Related papers: Spin on a 4D Feynman Checkerboard
Using the newly modified method developed for symbolic evaluation of Feynman amplitudes we examine two processes $2\to 2$ (including a case of Majorana fermions) at a tree level. Constructing special polarization basis for spinor particles,…
We propose a classical action for the motion of massless Weyl fermions in a background gauge field in (2N+1)+1 spacetime dimensions. We use this action to derive the collisionless Boltzmann equation for a gas of such particles, and show how…
Dirac semi-metals show a linear electronic dispersion in three dimension described by two copies of the Weyl equation, a theoretical description of massless relativistic fermions. At the surface of a crystal, the breakdown of fermion…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized…
We extract cubic interactions from the covariant equations of motion of Chiral Higher Spin Gravity and compute the corresponding amplitudes. These amplitudes are found to agree with earlier results obtained in the light-cone gauge. We also…
We study quantum dilaton coupled spinors in two and four dimensions. Making classical transformation of metric, dilaton coupled spinor theory is transformed to minimal spinor theory with another metric and in case of 4d spinor also in the…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…
We derive the quantum kinetic theory for fermions with arbitrary mass in a background electromagnetic field from the Wigner-function approach. Since spin of massive fermions is a dynamical degree of freedom, the kinetic equations with the…
An overlap method for regularizing Majorana--Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted…
The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field $B$ contains a $B$-independent "zeroth Landau level", protected by chiral symmetry. If the Dirac equation is discretized on…
We study the simplest geometrical particle model associated with null paths in four-dimensional Minkowski space-time. The action is given by the pseudo-arclength of the particle worldline. We show that the reduced classical phase space of…
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…
It is shown that the non-relativistic `Dirac' equation of L\'evy-Leblond, we used recently to describe a spin $1/2$ field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from $3+1$…
The theory of free Majorana-Weyl spinors is the prototype of conformal field theory in two dimensions in which the gravitational anomaly and the Weyl anomaly obstruct extending the flat spacetime results to curved backgrounds. In this…
Despite fermion doubling, a two-dimensional quasi-relativistic spin-1/2 system can still lead to true fractionalization of electrical charge, when a massive ordered phase supports a "half-vortex". Such topological defect is possible when…
We propose a framework for applying on-shell scattering amplitude methods to emergent relativistic phases of quantum matter. Many strongly correlated systems, from Dirac and Weyl semimetals to topological-insulator surfaces, exhibit…
We show that the spin (1/2-) particle from the (1/2,1)+(1,1/2) Lorentz irreducible sector of the four-vector spinor can not be described within a linear formalism but behaves as a genuinely quadratic fermion satisfying the generalized…
This article expands for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. Astonishingly, this leads to a new geometrical mechanism…
Right- and left-handed circularly polarized light interact differently with electronic charges in chiral materials. This asymmetry generates the natural circular dichroism and gyrotropy, also known as the optical activity. Here we…