Related papers: Trans-series from condensates
Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…
We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1 / q^{eta},…
The QCD vacuum condensates in the Operator Product Expansion are extracted from the final ALEPH data on vector and axial-vector spectral functions from $\tau$-decay. Weighted Finite Energy Sum Rules are employed in the framework of both…
It is known that the $q$-deformed Virasoro algebra can be constructed from a certain representation of the quantum toroidal $\mathfrak{gl}_1$ algebra. In this paper, we apply the same construction to the quantum toroidal algebra of type…
A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram…
In the paper we propose a direct method for recovering the Sturm-Liouville potential from the Weyl-Titchmarsh $m$-function given on a countable set of points. We show that using the Fourier-Legendre series expansion of the transmutation…
We study the initial-value problem for the nonlinear Schr\"odinger equation. Application of the inverse scattering transform method involves solving direct and inverse scattering problems for the Zakharov-Shabat system with complex…
The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Green's-functions, is a long-standing problem posing enormous challenges to numerical methods. When the spectral…
Motivated by the recent shocking results from RHIC and LHC that show quark-gluon plasma signatures in small systems, we study a simple model of a massless, noninteracting scalar field confined with Dirichlet boundary conditions. We use this…
We consider a natural dimension reduction technique for the Liouville-von Neumann equation for a mixed quantum system based on evaluation of a trace formula combined with a direct expansion in modified Chebyshev polynomials. This reduction…
We provide for primes $p\ge 5$ a method to compute valuations appearing in the "formal" Katz expansion of the family $\frac{E_{k}^{\ast}}{V(E_{k}^{\ast})}$ derived from the family of Eisenstein series $E_{k}^{\ast}$. The overconvergence…
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…
We calculate the nucleon parameters in nuclear matter using the QCD sum rules approach in Fermi gas approximation. Terms up to 1/q^2 in the operator product expansion (OPE) are taken into account. The higher moments of the nucleon structure…
We derive an exact version of the Schwinger Proper Time Renormalisation Group flow equation from first principles from the complete path integral, without using any perturbative expansion. We study the advantages of this flow equation as…
We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum, assuming absence of the trapping potential, in the so-called unitary regime (see, for instance, \cite{pitaevskii2008superfluid}) when the chemical…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
The full resurgent trans-series is found exactly in near-supersymmetric $\mathbb C P^1$ quantum mechanics. By expanding in powers of the SUSY breaking deformation parameter, we obtain the first and second expansion coefficients of the…
We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling $g^2$ and a gauge index $N$, as a system passes through a large $N$ phase transition, using the universal example of the…
We derive a systematic procedure of computing the vacuum functional and fermion condensate of the massive Schwinger model via a perturbative expansion in the fermion mass. We compute numerical results for the first nontrivial order.
We develop a large-N expansion for Gutzwiller projected spin states. We consider valence bonds singlets, constructed by Schwinger bosons or fermions, which are variational ground states for quantum antiferromagnets. This expansion is…