Editorial note to: Erwin Schrödinger, Dirac electron in the gravitational field I

Bernard S. Kay

doi:10.1007/s10714-019-2625-z

Editorial note to: Erwin Schrödinger, Dirac electron in the gravitational field I

Bernard S. Kay

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Editorial Note with a mathematical and historical introduction to a 1932 paper by Erwin Schrödinger on the generalization of the Dirac equation to a curved spacetime -- to appear in the 'Golden Oldie' section of the Journal of General Relativity and Gravitation alongside an English translation of that paper. The Schrödinger paper is of interest as the first place that the well-known formula gμν∇μ∇ν+m2+R4 was obtained for the 'square' of the Dirac operator in curved spacetime. This formula is known by a number of names and we explain why we favour the name 'Schrödinger-Lichnerowicz formula'. We also aim to explain how the modern notion of `spin connection' emerged from a debate in the physics journals in the period 1929-1933. We discuss the key contributions of Weyl, Fock and Cartan and explain how and why they were partly in conflict with the approaches of Schrödinger and several other authors. We reference and comment on some previous historical accounts of this topic.

Original language	English
Number of pages	14
Journal	General Relativity and Gravitation
Volume	52
Issue number	3
Early online date	19 Dec 2019
DOIs	https://doi.org/10.1007/s10714-019-2625-z
Publication status	Published - 2020

Bibliographical note

© Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Access to Document

10.1007/s10714-019-2625-z

1906.10765
© Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Accepted author manuscript, 214 KB

https://arxiv.org/abs/1906.10765

Cite this

@article{044856deaa704248bc209829bde53204,

title = "Editorial note to: Erwin Schr{\"o}dinger, Dirac electron in the gravitational field I",

abstract = "Editorial Note with a mathematical and historical introduction to a 1932 paper by Erwin Schr{\"o}dinger on the generalization of the Dirac equation to a curved spacetime -- to appear in the 'Golden Oldie' section of the Journal of General Relativity and Gravitation alongside an English translation of that paper. The Schr{\"o}dinger paper is of interest as the first place that the well-known formula gμν∇μ∇ν+m2+R4 was obtained for the 'square' of the Dirac operator in curved spacetime. This formula is known by a number of names and we explain why we favour the name 'Schr{\"o}dinger-Lichnerowicz formula'. We also aim to explain how the modern notion of `spin connection' emerged from a debate in the physics journals in the period 1929-1933. We discuss the key contributions of Weyl, Fock and Cartan and explain how and why they were partly in conflict with the approaches of Schr{\"o}dinger and several other authors. We reference and comment on some previous historical accounts of this topic.",

author = "Kay, {Bernard S.}",

note = "{\textcopyright} Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details. ",

year = "2020",

doi = "10.1007/s10714-019-2625-z",

language = "English",

volume = "52",

journal = "General Relativity and Gravitation",

issn = "0001-7701",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - Editorial note to: Erwin Schrödinger, Dirac electron in the gravitational field I

AU - Kay, Bernard S.

N1 - © Springer Science+Business Media, LLC, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2020

Y1 - 2020

N2 - Editorial Note with a mathematical and historical introduction to a 1932 paper by Erwin Schrödinger on the generalization of the Dirac equation to a curved spacetime -- to appear in the 'Golden Oldie' section of the Journal of General Relativity and Gravitation alongside an English translation of that paper. The Schrödinger paper is of interest as the first place that the well-known formula gμν∇μ∇ν+m2+R4 was obtained for the 'square' of the Dirac operator in curved spacetime. This formula is known by a number of names and we explain why we favour the name 'Schrödinger-Lichnerowicz formula'. We also aim to explain how the modern notion of `spin connection' emerged from a debate in the physics journals in the period 1929-1933. We discuss the key contributions of Weyl, Fock and Cartan and explain how and why they were partly in conflict with the approaches of Schrödinger and several other authors. We reference and comment on some previous historical accounts of this topic.

AB - Editorial Note with a mathematical and historical introduction to a 1932 paper by Erwin Schrödinger on the generalization of the Dirac equation to a curved spacetime -- to appear in the 'Golden Oldie' section of the Journal of General Relativity and Gravitation alongside an English translation of that paper. The Schrödinger paper is of interest as the first place that the well-known formula gμν∇μ∇ν+m2+R4 was obtained for the 'square' of the Dirac operator in curved spacetime. This formula is known by a number of names and we explain why we favour the name 'Schrödinger-Lichnerowicz formula'. We also aim to explain how the modern notion of `spin connection' emerged from a debate in the physics journals in the period 1929-1933. We discuss the key contributions of Weyl, Fock and Cartan and explain how and why they were partly in conflict with the approaches of Schrödinger and several other authors. We reference and comment on some previous historical accounts of this topic.

U2 - 10.1007/s10714-019-2625-z

DO - 10.1007/s10714-019-2625-z

M3 - Article

SN - 0001-7701

VL - 52

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

IS - 3

ER -