  A displacement operator d_\zeta is introduced, verifying commutation
relations [d_\zeta, a_f^\dagger]=[d_\zeta, a_f]=\zeta(f)d_\zeta with field
creation and annihilation operators that verify [a_f,a_g]=0,
[a_f,a_g^\dagger]=(g,f), as usual. f and g are test functions, \zeta is a
Poincare invariant real-valued function on the test function space, and (g,f)
is a Poincare invariant Hermitian inner product. The *-algebra generated by all
these operators, and a state defined on it, nontrivially extends the *-algebra
of creation and annihilation operators and its Fock space representation. If
the usual requirement for linearity is weakened, as suggested in
quant-ph/0512190, we obtain a deformation of the free quantum field.
