Nakanishi-Lautrup field




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 “BB” and one in degree -1, called the antighost field, usually denoted C¯\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 some Nakanishi who is sometimes misspelled as “Takanishi”.

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 12, 2017 at 18:19:26. See the history of this page for a list of all contributions to it.