Related papers: Stochastic quantization of massive fermions
We consider the quantum dynamics of $N$ interacting fermions in the large $N$ limit. The particles in the system interact with each other via repulsive interaction that is regularized Coulomb potential with a polynomial cutoff with respect…
We consider the Schr\"odinger functional with staggered one-component fermions on a fine lattice of size $(L/a)^3 \times (T/a)$ where $T/a$ must be an odd number. In order to reconstruct the four-component spinors, two different set-ups are…
We consider massive $SU(N)$ gauge theory with fermions. Gauge bosons become massive due to the interaction with the scalar field, whose vacuum average provides the spontaneous breakdown of gauge symmetry. We investigate Dyson - Schwinger…
We derive a systematic procedure to compute Green functions for the massive Schwinger model via a perturbation expansion in the fermion mass. The known exact solution of the massless Schwinger model is used as a starting point. We compute…
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups.…
We have gone through a detailed calculation of the two-point correlation function of vector currents at finite density and magnetic field by employing the real time formalism of finite temperature field theory and Schwinger's proper time…
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform…
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to…
The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive…
The Complex Langevin (CL) method sometimes shows convergence to the wrong limit, even though the Schwinger-Dyson Equations (SDE) are fulfilled. We analyze this problem in a more general context for the case of one complex variable. We prove…
We consider a Schr\"odinger quantum dynamics for the gravitational field associated to a generic cosmological model and then we solve the corresponding eigenvalue problem. We show that, from a phenomenological point of view, an Evolutionary…
We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and…
We solve the time evolution of the density matrix both for fermions and bosons in the presence of a homogeneous but time dependent external electric field. The number of particles produced by the external field, as well as their…
We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic…
We give a mathematical construction of Euclidean quantum field theory on certain curved backgrounds. We focus on generalizing Osterwalder-Schrader quantization, as these methods have proved useful to establish estimates for interacting…
As the new results for the massive Thirring model the L-matrix and the algebraic relations for its action angle variables are given. So it is shown most directly that this model which describes self-interacting relativistic Fermions in…
Starting from a general relativistic kinetic equation, a self-consistent mean-field equation for fermions is derived within a covariant density matrix approach of QED plasmas in strong external fields. A Schr\"odinger picture formulation on…