Fermionic determinant as an overlap between bosonic vacua

We find a representation for the determinant of a Dirac operator in an even number D = 2n of Euclidean dimensions as an overlap between two different vacua, each one corresponding to a bosonic theory with a quadratic action in 2n + 1 dimensions, with identical kinetic terms, but differing in their mass terms. This resembles the overlap representation of a fermionic determinant (although bosonic fields are used here). This representation may find applications to lattice field theory, as an alternative to other bosonized representations for Dirac determinants already proposed. (C) 1998 Published by Elsevier Science B.V. All rights reserved.