  Sobolev-Bregman forms, or $p$-forms, describe Markovian semigroups on $L^p$,
and they reduce to Dirichlet forms when $p = 2$. We prove a variant of the
Beurling-Deny formula for Sobolev-Bregman forms which correspond to an
arbitrary regular Dirichlet form. As a sample application, we prove the
corresponding Hardy-Stein identity. Our results require no further conditions
on the Dirichlet form or the associated Markovian semigroup.
