2006/10/10 by Peter Morgan, Morgan, Peter
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0610077
Relies on quant-ph/0512190. 12 pages. 2 figures
arxiv created 2006/10/10 · openalex publication_date 2006/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A displacement operator dζis introduced, verifying commutation relations [dζ, af^†]=[dζ, af]=ζ(f)dζwith field creation and annihilation operators that verify [af,ag]=0, [af,ag^†]=(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.