Weyl algebra

Meaning

Noun

• The ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form $f\_m(X)\; \backslash partial\_X^m\; +\; f\_\{m-1\}(X)\; \backslash partial\_X^\{m-1\}\; +\; \backslash cdots\; +\; f\_1(X)\; \backslash partial\_X\; +\; f\_0(X)$.

Origin

• Named after Hermann Weyl, who introduced them to study the Heisenberg uncertainty principle in quantum mechanics.