Feynman

Feynman diagrams versus Fermi-gas Feynman emulator

Supermanifolds from Feynman graphs

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying...

The Feynman-Kac formula

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

Random Feynman Graphs

We investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble those defined in random graphs with hidden color, generalizing the known relation of the Feynman graphs of simple one-dimensional integrals to random graphs wit...

Why Feynman Path Integration?

To describe physics properly, we need to take into account quantum effects. Thus, for every nonquantum physical theory, we must come up with an appropriate quantum theory. A traditional approach is to replace all the scalars in the classical description of this theory by the corresponding operators. The problem with the above approach is that due to non-commutativity of the quantum operators, t...