32 research outputs found
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 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
Wave-type equations of low regularity
We prove local existence and uniqueness of the Cauchy problem for a large
class of tensorial second order linear hyperbolic partial differential
equations with coefficients of low regularity in a suitable class of
generalized functions.Comment: 16 pages, 1 figur