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Foreword
Physics in the Space of the Inertial Local Frames.
(preliminary version)
M. Toller
1
via Malfatti n. 8
I-38100 Trento, Italy
Contents
Introduction
Notations and conventions
Some useful identities
The (extended) principal fiber bundle of the Lorentz frames
Tetrads
Tensor and spinor fields
Infinitesimal Lorentz transformations
Maxwell and Yang-Mills fields
Parallel transport
Covariant derivatives and spin connection
A compact formalism
Connection, soldering, curvature and torsion forms
Flat Minkowski spacetime and Poincaré group
The general space
of the (extended) inertial local frames
The basic geometric and topological stucture of the space
The operational interpretation and the relativity principle
The spacetime coincidence
The equity principle, the minimum time principle and the fundamental length
Dynamical variables and symmetry properties
Critical remarks
Feasibility of infinitesimal transformations and geometric symmetry groups
A wedge
in the vector space
The Lorentz invariant cone
The symmetry group
Orbits in
and causal influence
spinors and
tensors
Subgroups of
The spinor representation of the structure coefficients
Subgroups of
as gauge groups?
Lagrangian dynamics of classical fields
Conserved forms
The action principle and the field equations
Noether's theorem
Minimal coupling and the balance equations
Pre-symplectic formalism and double differential forms
Reformulation of some classical field theories
The Einstein-Cartan theory of gravitation
Internal gauge theories
Scalar fields
Spinor fields
Fermions in the Standard Model of elementary particles
Theories with a variable gravitational coupling
A geometrized scalar-tensor theory of gravitation
Macroscopic physical interpretation
Microscopic considerations and dilatations of
.
Lagrangian constraints and pre-symplectic double forms
Classical field theories with
symmetry (not complete)
Higher symmetries and a substitution rule
Normal field equations and use of the symmetry property.
Two examples of Lagrangians invariant under
.
Test particles in geometric fields (not ready)
Cosmological applications (not ready)
Graded field algebras and antiderivations (not ready)
Quantum fields in a fixed geometric background (not ready)
Bibliography
Index
About this document ...
Marco Toller
2007-11-25
of the (extended) inertial local frames
in the vector space 
and causal influence
spinors and 
tensors
as gauge groups?
.
symmetry (not complete)
.