nLab
Dirac current

Contents

Context

Fields and quanta

field (physics)

standard model of particle physics

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
f1-meson
a1-meson
strange-mesons:
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
baryonsnucleons:
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)

solitons

minimally extended supersymmetric standard model

superpartners

bosinos:

sfermions:

dark matter candidates

Exotica

auxiliary fields

Spin geometry

Contents

Idea

In the Lagrangian field theory of the Dirac field, the Dirac current is a conserved current whose interpretation is literally the current of the spinor particles that are the quanta of the Dirac field. Therefore the corresponding charge is fermion number. As such the Dirac current (or rather its chiral version) plays a key role for instance in baryogenesis.

The Dirac current is the conserved current which is associated via Noether's theorem I to the infinitesimal symmetry of the Lagrangian given by multiplying the Dirac field by a complex phase.

Definition

In the usual standard coordinates, the Dirac current is of the form

ψ¯γ μψι μdvol ΣΩ p,0. \overline{\psi}\gamma^\mu \psi \, \iota_{\partial_\mu} dvol_\Sigma \;\in\; \Omega^{p,0} \,.

For details see at geometry of physics – A first idea of quantum field theory this example.

Last revised on March 25, 2020 at 10:19:51. See the history of this page for a list of all contributions to it.