Hello, The Hubbard-Stratonovich transformation

$\exp(x^2) = \frac{1}{\sqrt{4 \pi}} \int_{-\infty}^{+\infty} du \exp(-\frac{u^2}{4} - xu)$

allows one to wirte the exponential of a the square of a number $x$ as an integral over a Gaussian variable $u$. Is there a transformation analogous to the Hubbard-Stratonovich transformation to write the exponential of a product of two numbers $x,y$

$\exp(xy)$

?

Thank you

Michele