On Symmetric Gauge Fields for arbitrary Gauge and Symmetry Groups

Othmar Brodbeck

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On Symmetric Gauge Fields for arbitrary Gauge and Symmetry Groups

Othmar Brodbeck

General Relativity and Quantum Cosmology · Submitted 15 Oct 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.41 · mentions code or data availability 0.01.

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A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's theorem (classifying the invariant connections) is proven and local expressions for the gauge potential of an invariant connection are given.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived.	result 0.60	0.92	0.57	asserted 1.00
s1	A generalization of Wang's theorem (classifying the invariant connections) is proven and local expressions for the gauge potential of an invariant connection are given.	contribution 0.64	0.93	0.36	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's theorem (classifying the invariant connections) is proven and local expressions for the gauge potential of an invariant connection are given.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quasitopological Gravity with Matter: Modified Double-Copy Approach
gr-qc 2026-08 conditional novelty 6.0 of 10

Spherically symmetric quasitopological gravity with matter is mapped exactly to a flat-space nonlinear gauge theory in D+1 dimensions, with the Einstein limit giving Maxwell theory.
Stationary Black Holes: Uniqueness and Beyond
gr-qc 2012-05 accept novelty 3.0 of 10

Under stated regularity, analyticity and non-degeneracy hypotheses, stationary electrovacuum black holes are Kerr-Newman; outside electrovacuum the no-hair classification provably fails, and the review catalogues exac...
Loop Quantum Cosmology
gr-qc 2006-01 accept novelty 2.0 of 10

Loop quantum cosmology replaces the big bang singularity with a discrete difference equation whose solutions extend through the classically singular point, and this review lays out the effective equations and full-the...

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6 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Uses its method or tool 2 papers

Using a general result on symmetric connections [ref] , one obtains a parametrization of isotropic Bianchi I connections by $A=c·δ^I_a dx^a⊗τ_I$.

Symmetry Reduction of Loop Quantum Gravity · Holonomy ODE for Homogeneous Isotropic Cosmological Model · 0.92
There exists standard technique in the literature allowing one to obtain the relevant expression; see, e.g., [ref] .

Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars · Spherically symmetric Lie-algebra-valued two-form · 0.98

Cites it as background 1 paper

The general classification of gauge groups supporting such configurations, together with the corresponding existence theorems based on invariant connections over homogeneous spaces, can be found, for example, in Refs. [ref] .

Quasitopological Gravity with Matter: Modified Double-Copy Approach · Yang-Mills fields · 0.92

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