The corresponding expression of the Feynman integral
Johnson, "The equivalence of two approaches to the Feynman integral
," Journal of Mathematical Physics, vol.
In perturbative QFT, one has to consider Feynman graphs, and to associate to each such a graph a Feynman integral
(further related to quantities actually measured in physical experiments).
Thus the fractional QM (FQM) based on the Levy path integral generalizes the standard QM based on the Feynman integral
Among those topics are processes in Euclidean spaces, heat kernels for stable-like processes, and complex Markov chains and Feynman integral
This phenomenon is very much like the case of Feynman integral
, which had been regarded as a finitely additive measure with unbounded total variation before the theory of white noise was introduced by T.
Then similarly we have the Feynman rules such that the one-loop electron self-energy is given by the following Feynman integral:
Similarly we have the Feynman rules that the one-loop vertex correction is given by the following Feynman integral:
It allows infinite dimensional Feynman integrals
to be reduced to finite dimensional integrals over a compact group.
Among the topics are integrable lattice models from four-dimensional field theories, the physics and the mixed Hodge structure of Feynman integrals
, a quick guide to defect orbifolds, Calabi-Yau fourfolds in products of projective space, strict deformation quantization of the G-connections via lie groupoid, and instanton-soliton loops in five-dimensional super-Yang-Mills.
They consider such topics as the uniqueness of bounded solutions to aggregation equations by optimal transport methods, effective equidistribution and spectral gap, positive definite functions in distance geometry, topological field theories in two dimensions, Brouwer's dissertation and the revolution of 1907, new developments in combinatorial number theory and applications, geometry and non-archimedian integrals, Feynman integrals
and motives, computational complexity and numerical stability of linear problems, and high-dimensional distributions with convexity properties.
Srivastava, The [bar.H]-function associated with a certain class of Feynman integrals