9 citations · 32 across the 10 of their papers we have counts for
6 papers · 1 filter
Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities
J. Aragona, P. Catuogno, J. F. Colombeau +2
In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically,…
The Heisenberg-Pauli canonical formalism of quantum field theory in the rigorous setting of nonlinear generalized functions (Part I)
Jean-Francois Colombeau, Andre Gsponer
The unmodified Heisenberg-Pauli canonical formalism of quantum field theory applied to a self-interacting scalar boson field is shown to make sense mathematically in a framework of…
Mathematical problems on generalized functions and the canonical Hamiltonian formalism
J. F. Colombeau
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by…
Nonlinear generalized functions and the Heisenberg-Pauli foundations of Quantum Field Theory
Jean-Francois Colombeau, Andre Gsponer, Bernard Perrot
In 1929 Heisenberg and Pauli laid the foundations of QFT by quantizing the fields (method of canonical quantization). This general theory of quantized fields has remained undispute…
Nonlinear generalized functions and nonlinear numerical simulations in fluid and solid continuum mechanics
J. F. Colombeau
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear…
Generalized functions as a tool for nonsmooth nonlinear problems in mathematics and physics
J. F. Colombeau
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to…