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

• Main Author: Tom T. S. Chang
• Format: Article
• Language: English
• Published: MDPI AG 2017-12-01
• Series: Symmetry
• Subjects: complexity; symmetry; virtual particles; antiscreening; renormalization group; fractional calculus; Lifshitz ordering; dark matter
• Online Access: https://www.mdpi.com/2073-8994/9/12/306

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.