d'Alembert operator

English

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d'Alembert operator

Wikipedia

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)

1. (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 ${\displaystyle \nabla ^{2}}$ 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
• quabla operator
• wave operator

References

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