### 2.10 Entropy of massive fields

The heat kernel of a massive field described by the wave operator is expressed in
terms of the heat kernel of a massless field,
Thus,
one finds
where the trace of the heat kernel for vanishing mass is given by Eq. (27). Therefore, the entanglement
entropy of a massive field is
In particular, if , one finds that
The logarithmic term in the entropy that is due to the mass of the field appears in any even dimension .
The presence of a UV finite term proportional to the -th power of mass is the other general feature
of (30), (31).