相关论文: Perturbation theory without power series: iterativ…
Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either…
This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda…
The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The…
The non-Hermitian but $\mathcal{PT}$-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a "heavy" sector into the physical observables of the "light" (or low energy)…
The stationary Schr\"odinger equation for an electron in a constant electromagnetic field with a non-Hermitian linear perturbation is studied. The wave function and the spectrum of the system are derived analytically, with the spectrum…
We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for…
We revisit scalar $\phi^4$ theory and construct a reorganized perturbative expansion in which the kinetic operator, rather than the quartic interaction, is treated as the perturbation. Starting from the exactly solvable $0$-dimensional…
The general behaviour of perturbation series in non-equilibrium scalar field theory is analysed in some detail, with a particular emphasis on the ``pathological terms'', generated by multiple products of $\delta$-functions. Using an…
We give an intuitive proof of a new non-renormalization theorem in supersymmetric field theories. It applies both perturbatively and non-perturbatively. The superpotential is not renormalized in perturbation theory but receives…
The perturbative expansion of static force and potential is reanalyzed concerning its practical applicability. A well behaved perturbative prediction is given by the integration of the renormalization group equation for the coupling…
We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random…
It has long been understood that the inclusion of temperature in the perturbative treatment of quantum field theories leads to complications that are not present at zero temperature. In these proceedings we report on the non-perturbative…
The notion of non-perturbative renormalization is discussed and extended. Within the extended picture, a new non-perturbative representation for the generating functional of Green functions of quantum field theories is suggested. It is…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
We consider the stochastically driven one dimensional nonlinear oscillator $\ddot{x}+2\Gamma\dot{x}+\omega^2_0 x+\lambda x^3 = f(t)$ where f(t) is a Gaussian noise which, for the bulk of the work, is delta correlated (white noise). We…