  We can attach a local constant to every finite dimensional continuous complex
representation of a local Galois group of a non-archimedean local field
$F/\mathbb{Q}_p$ by Deligne and Langlands. Tate \cite{JT1} gives an explicit
formula for computing local constants for linear characters of $F^\times$, but
there is no explicit formula of local constant for any arbitrary representation
of a local Galois group. In this article we study Heisenberg representations of
the absolute Galois group $G_F$ of $F$ and give invariant formulas of local
constants for Heisenberg representations of dimension prime to $p$.
