Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat