Narrow Results

In this paper, we aim to extend to interacting massive and massless fermionic theories the recent perturbative construction of equilibrium states developed within the framework of perturbative algebraic quantum field theory on Lorentzian spacetime. We analyze the case of interactions which depend on time by a smooth switch-on function and on space by a suitably bounded function that multiplies an interaction Lagrangian density constructed with the field of the theory. The construction is achieved by first considering the case of compact support and, in a second step, by removing the space cutoff with a suitable limit (adiabatic limit). As an application, we consider a Dirac field interacting with a classical stationary background electromagnetic potential, and we compute at first perturbative order (linear response) the expectation value of the conserved current on the equilibrium state for the interacting theory. The resulting expectation value is written as a convolution, in the space coordinates, between the electromagnetic potential and an integral kernel which, at vanishing conjugate momentum, gives the inverse of the square Debye screening length at finite temperature. The corresponding Debye screening effect is visible in the backreaction treated semiclassically of this current on the classical background electromagnetic potential sourced by a classical external current.

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

In this paper, based on [N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime, Commun. Math. Phys.374(3) (2020) 2097–2150; N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas, Invent. Math.225(3) (2021) 885–979; N. Benedikter, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas with large interaction potential, preprint (2021), arXiv:2106.13185], we present a recent estimate for the correlation energy of a Fermi gas in the so-called mean-field regime and we outline some of the main ideas of its proof.

All known Quantum-Monte-Carlo algorithms for fermions suffer from the so-called “minus-sign-problem” which is detrimental to the application of these simulation methods to fermion systems at very low temperatures and/or of very many lattice sites. We identify the origin of this fundamental problem, demonstrate that it is a very general feature, not necessarily related to the presence of fermionic degrees of freedom. We describe an novel algorithm which does not suffer from the minus-sign problem. Illustrative results for the two-dimensional Hubbard model are presented

After a prologue which clarifies some issues left open in my last paper, the main features of the tetron model of elementary particles are discussed in the light of recent developments, in particular the formation of strong and electroweak vector bosons and a microscopic understanding of how the observed tetrahedral symmetry of the fermion spectrum may arise.

Recent research on Hawking radiations of the Rindler spacetime and spherically symmetric uncharged spacetime shows that the Hawking temperature can be obtained by fermions tunnelling method. In this paper, we extend this work to the charged rotating spacetime and review the Hawking radiation of the Kerr–Sen dilaton–axion black hole by fermions tunnelling. The Hawking temperature is recovered and is exactly the same as that obtained by other methods.

A model for the universe with tachyonic and fermionic fields interacting through a Yukawa-type potential is investigated. It is shown that the tachyonic field answers for the initial accelerated regime and for the subsequent decelerated regime so that it behaves as an inflaton at early times and as a matter field at intermediate times, while the fermionic field has the role of a dark energy constituent, since it leads to an accelerated regime at later times. The interaction between the fields via a Yukawa-type potential controls the duration of the decelerated era, since a stronger coupling makes a shorter decelerated period.

In this paper, we derived Hamilton–Jacobi equation for spin 1/2 and 3/2 fermions from Dirac equation and Rarita–Schwinger equation. Then, by using the Hamilton–Jacobi equation and general tortoise coordinate transformation, the tunneling rate and Hawking temperatures of a nonstationary axisymmetric symmetry black hole are investigated. The result shows that the tunneling rate, temperature and surface gravity are all related to the properties of horizons of the black hole, the cosmological constant $\lambda$, the charge $Q$, mass of black hole $m$ and the Eddington time $\upsilon$.

In this paper, we discuss fundamental aspects related to the helicity and dynamics of the spin-1/2 fermions encompassed within the very well-known Lounesto’s classification. More specifically, we investigate how the bi-spinorial structures behave under discrete symmetries, as well as analyze some consequences on the spinors dynamics. In addition, we find an interesting relation between the spinor helicity and the Lounesto spinor classification.

In this study, we work on understanding the behavior of relativistic fermions within the framework of a (2+1)-dimensional gravitational wave environment. Our main objective is to uncover an analytical solution for the massless Dirac equation in this particular scenario. Initially, we derive a set of coupled equations that describe the quantum dynamics of the system under consideration. Subsequently, we embark on finding an analytical solution for the resulting wave equation governing Weyl fermions by utilizing the generators associated with the $s{\ell }_2$ algebra. This approach enables us to determine the relativistic frequency modes of the system. We then delve into examining how the parameters of the gravitational wave spacetime influence the real oscillation modes of Weyl fermions. Our findings highlight the sensitivity of Weyl fermions to the specific gravitational wave spacetime background being considered.

