Warning: Students, stay away from antiquities. The aim to learn is to survive.

Hi. Today the nomenclatures *Feynman gauge* and *Landau gauge* seem established, but could you explain the history? It's two-fold: 1. Who used first such gauges and how? 2. How did the terminology gain ground?

It also inevitably asks some history of the Lorenz gauges in QFT. In particular, when was it realized that the freedom (and need) of the gauge parameter $\xi$ lies in quantum theory?

First I apologize that I have only limited access to literature on asking such questions. My preliminary studies revealed below.

1 **Terminology in literature**

Schweber (1961) is not gauge-parameter conscious, and "Lorentz[sic] gauge" (in Feynman gauge) is opposed to coulomb. But it also refers to today's Yennie gauge in sec 15g, saying Fried and Yennie (1958) found it is possible to take gauge where the photon propagator $\propto g + 2pp/p^2$.

In Nakanishi (1966), the word "Landau gauge" is seen, and it cites several near-past articles regarding Landau gauge quantization. (It is an important paper in canonical quantization in Landau gauge, together with Lautrup (1967). Nakanishi was a strong proponent of the Landau gauge.)

In p. 74 of Nakanashi (1972), it reads "Feynman gauge or Fermi gauge" and "Landau-Khalatonikov[sic] gauge, or simply Landau gauge". Landau and Khalatnikov (1955) is listed in the bibliography section, but I couldn't find which part of Nakanishi actually cites it. Nakanishi (1972) is a review article, one of whose main topics is canonical quantization of EM field in arbitrary Lorenz gauge, i.e., for any gauge parameter.

In p 134 of Itzykoson & Zuber, (1980) the words "Feynman gauge" and "Landau gauge" are used. Were the names settled at that time?

Hmm, in p 389 of Siegel (1999), "Fermi-Feynman gauge" is introduced. Srednicki (2007) uses the word "$R_\xi$" for QED, remarking "[it] has been historically used only in the context of spontaneous symmetry broken [...] but we will use it here as well."

2 **Gauge parameter symbol**

ξ is now usual. Is it due to Fujikawa, Lee and Sanda (1972)?

For other symbols, I mention $\alpha$. Nakanishi (1972) uses it, and even after Fujikawa, Lee and Sanda (1972) it is sometimes used, for example and in Siegel (1999).

3 **Theory Timeline**

1930 - Fermi: P. 240 of Schweber (1961) says Fermi proposed to add $-\frac{1}{2} (\partial A)^2$ to the Langrangian. (Fermi was the first to introduce a subsidiary condition, but it was not perfect. See also Gupta and Bleuler below.) Although I haven't checked Fermi's papers, it may be better to call "Fermi-Feynman(-'t Hooft) gauge."

1948 - Feynman: Feynman simply justifies the use of Feynman gauge in the section 8 of Feynman (1949). Before Feynman, it wasn't Lorentz covariant, and transverse photons were separated. Feynman says it's not necessary, and it's ok to do $\gamma^\mu$...$\gamma_\mu$.

1950 - Gupta & Bleuler: They say Gupta and Bleuler succeeds in covariant canonical quantization in Feynman gauge, by discovering the correct subsidiary condition.

1956 - Landau & Khalatnikov: See Nakanishi (1972) above.

1958 - Yennie gauge: It is said Fried and Yennie (1958) uses the "Yennie gauge" of today, $\xi = 3$, in bound state problems.

Early or mid 60's - Rise of interest in Landau gauge? See Nakanishi (1966) above.

1966 - 67 Nakanishi & Lautrup: canonical quantization of EM field for any ξ.

1967 - Faddeev & Popov

1971 - 't Hooft: In 1971, 't Hooft used "Feynman-'t Hooft gauge" or simply "'t Hooft gauge" for broken gauge symmetry. Fujikawa, Lee and Sanda (1972) generalized to any ξ. Its abstract uses the word "Feynman-'t Hooft gauge". (According to Weinberg. Haven't read both two.)

1972 - Still canonical quantization for arbitrary ξ is of interest, including massive vector field. See Nakanishi (1972).

4 Loren't'z gauge (misspelling)

You may know that in the 20th century, the common spelling was "Lorentz gauge", with extra "t". I couldn't find any exceptions at my hand. The turning point might be the errata of Peskin & Schroeder. Srednicki and Siegel spell it correctly.

5 **Bibliography**

- Fermi, E., Atti. Acad. Lincei.
**9** (1929) 881, Atti. Acad. Lincei. **12** (1939) 431, Rev. Mod. Phys. **4** (1932) 87.
- Feynman, R., Phys. Rev.
**76** (1949) 769.
- Fried H.M., Yennie, D.R., Phys. Rev.
**112** (1958) 1391.
- Fujikawa, Lee and Sanda, PRD
**6** (1972) 2923
- Itzykson & Zuber "Quantum field theory", 1980.
- Landau, L. D., Khalatnikov, I. M., J. Exper. Theor. Phys. USSR 29 (1955), 89 [English translation: Sov. Phys. JETP 2 (1956), 69].open access pdf
- Lautrup, B., Mat. Fys. Medel. Dan. Vid. Selsk. 35 (1967), No. 11.
- Nakanishi, N., Prog. Theor. Phys.
**35** (1966) 1111 (Open access)
- Nakanishi, N., Prog. Theor. Phys. Supple.
**51** (1972) 1 (Open access)
- Schweber, "An introduction to relativistic quantum field theory", 1961.
- Siegel, W., "Fields", arXiv:hep-th/9912205
- Srednicki, (2007)
*Quantum field theory*

6 **Revisions of this question**

Until 2014 (was in PSE)

This post imported from StackExchange Physics at 2016-06-21 08:20 (UTC), posted by SE-user teika kazura