2002/05/31 by Mario Serna, Kevin Cahill · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #gr-qc #hep-th
paper · pdf · doi:10.1088/1126-6708/2003/10/054
published as JHEP 0310 (2003) 054 · Improved the explanations, added references, added 3 figures and an appendix, corrected a sign error in the old figure 4 (now figure 5). Now 33 pages, 7 figures and 2 tables. E-mail Serna for annimations
openalex publication_date 2003/10/23 · arxiv created 2004/06/17 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In a traditional gauge theory, the matter fields ϕa and the gauge fields Acμare fundamental objects of the theory. The traditional gauge field is similar to the connection coefficient in the Riemannian geometry covariant derivative, and the field-strength tensor is similar to the curvature tensor. In contrast, the connection in Riemannian geometry is derived from the metric or an embedding space. Guided by the physical principal of increasing symmetry among the four forces, we propose a different construction. Instead of defining the transformation properties of a fundamental gauge field, we derive the gauge theory from an embedding of a gauge fiber F=Rn or F=Cn into a trivial, embedding vector bundle F=RN or F=CN where N>n. Our new action is symmetric between the gauge theory and the Riemannian geometry. By expressing gauge-covariant fields in terms of the orthonormal gauge basis vectors, we recover a traditional, SO(n) or U(n) gauge theory. In contrast, the new theory has all matter fields on a particular fiber couple with the same coupling constant. Even the matter fields on a C1 fiber, which have a U(1) symmetry group, couple with the same charge of +/- q. The physical origin of this unique coupling constant is a generalization of the general relativity equivalence principle. Because our action is independent of the choice of basis, its natural invariance group is GL(n,R) or GL(n,C). Last, the new action also requires a small correction to the general-relativity action proportional to the square of the curvature tensor.