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Symmetry 2017, 9(12), 306; doi:10.3390/sym9120306

Complexity Phenomena Induced by Novel Symmetry and Symmetry-Breakings with Antiscreening at Cosmological Scales—A Tutorial

Kavli Institut for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Received: 11 November 2017 / Revised: 3 December 2017 / Accepted: 4 December 2017 / Published: 7 December 2017
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Abstract

Complexity phenomena in cosmological evolution due to the scale-running of the propagator coupling constant can yield new insights related to virtual particles and antiscreening effects with dark matter consequences. This idea was developed in accordance with the differential-integral functional formulation of the Wilsonian renormalization group based on the one-particle irreducible scale-dependent effective action for gravitational evolution. In this tutorial communication, we briefly describe the essence of the result with minimal mathematical details and then consider a few simple examples to provide a basic understanding of such an interesting and intriguing complexity process in terms of fractional calculus. View Full-Text
Keywords: complexity; symmetry; virtual particles; antiscreening; renormalization group; fractional calculus; Lifshitz ordering; dark matter complexity; symmetry; virtual particles; antiscreening; renormalization group; fractional calculus; Lifshitz ordering; dark matter
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chang, T.T.S. Complexity Phenomena Induced by Novel Symmetry and Symmetry-Breakings with Antiscreening at Cosmological Scales—A Tutorial. Symmetry 2017, 9, 306.

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