Related papers: Half-Differentials and Fermion Propagators
A massless Weyl-invariant dynamics of a scalar, a Dirac spinor, and electromagnetic fields is formulated in a Weyl space, $W_4$, allowing for conformal rescalings of the metric and of all fields with nontrivial Weyl weight together with the…
Consistency conditions for the local existence of massless spin 3/2 fields has been explored that the field equations for massless helicity 3/2 are consistent iff the space-time is Ricci-flat and that in Minkowski space-time the space of…
In Ref. \cite{Horava2005} Ho\v{r}ava suggested, that the multi - fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions.…
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…
Chiral anomaly (CA), a hallmark of Weyl fermions, has emerged as a cornerstone of condensed matter physics following the discovery of Weyl semimetals. While the anomaly in pseudospin-1/2 (Weyl) systems is well-established, its extension to…
We extend our program, of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones…
We present an approach to bosonic ($Z^0, W^{\pm}$) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for the $Z^0$-boson propagator we extend previous analyses and…
We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED$_3$) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting…
We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the…
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
The recent discovery of Weyl fermions in solids enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. They are constituted of pairs of Weyl points with two-fold band degeneracy, which…
We consider the fermionization of a bosonic free theory characterized by the 3+1D scalar - tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the 4+1D topological BF theory. In this…
In this paper, we explore the field propagator with a structure that is general enough to encompass both the case of newly-defined mass-dimension $1$ fermions and spin-$1/2$ bosons. The method we employ is to define a map between spinors of…
Semiclassical expansion of the Wigner function for spin-1/2 fermions having an effective spacetime-dependent mass is used to analyze spin-polarization effects. The existing framework is reformulated to obtain a differential equation…
The fermion propagators in the fivebrane background of type II superstring theories are calculated. The propagator can be obtained by explicitly evaluating the transition amplitude between two specific NS-R boundary states by the propagator…
Conditions for the existence of shear-free and expansion-free non-null vector fields in spaces with affine connections and metrics are found. On their basis Weyl's spaces with shear-free and expansion-free conformal Killing vectors are…
Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones.…
Inter-band effects of magnetic field on orbital magnetic susceptibility and Hall effect in weak magnetic field have been studied theoretically at absolute zero for the model of massless Fermions in two dimension described by Weyl equation…
The general formalism of the free Dirac fermions on spatially flat $(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetimes is developed in momentum representation. The mode expansions in terms of the fundamental spinors…
A model is presented of the leptons, quarks and bosons as non-elementary particles being composed of spinons. They are defined as massless fermions obeying the Weyl equations, but in addition are charged and assumed to have two internal…