8 research outputs found
Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation
According to Yang \& Mills (1954), a {\it conserved} current and a related
rigid (`global') symmetry lie at the foundations of gauge theory. When the
rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a
new interaction emerges as gauge potential ; its field strength is . In gravity, the conservation of the energy-momentum current of
matter and the rigid translation symmetry in the Minkowski space of special
relativity lie at the foundations of a gravitational gauge theory. If the
translation invariance is made local, a gravitational potential
arises together with its field strength . Thereby
the Minkowski space deforms into a Weitzenb\"ock space with nonvanishing
torsion but vanishing curvature. The corresponding theory is reviewed and
its equivalence to general relativity pointed out. Since translations form a
subgroup of the Poincar\'e group, the group of motion of special relativity,
one ought to straightforwardly extend the gauging of the translations to the
gauging of full Poincar\'e group thereby also including the conservation law of
the {\it angular momentum} current. The emerging Poincar\'e gauge (theory of)
gravity, starting from the viable Einstein-Cartan theory of 1961, will be
shortly reviewed and its prospects for further developments assessed.Comment: 46 pages, 4 figures, minor corrections, references added,
contribution to "One Hundred Years of Gauge Theory" edited by S. De Bianchi
and C. Kiefe