Photon inner product and the Gauss linking number

Abstract

It is shown that there is an interesting interplay between self-duality, loop representation and knots invariants in the quantum theory of Maxwell fields in Minkowski space-time. Specifically, in the loop representation based on self-dual connections, the measure that dictates the inner product can be expressed as the Gauss linking number of thickened loops.

18 pages, Revtex. No figures. To appear in Class. Quantum Grav

References in corpus (5)

• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• An algebraic extension of Dirac quantization: Examples
• A Loop Representation for the Quantum Maxwell Field
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• Self Duality and Quantization

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• Quantization of static space-times
• QED Representation for the Net of Causal Loops
• Application of abelian holonomy formalism to the elementary theory of numbers
• Embedded graph invariants in Chern-Simons theory
• Towards Gaussian states for loop quantum gravity
• The inverse spatial Laplacian of spherically symmetric spacetimes
• Note on Self-Duality and the Kodama State