Nakanishi-Lautrup field

**standard model of particle physics**

**matter field fermions** (spinors, Dirac fields)

flavors of fundamental fermions in the standard model of particle physics | |||
---|---|---|---|

generation of fermions | 1st generation | 2nd generation | 3d generation |

quarks | |||

up-type | up quark | charm quark | top quark |

down-type | down quark | strange quark | bottom quark |

leptons | |||

charged | electron | muon | tauon |

neutral | electron neutrino | muon neutrino | tau neutrino |

**hadron** (bound states of the above quarks)

**minimally extended supersymmetric standard model**

bosinos:

**dark matter candidates**

**Exotica**

In BV-BRST formalism, for gauge fixing Yang-Mills theory (to Lorenz gauge or similar) a contractible chain complex of auxiliary field bundles is introduced for two Lie algebra-valued fields, one in degree zero, called the *Nakanishi-Lautrup field*, usually denoted “$B$” and one in degree -1, called the *antighost field*, usually denoted $\overline{C}$. See at *quantization of Yang-Mills theory*.

Beware that there are also the antifields of the ghost fields, which technically are hence “anti-ghostfields” as opposed to the Nakanishi-Lautrup “antighost-fields”. Whoever is responsible for this bad terminology should be blamed.

Named after Benny Lautrup and Noburo Nakanishi, who is sometimes misspelled as “Takanishi”.

- Noburo Nakanishi,
*Covariant quantization of the electromagnetic Field in the Landau Gauge*, Prog. Theor. Phys. 35, 1111 (1966) - Benny Lautrup,
*Canonical quantum electrodynamics in covariant gauges*, Kong. Dan. Vid. Sel. Mat. Fys. Med. 35, 29 (1967)

Review for the case of electromagnetism and with path integral terminology is in

- Marc Henneaux, section 9.1 of
*Lectures on the Antifield-BRST formalism for gauge theories*, Nuclear Physics B (Proceedings Supplement) 18A (1990) 47-106 (pdf)

while discussion for general Yang-Mills theory in the context of causal perturbation theory/perturbative algebraic quantum field theory is in

- Katarzyna Rejzner, section 7.2 of
*Perturbative Algebraic Quantum Field Theory*, Mathematical Physics Studies, Springer 2016 (web)

Last revised on October 20, 2019 at 16:21:49. See the history of this page for a list of all contributions to it.