A formulation of lattice field theory (LFT) for curved manifolds uses the Regge's triangulated (simplicial) manifold for the Einstein Hilbert action that solves the equation of motion (EOM) for classical GR in the continuum. For the metric field, $g_{\mu \nu}(x)$, this is piece-wise constant finite element method (FEM) which applies equally to the classical field PDEs. But quantizing lattice...
I will review several key features associated with the conventional sign problem and argue that for regular interacting fermionic systems none of them applies if the calculation is done with the help of Feynman diagrams. The diagrammatic approach generically solves the computational complexity problem and can be used for obtaining numerical solutions for interacting fermions. I will illustrate...
The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address this issue: series resummation by conformal mapping, changing the nature of the starting point of the expansion by shifted action tools, and applying the...
