d'Alembert operator

English

Named after Jean le Rond d'Alembert (1717–1783), a French mathematician, mechanician, physicist, philosopher, and music theorist.

d'Alembert operator (plural d'Alembert operators)

(physics) A differential operator which may be expressed as ${\\displaystyle \\partial _{\\mu }\\partial ^{\\mu }=\\sum _{\\mu =0}^{3}{\\partial \\over \\partial x^{\\mu }}{\\partial \\over \\partial x_{\\mu }}}$ ; it is the four-dimensional (Minkowski space) equivalent of the three-dimensional Laplace operator.

It may be denoted as ${\\displaystyle \\Box ^{2}}$ (in analogy with the ${\\displaystyle \abla ^{2}}$ symbol for the Laplacian) or as ${\\displaystyle \\Box }$ (in analogy with the ${\\displaystyle \\Delta }$ symbol for the Laplacian).
It may also be denoted as ${\\displaystyle \\partial ^{2}}$ .

Robert D. Klauber (2013) Student Friendly Quantum Field Theory, Second edition, Fairfield, Iowa: Sandtrove Press, published 2018, →ISBN, OCLC 1100253371, §3.2.3, page 49

单词	d'Alembert operator
释义	d'Alembert operator English Etymology Named after Jean le Rond d'Alembert (1717–1783), a French mathematician, mechanician, physicist, philosopher, and music theorist. Noun d'Alembert operator (plural d'Alembert operators) (physics) A differential operator which may be expressed as ${\\displaystyle \\partial _{\\mu }\\partial ^{\\mu }=\\sum _{\\mu =0}^{3}{\\partial \\over \\partial x^{\\mu }}{\\partial \\over \\partial x_{\\mu }}}$ ; it is the four-dimensional (Minkowski space) equivalent of the three-dimensional Laplace operator. Usage notes It may be denoted as ${\\displaystyle \\Box ^{2}}$ (in analogy with the ${\\displaystyle \abla ^{2}}$ symbol for the Laplacian) or as ${\\displaystyle \\Box }$ (in analogy with the ${\\displaystyle \\Delta }$ symbol for the Laplacian). It may also be denoted as ${\\displaystyle \\partial ^{2}}$ . Synonyms box operator d'Alembertian wave operator References Robert D. Klauber (2013) Student Friendly Quantum Field Theory, Second edition, Fairfield, Iowa: Sandtrove Press, published 2018, →ISBN, OCLC 1100253371, §3.2.3, page 49
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