Spinor-valued one-forms (Rarita–Schwinger fields) are normally used in the context of supergravity, where they describe spin 3/2 particles (gravitinos). Indeed, when decomposed into irreducible representations of the Lorentz group such a field contains both a spin 1/2 and a spin 3/2 component, and the Rarita–Schwinger Lagrangian is designed to make only the spin 3/2 propagate. The opposite construction is also known to be possible. We propose and study a new simple spinor-valued one-form field Lagrangian that describes a propagating spin 1/2 particle.

Fermion production in external electric field on de Sitter expanding universe is analyzed. The amplitude and probability of pair production are computed. We obtain from our calculations that the modulus of the momentum is no longer conserved. The rate of pair production in an electric field is found to be important in the early universe when the expansion factor was large comparatively with the particle mass. A computation of the total probability is presented in a particular case and the result proves to be nonvanishing only in strong gravitational fields.

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schrödinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant $\mathrm{\Lambda }$. The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.

In this work, we study the thermodynamic functions of quantum gases confined to spaces of various shapes, namely, a sphere, a cylinder and an ellipsoid. We start with the simplest situation, namely, a spinless gas treated within the canonical ensemble framework. As a next step, we consider noninteracting gases (fermions and bosons) with the usage of the grand canonical ensemble description. For this case, the calculations are performed numerically. We also observe that our results may possibly be applied to Bose–Einstein condensate and to helium dimer. Moreover, the bosonic sector, independently of the geometry, acquires entropy and internal energy greater than for the fermionic case. Finally, we also devise a model allowing us to perform analytically the calculations in the case of interacting quantum gases, and, afterwards, we apply it to a cubical box.

In this paper, a class of the warp drive (WD) type metrics is proposed in the form of spherical and plane waves or shells. In particular, these metrics can describe the passage of spherical WD through the horizon of a black hole (BH) from the inside out. In this metrics, nonsingular evolution of physical fields is possible, which is demonstrated by examples of scalar, vector and fermion fields. The passage of a warp-wave through the fields is accompanied by soliton-like configurations (kinks). The limiting case of Planck-scale WD can lead to the evaporation of singularities inside BHs with the escape of particles and information into outer space, and the EPR = WD conjecture can also be proposed.

This paper explores the relativistic behavior of spin-half particles possessing an Electric Dipole Moment (EDM) in a curved space–time background induced by a spiral dislocation. A thorough review of the mathematical formulation of the Dirac spinor in the framework of quantum field theory sets the foundation for our investigation. By deriving the action that governs the interaction between the spinor field, the background space–time, and an external electric field, we establish a framework to study the dynamics of the system. Solving the resulting wave equation reveals a set of coupled equations for the radial components of the Dirac spinor, which give rise to a modified energy spectrum attributed to the EDM. To validate our findings, we apply them to the geometric phase and thermodynamics.

We investigate a cosmological model using the covariant formalism proposed by Canuto et al., considering bosonic and fermionic fields as sources, including both self-interacting potentials. Following that path, it is possible to determine, first, a family of symmetries using the Noether procedure. That permits to obtain the conformal function $\beta (t)$, part of the covariant formalism, that maps the physics between descriptions. In gravitational units (old universe) it is verified that the bosonic/fermionic combination behaves as a dark constituent. In atomic units what emerges is an initially accelerated universe, followed a decelerated period, that would correspond to a primordial era considered as an analog of inflation.

A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that 0s in a qubit string do not contribute to the value of a number. They serve only as place holders. The representation is based on the distribution of four types of systems, corresponding to +1, -1, +i, -i, along an integer lattice. Complex rational numbers correspond to arbitrary products of four types of creation operators acting on the vacuum state. An occupation number representation is given for both bosons and fermions.

We give a brief overview of recent studies of quantum degenerate regimes in ultracold Fermi gases. The attention is focused on the regime of Bose-Einstein condensation of weakly bound molecules of fermionic atoms, formed at a large positive scattering length for the interspecies atom-atom interaction. We analyze remarkable collisional stability of these molecules and draw prospects for future studies.

This paper generalizes Luttinger's model by introducing curvature (d²ε(k)/dk²≠0) into the kinetic energy. An exact solution for arbitrary interactions is still possible in principle, but it now requires disentangling the eigenvalue spectrum of an harmonic string of interacting boson fields at each value of q. The additional boson fields, extracted from the excitation spectrum of the Fermi sea, are self-selected according to the nature and strength of the dispersion.