The DOI matches its Crossref record.
Non-Linear Field Theories
Abstract
This is the first paper in a program concerned with the quantization of field theories which are covariant with respect to general coordinate transformations, like the general theory of relativity. All these theories share the property that the existence and form of the equations of motion is a direct consequence of the covariant character of the equations. It is hoped that in the quantization of theories of this type some of the divergences which are ordinarily encountered in quantum field theories can be avoided. The present paper lays the classical foundation for this program: It examines the formal properties of covariant field equations, derives the form of the conservation laws, the form of the equations of motion, and the properties of the canonical momentum components which can be introduced.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Conservation Laws in General Relativity as the Generators of Coordinate Transformations
Bergmann, P. G. (1958) · Physical Review · doi:10.1103/physrev.112.287 · Cited by 99
Self-citationRovelli, C. (2007) · Philosophy of Physics · doi:10.1016/b978-044451560-5/50015-4 · Cited by 86
Noether symmetries, energy–momentum tensors, and conformal invariance in classical field theory
Pons, J. M. (2011) · Journal of Mathematical Physics · doi:10.1063/1.3532941 · Cited by 57
Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces
Hu, B.-L. (2021) · Universe · doi:10.3390/universe7110424 · Cited by 8
Metadata
- Authors
- Bergmann, P. G.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1949-02-15
- Volume
- 75
- Issue
- 4
- Pages
- 680-685
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W1977888909
- Cited by
- 308
- References
- 0
- FWCI
- 34.72
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Non-Linear Field Theories. https://app.cochat.ai/papers/10.1103/physrev.75.680
- The paper
- Bergmann, P. G. (1949). Non-Linear Field Theories. Physical Review. https://doi.org/10.1103/physrev.75.680
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
