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Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. The new methods also yield new perturbative expansions when the integrals cannot be solved analytically. Here, we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives. The new methods can be used to express path integrals in terms of functional differentiation, and they also suggest new perturbative expansions in quantum field theory.
This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus. On
It is shown that the causal structure associated to string-like solutions of the Fadeev-Niemi (FN) model is described by an effective metric. Remarkably, the surfaces characterising the causal replacement depend on the energy momentum tensor of the b
We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) bou
These notes give an introduction to the mathematical framework of the Batalin-Vilkovisky and Batalin-Fradkin-Vilkovisky formalisms. Some of the presented content was given as a mini course by the first author at the 2018 QSPACE conference in Benasque.
Starting from a $dtimes d$ rational Lax pair system of the form $hbar partial_x Psi= LPsi$ and $hbar partial_t Psi=RPsi$ we prove that, under certain assumptions (genus $0$ spectral curve and additional conditions on $R$ and $L$), the system satisfie