Related papers: Non-perturbative computation of lattice correlatio…
Perturbation theory is a powerful tool in manipulating dynamical system. However, it is legal only for infinitesimal perturbations. We propose to dispose this problem by means of perturbation group, and find that the coupling constant…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard…
In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of integrable discrete autonomous equations on a square lattice with a non-standard structure of generalized symmetries is constructed. We build modified series by…
In our previous work \cite{Feng:2013pba}, we have shown a curvaton model where the curvaton has a nonminimal derivative coupling to gravity. Such a coupling could bring us scale-invariance of the perturbations for wide range constant values…
We analyze the pressure and density equations of state of unpolarized non-relativistic fermions at finite temperature in one spatial dimension. For attractively interacting regimes, we perform a third-order lattice perturbation theory…
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…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
The complete knowledge of a theory is encoded in its correlation functions. Thus non-perturbative effects, like confinement in QCD, is necessarily contained in these correlation functions. As a consequence, a number of confinement scenarios…
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…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important…
We propose a new method to compute the running coupling constant of gauge theories on the lattice. We first give the definition of the running coupling in the new scheme using the Wilson loops in a finite volume, and explain how the running…
We revisit the question of how to calculate correlations of the curvature perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice…
We compute the running coupling of non-Abelian gauge theories in the Schr\"odinger-functional scheme, by means of non-equilibrium Monte Carlo simulations on the lattice.
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is…
A general technique of exact calculation of any correlation functions for the special class of one-dimensional spin models containing small clusters of quantum spins assembled to a chain by alternating with the single Ising spins is…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative…