Explicit partial and functional differential equations for beables or observables

2015/05/13 by Edward Anderson, Anderson, Edward · 8 citations
Physics and Astronomy · Mathematics · #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1505.03551

Abstract

We provide explicit partial differential equations - in finite cases - and functional differential equations - in field-theoretic cases - which determine observables or beables in the senses of Kuchař and of Dirac. These cover a wide range of relational mechanics models as well as Electromagnetism, Yang--Mills Theory and General Relativity. We give an underlying reason why pure-configuration Kuchař observables are already well-known: various types of shape, E-fields, B-fields, loops and 3-geometries. The partial differential equations or functional differential equations for pure-momentum observables are also posed, as are those for observables which have a mixture of configuration and momentum functional dependence.

Citations

• The Problem of Time and Quantum Cosmology in the Relational Particle\n Mechanics Arena

Cited by

• The Smallest Shape Spaces. I. Shape Theory Posed, with Example of 3 Points on the Line
• The Smallest Shape Spaces. III. Triangles in 2- and 3-d
• A Local Resolution of the Problem of Time
• Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed
• Monopoles of Twelve Types in 3-Body Problems
• A Local Resolution of the Problem of Time. I. Introduction and Temporal\n Relationalism
• Topological Shape Theory
• A Local Resolution of the Problem of Time. III. The other classical facets piecemeal

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