Remarks about Dirac's idea of cosmological variation of so called ‘constants of nature’

Recent developments in quantum gravity suggest that wormholes may influence the observed values of the constants of nature. The Euclidean formulation of quantum gravity predicts that wormholes induce a probability distribution in the space of possible fundamental constants. In particular, the effective action on a large spherical space may lead to the vanishing of the cosmological constant and possibly determine the values of other constants of nature. The ability to perform calculations involving interacting quantum fields, particularly non-Abelian models, on a four-sphere is vital if one is to investigate this possibility. In this paper we present a new formulation of field theory on a four-sphere using the angular momentum space representation of SO(5). We give a review of field theory on a sphere and then show how a matrix element prescription in angular momentum space and a new summation technique based on the complex l plane, overcome previous limitations in calculational techniques. The standard one-loop graphs of QED are given as examples.

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6. Quantum matter

Matter: A Very Short Introduction ◽

10.1093/actrade/9780198806547.003.0006 ◽

2019 ◽

pp. 78-96

Author(s):

Geoff Cottrell

Keyword(s):

Electrical Resistance ◽

Exotic Matter ◽

Basic Unit ◽

Fundamental Constants ◽

Quantum Fluid ◽

Macroscopic Level ◽

Quantum Matter ◽

Measurement Devices ◽

Coherent Quantum ◽

Constants Of Nature

When vast numbers of particles cluster together, they can, under special conditions, display coherent quantum behaviour at the macroscopic level. ‘Quantum matter’ explains how this produces some of the most exotic matter of which we know: superfluids, in which a quantum fluid suddenly loses all its viscosity, and superconductors, where all electrical resistance is lost. The results are dramatic and spectacular. These phenomena have led to the development of measurement devices that allow the basic unit of mass, the kilogram, to be defined in terms of the fundamental constants of nature to an unprecedented degree of precision.

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