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)

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

Usage notes

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

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