Related papers: Nonperturbative correlation functions from homotop…
We present expressions for correlation functions of scalar field theories in perturbation theory using quantum $A_\infty$ algebras. Our expressions are highly explicit and can be used for theories both in Euclidean space and in Minkowski…
We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential…
We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
Perturbation theory of a large class of scalar field theories in $d<4$ can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the $\lambda \phi^4$ theory in two dimensions in the…
Classical and quantum correlation functions are derived for a system of non-interacting particles moving on a circle. It is shown that the decaying behaviour of the classical expression for the correlation function can be recovered from the…
We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action $S(\phi)=\frac{\sigma }{2}\phi^{2}+\frac{\lambda}{4}\phi^{4}$. Using the Lefschetz thimble decomposition and the…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
The concept of effective particles as degrees of freedom in a relativistic quantum field theory is defined using a non-perturbative renormalization group procedure for Hamiltonians. However, every candidate for a basic physical theory…
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation.…
We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field…
Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological…
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 calculate Euclidean correlation functions through next-to-leading order in the low energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop…
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…
In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative…
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the…
Starting from a parameterisation of the quantum effective action for gravity we calculate correlation functions for observable quantities. The resulting templates allow to reverse-engineer the couplings describing the effective dynamics…
In the framework of the analytic approach to Quantum Chromodynamics a new model for the strong running coupling has recently been developed. Its underlying idea is to impose the analyticity requirement on the perturbative expansion of the…