Volume-forms and Minimal Action Principles in Affine Manifolds

Abstract

Through the analyses of volume-forms in differentiable manifolds, it is shown that the usual way of defining minimal action principles for field theory on curved space-times is not appropriate on non-riemannian manifolds. An alternative approach, based in a new volume-form, is proposed and confronted with the standard one. The new volume element is explicitly used in the study of Einstein-Cartan theory of gravity and its relation to string theory, in connection with some recent results on the subject.

14 pages, IFUSP/P-1068

References in corpus (1)

• Gauge fields on Riemann-Cartan space-times

Cited by in corpus (15)

• Minimal coupling in presence of non-metricity and torsion
• A geometrical action for dilaton gravity
• Einstein-Cartan gravity with Holst term and fermions
• Neutron star in presence of torsion-dilaton field
• Trapped surfaces and nature of singularities in Lyra's geometry
• Volume elements and torsion
• Local electromagnetic duality and gauge invariance
• Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics
• Frames of reference in spaces with affine connections and metrics
• Spinless Matter in Transposed-Equi-Affine Theory of Gravity
• Nonuniqueness of gravity-induced fermion interaction in the Einstein-Cartan theory
• Solar System Experiments and the Interpretation of Saa's Model of Gravity with Propagating Torsion as a Theory with Variable Plank "Constant"
• Modified coupling procedure for the Poincaré gauge theory of gravity
• On the choice of coupling procedure for the Poincaré gauge theory of gravity
• The geometrical form for the string space-time action