Related papers: Unified genus-1 potential and a parametric perturb…
We present a new perturbative/nonperturbative (P/NP) relation that applies to a broader class of genus-1 potentials, including those that possess real and complex instantons parametrized by a deformation parameter, such as polynomial and…
Recently, it is realized that non-perturbative instanton effects can be generated to all orders by perturbation theory around a degenerate minima via Dunne-Unsal relation in several quantum mechanical systems. In this work we verify the…
Spectra of standard 1d potentials (double-well, sin-Gordon etc) are given by trans-series in coupling, including (badly divergent) perturbative series (PS), and nonperturbative terms. All of them are badly defined (e.g. PS are badly…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
We introduce N-parameter perturbation theory as a new tool for the study of non-linear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to…
We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to…
Perturbative corrections to N=1/2 supersymmetric U(N) gauge theory at one-loop order are studied. It is shown that whereas the quantum corrections to N=1 sector of the theory are not affected by the C-deformation, the non(anti)commutativity…
We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system…
In this work we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the…
We apply a recently developed 1/(N-1) expansion to the full counting statistics for the N-fold degenerate Anderson impurity model in the Kondo regime. This approach is based on the perturbation theory in the Coulomb interaction U and is…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all…
The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A…
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a…
On the perturbatively non-renormalizable and non-perturbatively finite examples (delta-function type potential in non-relativistic quantum mechanics and the mathematical model of the propagator by Redmond and Uretsky in quantum field…
This paper describes and proves a canonical procedure to decouple perturbations and optimize their gauge around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, while preserving locality in this dimension.…
We study a reduction of deformation parameters in non(anti)commutative N=2 harmonic superspace to those in non(anti)commutative N=1 superspace. By this reduction we obtain the exact gauge and supersymmetry transformations in the Wess-Zumino…
We study N=2 supersymmetric U(1) gauge theory in non(anti)commutative N=2 harmonic superspace with the chirality preserving non-singlet deformation parameter. By solving the Wess-Zumino gauge preserving conditions for the analytic…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
We investigate possible extensions of the (2+1) dimensional $CP^{N-1}$ model to the noncommutative space. Up to the leading nontrivial order of 1/N, we prove that the model restricted to the left fundamental representation of the gauge…