Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities

In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so called "`infinite quantities"' make...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Authors: Aragona, J, Catuogno, P, Colombeau, J F, Juriaans, S O, Olivera, C
Format: Article
Language:English
Subjects:
Field theory
Markov analysis
Mathematical analysis
Multiplication
Operators (mathematics)
Quantum field theory
Quantum theory
Real numbers
Transition probabilities
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Summary:In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so called "`infinite quantities"' make sense unambiguously (but are not classical real numbers). The perturbation series does not make sense. A novelty appears when one starts to compute the transition probabilities. The transition probabilities have to be computed in a nonperturbative way which, at least in simplified mathematical examples (even those looking like nonrenormalizable series), gives real values between 0 and 1 capable to represent probabilities. However these calculations should be done numerically and we have only been able to compute simplified mathematical examples due to the fact these calculations appear very demanding in the physically significant situation with an infinite dimensional Fock space and the QFT operators.
ISSN:2331-8422