N ov 2 00 8 CAUSAL VARIATIONAL PRINCIPLES ON MEASURE SPACES

Ja n 20 09 CAUSAL VARIATIONAL PRINCIPLES ON MEASURE SPACES

Causal variational principles on measure spaces are introduced. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied to variational principles formulated in indefinite inner product spaces.

Ju n 20 09 CAUSAL VARIATIONAL PRINCIPLES ON MEASURE SPACES

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied t...

Causal variational principles on measure spaces

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied t...

2 8 N ov 2 00 5 Moduli spaces of local systems and higher Teichmüller theory

A dialectical view of the variational principles of mechanics

The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical view of the world: any smooth motion in nature is the consequence of the interplay and dynamical balance between pairs of opposite elements of the motion. We s...