci
D'Alembert operator
D'Alembert-operatoren
D'Alembertův operátor
D’Alembert-Operator
D’Alembertov operátor
m.01qx9m
Operador de d'Alembert
Operador de d'Alembert
Operator d’Alemberta
Operatore di d'Alembert
Operatoro de d'Alembert
Q911268
Д'Аламберов оператор
Оператор Д’Аламбера
Оператор д'Аламбера
Оператор на Д'Аламбер
ד'אלמברטיאן
عملگر دالامبر
ダランベール演算子
达朗贝尔算符
달랑베르 연산자
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Category:Differential operators
Category:Hyperbolic partial differential equations
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end'Alembertian
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