Related papers: Path integrals and deformation quantization:the fe…
We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using Bargmann-Fock representations with commuting and non-commuting variables, the differential calculi being…
A fermionic supersymmetric extension is established for the Gauss-Weingarten and Gauss-Codazzi equations describing conformally parametrized surfaces immersed in a Grassmann superspace. An analysis of this extension is performed using a…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations…
We revisit the phenomenon of the resonant transmission of fermionic carriers through a quantum device connected to two contacts with different chemical potentials. We show that, besides the traditional in solid-state physics…
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 fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing…
This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…
In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic Hamiltonian for large numbers N of particles by analytical means into a shape such that…
We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
In this work, we establish formally exact stochastic equations of motion (SEOM) theory to describe the dissipative dynamics of fermionic open systems. The construction of the SEOM is based on a stochastic decoupling of the dissipative…
The fermion sign problem constitutes one of the most fundamental obstacles in quantum many-body theory. Recently, it has been suggested to circumvent the sign problem by carrying out path integral simulations with a fictitious quantum…
The complex exponential weighting of Feynman formalism is seen to happen at the classical level. (Finiteness of) Feynman path integral formula is suspected then to appear as a consistency condition for the existence of certain Dirac…
The quantum Dirac-like equation and the QED vertex operator for a composite particle are suggested. The vertex operator and the fermionic propagator are connected by the QED Ward identity. It is shown that all of the Feynman QED-integrals…
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
In this work we analyze the effects produced by bosonic and fermionic constituents, including quantum corrections, in two-dimensional (2D) cosmological models. We focus on a gravitational theory related to the…
In a previous paper we have shown how, for bosonic fields, the generating functional in both relativistic quantum field theory and thermal field theory can be evaluated by use of a standard quantum mechanical path integral. In this paper we…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…