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• W2769595152 endingPage "245011" @default.
• W2769595152 startingPage "245011" @default.
• W2769595152 abstract "A possible avenue towards a non-perturbative Quantum Field Theory (QFT) on Minkowski space is the constructive approach which employs the Euclidian path integral formulation, in the presence of both ultraviolet (UV) and infrared (IR) regulators, as starting point. The UV regulator is to be taken away by renormalisation group techniques which in case of success leads to a measure on the space of generalised Euclidian fields in finite volume. The IR regulator corresponds to the thermodynamic limit of the system in the statistical physics sense. If the resulting measure obeys the Osterwalder-Schrader axioms, the actual QFT on Minkowski space is then obtained by Osterwalder-Schrader reconstruction. In this work we study the question whether it is possible to reformulate the renormalisation group non-perturbatively directly at the operator (Hamiltonian) level. Hamiltonian renormalisation would be the natural route to follow if one had easier access to an interacting Hamiltonian operator rather than to a path integral, at least in the presence of UV and/or IR cut-off, which is generically the case in complicated gauge theories such as General Relativity. Our guiding principle for the definition of the direct Hamiltonian renormalisation group is that it results in the same continuum theory as the covariant (path integral) renormalisation group. In order to achieve this, we invert the Osterwalder-Schrader reconstruction, which may be called Osterwalder-Schrader construction of a Wiener measure from the underlying Hamiltonian theory. The resulting correspondence between reflection positive measures and Osterwalder-Schrader data consisting of a Hilbert space, a Hamiltonian and a ground state vector allows us to monitor the effect of the renormalisation flow of measures in terms of their Osterwalder-Schrader data which motivates a natural direct Hamiltonian renormalisation scheme." @default.
• W2769595152 created "2017-12-04" @default.
• W2769595152 creator A5006273300 @default.
• W2769595152 creator A5043914194 @default.
• W2769595152 creator A5084641345 @default.
• W2769595152 date "2018-11-28" @default.
• W2769595152 modified "2023-10-01" @default.
• W2769595152 title "Hamiltonian renormalisation I: derivation from Osterwalder–Schrader reconstruction" @default.
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• W2769595152 doi "https://doi.org/10.1088/1361-6382/aaec56" @default.
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