Displacement deformed quantum fields

Abstract

A displacement operator d_ζis introduced, verifying commutation relations [d_ζ, a_f^\dagger]=[d_ζ, a_f]=ζ(f)d_ζwith 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, ζis 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.