Weyl fermion

Weyl fermion
Name	Weyl fermion
Field	Theoretical physics; Condensed matter physics
Discovered	1929
Discoverer	Hermann Weyl
Related	Dirac fermion; Majorana fermion; neutrino

Weyl fermion

Weyl fermions are massless spin-1/2 particles described by Weyl's two-component equation, introduced by Hermann Weyl in 1929, and have played a role in the development of quantum field theory, general relativity, and gauge theory. Their conceptual lineage connects to foundational work by Paul Dirac, Wolfgang Pauli, Enrico Fermi, and Ettore Majorana, influencing research at institutions such as Princeton University, University of Göttingen, and CERN. Weyl fermions appear as elementary excitations in high-energy contexts discussed at venues like International Conference on High Energy Physics and as quasiparticles in materials studied at laboratories including Max Planck Institute for Solid State Research, MIT, and Bell Labs.

Introduction

Weyl fermions were proposed by Hermann Weyl as solutions to a chiral, two-component form of the Dirac equation shortly after the development of quantum mechanics and special relativity. Historically they influenced debates involving Paul Dirac's relativistic electron theory, Ettore Majorana's real spinors, and symmetry analyses by Emmy Noether and Hermann Minkowski. In modern contexts, Weyl fermions are central to discussions at CERN Large Hadron Collider, KITP Santa Barbara workshops, and conferences like APS March Meeting, and they bridge communities including researchers from Harvard University, Stanford University, and University of Cambridge.

Mathematical formulation

Mathematically, a Weyl fermion is described by a two-component spinor that satisfies the Weyl equation, obtained by projecting the Dirac spinor with chiral projectors derived from the gamma matrices introduced by Paul Dirac and formalized by Claude Chevalley. The Weyl equation can be written using representations of the Lorentz group classified by Eugene Wigner and realized through the SL(2,C) spinor formalism developed at places like Mandelstam Research Group and by researchers including Roger Penrose. Weyl spinors transform under the (1/2,0) or (0,1/2) irreducible representations, linking to mathematical structures studied by Élie Cartan, Hermann Weyl, and Felix Klein. The formulation employs covariant derivatives similar to those in Yang–Mills theory developed by Chen Ning Yang and Robert Mills and can be coupled to gauge fields of groups such as U(1), SU(2), and SU(3) used in Standard Model constructions by Sheldon Glashow, Steven Weinberg, and Abdus Salam.

Physical properties and chirality

Weyl fermions are massless and exhibit definite chirality, a handedness property tied to representations of the Poincaré group explored by Eugene Wigner and symmetry classifications by Noether. Chirality distinguishes left-handed and right-handed Weyl spinors and connects to parity violation observed in weak interactions by Chien-Shiung Wu and interpreted by Tsung-Dao Lee and Chen Ning Yang. The helicity of a Weyl fermion equals its chirality in the massless limit, a relation central to analyses by Yoichiro Nambu and Murray Gell-Mann. Conservation or anomaly-induced nonconservation of chiral charge is governed by the chiral anomaly first computed by Adler and Bell and Jackiw, with implications discussed in work at SLAC and CERN.

Weyl fermions in particle physics

In particle physics, Weyl fermions appear in chiral formulations of the Standard Model where left- and right-handed components transform differently under SU(2)_L and U(1)_Y gauge groups developed by Sheldon Glashow, Steven Weinberg, and Abdus Salam. The neutrino was historically modeled as a Weyl fermion by Enrico Fermi and later reexamined after the discovery of neutrino mass at experiments like Super-Kamiokande and Sudbury Neutrino Observatory led by collaborations including Kamioka Observatory researchers and Arthur McDonald. Grand unified theories by Howard Georgi and Sheldon Glashow and anomaly cancellation conditions analyzed by Gerard 't Hooft and John Preskill constrain possible Weyl fermion content, while supersymmetry frameworks by Pierre Fayet and Sergio Ferrara use Weyl spinors in supermultiplets studied at CERN Theory Division.

Weyl semimetals and condensed matter realizations

Condensed matter realizations of Weyl fermions were predicted in materials hosting band-touching points called Weyl nodes by theorists including Xiao-Liang Qi, Shou-Cheng Zhang, and Ashvin Vishwanath and experimentally observed in compounds studied by groups at Princeton University, Harvard University, and Duke University. Weyl semimetals such as tantalum arsenide discovered by collaborations including Zhi Fang's network exhibit Fermi arcs on surfaces predicted in theoretical proposals by Armitage, Burkov, and Balents. These materials often crystallize in noncentrosymmetric lattices identified via measurements at facilities like Argonne National Laboratory and National High Magnetic Field Laboratory, linking to topological band theory developed by David Thouless, F. D. M. Haldane, and Charles Kane.

Experimental detection and signatures

Experimental signatures of Weyl fermions include angle-resolved photoemission spectroscopy (ARPES) spectra revealing Weyl nodes and Fermi arcs in experiments at beamlines associated with SLAC National Accelerator Laboratory, Synchrotron Radiation Lightsource, and facilities used by teams from University of California, Berkeley and Stanford. Transport phenomena such as the chiral magnetic effect and negative magnetoresistance have been reported in magnetotransport studies at Los Alamos National Laboratory and Max Planck Institute groups. Quantum oscillation measurements, scanning tunneling microscopy performed by groups at Columbia University and University of Tokyo, and optical probes used by researchers at Caltech provide complementary evidence, while cold-atom simulators at MIT and Institute for Quantum Optics and Quantum Information offer engineered platforms.

Theoretical extensions and relations to other fermions

Theoretical extensions connect Weyl fermions to Dirac fermions via mass terms that couple opposite chiralities as in Dirac equation studies by Paul Dirac and to Majorana fermions when particle equals antiparticle as investigated by Ettore Majorana and pursued in contexts at Microsoft Station Q and James McMahon's collaborations. Weyl fermions figure in anomaly inflow arguments by Edward Witten and Alvarez-Gaumé and in topological quantum field theories studied by Michael Atiyah and Graeme Segal. Proposals link Weyl physics to phenomena in cosmology studied at Institute for Advanced Study and to engineered systems in photonic crystals researched at ETH Zurich and Nanyang Technological University.

Category:Quantum field theory Category:Condensed matter physics Category:Particle physics