Related papers: Relationship between Conformal Geometrodynamics an…
This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4d. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in…
We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by…
The electrodynamics of Weyl semimetals (WSMs) is an extension of Maxwell's theory where in addition to field strength tensor $F_{\mu\nu}$, an axion field enters the theory which is parameterized by a four-vector $b^\mu=(b_0,\bf b)$. In the…
We show that on a surface locally every affine torsion-free connection is projectively equivalent to a Weyl connection. First, this is done using exterior differential system theory. Second, this is done by showing that the solutions of the…
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
For a compact Riemannian manifold, Weyl's law describes the asymptotic behavior of the counting function of the eigenvalues of the associated Laplace operator. In this paper we discuss Weyl's law in the context of automorphic forms. The…
Causal systems describe the localizability of relativistic quantum systems complying with the principles of special relativity and elementary causality. At their classification we restrict ourselves to real mass and finite spinor systems.…
Hamilton's action principle is formulated and extended in conformity with the gauge transformations underlying Weyl's geometry. The extended principle characterizes infinitely many equally likely trajectories with a particle traveling along…
This is a pedagogical article which discusses various kinds of fermion fields: Dirac, Majorana and Weyl. The definitions and motivations for introducing each kind of fields is discussed, along with the connections between them. It is…
Two real vector fields are revealed as spin connections of the spinor field, which is introduced as a representation of the local Lorentz group by Dirac spinors. One of these fields is identified as the Maxwell field. Another one is the…
Pseudoclassical supersymmetric model to describe massive particles with higher spins (integer and half-integer) in $2+1$ dimensions is proposed. The quantization of the model leads to the minimal (with only one polarization state) quantum…
The term Weyl semimetal originates from the fact that its energy dispersion obeys a Weyl equation. However, a Weyl equation itself cannot fully describe the electron states in an actual bounded geometry. For example, the appearance of…
We examine in detail the effect of the conformal factor associated with the Friedmann-Robertson-Walker spacetimes on the discrete symmetries usually present in the Dirac theory and analyze the behavior of the Dirac wavefunction near the…
Systems with strong spin-orbit coupling, which competes with other interactions and energy scales, offer a fertile playground to explore new correlated phases of matter. Weyl semimetals are an example where the phenomenon leads to a low…
Different bases for the spin-1 density matrix are discussed to clarify the connection between its components and observables measured in heavy-ion collisions. The theoretical advantage of using the adjoint representation for spin matrices…
We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use…
This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: $\partial\to \partial +\omega…
In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the…
We present a unified derivation of the dynamical correlation functions including density-density, density-current and current-current, of three-dimensional Weyl/Dirac semimetals by use of the Passarino-Veltman reduction scheme at zero…