2010/08/05 by Michael Freedman, Freedman, Michael
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #gr-qc #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1008.1045
Minor changes
arxiv created 2010/12/01 · arxiv updated 2010/12/02
The macroscopic dimensions of space should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: positive versus indefinite manifold pairings. It is used to build an action on a formal chain of combinatorial space-times of arbitrary dimension. The context for such actions is 2-field theory where Feynman integrals are not over classical, but previously quantized configurations. A topologically enforced singularity of the action terminates the dimension at four and, in fact, the final fourth dimension is Lorentzian due to light-like vectors in the four dimensional manifold pairing. Our starting point is the action of causal dynamical triangulations but in a dimension-agnostic setting. It is encouraging that some hint of extra small dimensions emerges from our action.