Related papers: Modelling financial time series with $\phi^{4}$ qu…
After the success of affine quantization in proving through Monte Carlo analysis that the covariant euclidean scalar field theory, $\varphi^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ with $s$ the spatial…
The time evolution of O(N) symmetric lambda Phi^4 scalar field theory is studied in the large N limit. In this limit the <Phi> mean field and two-point correlation function <Phi Phi> evolve together as a self-consistent closed Hamiltonian…
Sophisticated machine learning (ML) models to inform trading in the financial sector create problems of interpretability and risk management. Seemingly robust forecasting models may behave erroneously in out of distribution settings. In…
A finite size scaling theory for the partition function zeros and thermodynamic functions of O(N) phi^4-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with…
We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the…
In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing $ig\phi^3$ and $-g\phi^4$ field theories, still possess real positive spectra so long as the weaker condition of ${\cal PT}$ symmetry holds.…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…
The Higgs field is an attractive candidate for the inflaton because it is an observationally confirmed fundamental scalar field. Importantly, it can be modeled by the most general renormalizable scalar potential. However, if the classical…
Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
In this work, we revisit the Witten-O'Raifeartaigh model of inflation, in which the potential takes a $\operatorname{log}^2(\phi/M)$ form, when the scalar field is non-minimally coupled to gravity. We investigate the impact of the coupling…
The quest for finding self-consistent background solutions in quantum field theory is closely related to the way one decides to set the renormalization scale $k$. This freedom in the choice of the scale setting can lead to ambiguities and…
We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into…
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…
We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the…
An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $\phi^4$ theory in 1+1 dimensions. We…
We present an explicit cosmological model where inflation and dark energy both could arise from the dynamics of the same scalar field. We present our discussion in the framework where the inflaton field $\phi$ attains a nearly constant…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Financial time series (FinTS) record the behavior of human-brain-augmented decision-making, capturing valuable historical information that can be leveraged for profitable investment strategies. Not surprisingly, this area has attracted…