Displacement deformed quantum fields

Details Displacement deformed quantum fields Displacement deformed quantum fields

2006-10-10

arxiv.org/abs/quant-ph/0610077v1

Physics

Quantum Physics

Relies on quant-ph/0512190. 12 pages. 2 figures

Scientific paper

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.

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