standard model of particle physics
photon - electromagnetic field (abelian Yang-Mills field)
matter field fermions (spinors, Dirac fields)
hadron (bound states of the above quarks)
minimally extended supersymmetric standard model
bosinos:
dark matter candidates
Exotica
spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
In physics, specifically in field theory, a Dirac field is an electromagentially charged and possibly massive a fermionic spinor field.
This includes fermions in the standard model of particle physics, such as electrons, quarks, neutrinos and muons, after the Higgs mechanism has equipped them with mass.
Mathematically, the Dirac field is the field whose field bundle is a spinor bundle with typical fiber a Dirac representation in odd super-degree and whose equation of motion is a Dirac equation.
Notice that there are other spinor fields which would not be called “Dirac fields”, such as those transforming in a Majorana representation or a Weyl representation, or for example the gravitino field which would be called a Rarita-Schwinger field.
A concise collection of the details over Minkowski spacetime is in
with background on spinor fields in
A textbook account in the context of causal perturbation theory is in
Günter Scharf, section 2.2 of Finite Quantum Electrodynamics – The Causal Approach, Berlin: Springer-Verlag, 1995, 2nd edition
Günter Scharf, section 1.8 of Quantum Gauge Theories – A True Ghost Story, Wiley 2001
Last revised on January 20, 2018 at 11:29:36. See the history of this page for a list of all contributions to it.