SMOOTH CUTOFF

The above discussion obviously applies also when

0(x) and φ(χ) are classical variables instead of quantum

mechanical operators.

The replacement of δ-functions by a smooth func-

tion P [σ , φ ] such as the Gaussian (A. 6) smears up the

variable φ its e l f in contrast to smearing its spatial

dependence as in (A. 3) . It rem oves some unpleasant

mathematical features of δ-functions. It also produces

extra terms like the 1/w in (A. 16) which must be care-

produce different extra terms.