Related papers: Correlation Functions and Stochastic Feynman Rules…
We elaborate on the functional integral describing the stochastic dynamics of a spectator field during inflation, comparing its diagrammatic expansion to that obtained directly from a perturbative solution of the corresponding Langevin…
We consider a massive scalar field with quartic self-interaction $\lambda/4!\,\phi^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman…
The aim of this paper is two-fold: in probing the statistical mechanical properties of interacting quantum fields, and in providing a field theoretical justification for a stochastic source term in the Boltzmann equation. We start with the…
We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent…
We review the method of stochastic quantization for a scalar field theory. We first give a brief survey for the case of self-interacting scalar fields, implementing the stochastic perturbation theory up to the one-loop level. The…
We introduce a second-order stochastic effective theory for light scalar fields in de Sitter spacetime, extending the validity of the stochastic approach beyond the massless limit and demonstrating how it can be used to compute…
It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the…
We provide a general formalism to calculate the infrared correlators of multiple interacting scalar fields in the de Sitter space by means of the stochastic approach. These scalar fields are treated as test fields and hence our result is…
In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the…
The stochastic effective theory approach, often called stochastic inflation, is widely used in cosmology to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative than quantitative because…
For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Few analytical methods exist for quantitative studies of large fluctuations in stochastic systems. In this article, we develop a simple diagrammatic approach to the Chemical Master Equation that allows us to calculate multi-time correlation…
The stochastic quantization of the fermion field is performed starting from Dirac equations. The statistical properties of stochastic terms in Langevin equations are described by explicit formulae of a Markov process. The interaction of the…
This thesis introduces an effective theory for the long-distance behaviour of scalar fields in de Sitter spacetime, known as the second-order stochastic theory, with the aim of computing scalar correlation functions that are useful in…
The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or…
A long-standing problem in primordial cosmology is to understand the precise relation between the stochastic formalism and standard perturbation theory for light scalar fields in inflationary spacetimes. A complete correspondence between…
Combining the stochastic and $\delta N$ formalisms, we derive non perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered…
A technique to build perturbative series for the spectator field's correlation functions in de Sitter space through the Fokker-Planck equation is proposed. We derive from the first-order differential equation the iterative integral relation…
A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the…