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Title:
UV finiteness and adiabatic limit on Quantum Spacetime through perturbative Algebraic QFT
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Abstract:
We define a scalar interacting QFT on Quantum Spacetime (QST) replacing the fields at a point in the interaction Lagrangian by the fields at a quantum point, described by an optimally localized state on QST; the resulting Lagrangian density agrees with the one of Bahns, Doplicher, Fredenhagen, Piacitelli (2003) after spacetime integration, but gives rise to a different interaction hamiltonian. But now the methods of perturbative Algebraic Quantum Field Theory can be applied, and produce an ultraviolet finite perturbation expansion of the interacting observables. If the obtained theory is tested in an equilibrium state at finite temperature the adiabatic cutoff in time becomes immaterial, namely it has no effect on the correlation function at any order in perturbation theory. Moreover, the spatial adiabatic cutoff can be removed and the interacting vacuum state can be obtained in the vanishing temperature limit. (Joint work with S. Doplicher and N. Pinamonti.)
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