 Feb 2023

www.youtube.com www.youtube.com

One of the problems in approaching quantum gravity is the choice for how to best represent it mathematically. Most of quantum mechanics is algebraic in nature but gravity has a geometry component which is important. (restatement)
This is similar to the early 20th century problem of how to best represent quantum mechanics: as differential equations or using group theory/Lie algebras?
This prompts the question: what other potential representations might also work?
Could it be better understood/represented using Algebraic geometry or algebraic topology as perspectives?
[handwritten notes from 20230202]

 Jan 2023

ncatlab.org ncatlab.org

In particular Erwin Schrödinger is said (Wigner (1981)) to have spoken of the Gruppenpest (German for “plague of group theory”) which ought to be abandoned. In his autobiography John Slater, an MIT physicist, claimed: It was at this point that Wigner, Hund, Heitler, and Weyl entered the picture with their “Gruppenpest”: the pest of the group theory… The authors of the “Gruppenpest” wrote papers which were incomprehensible to those like me who had not studied group theory, in which they applied these theoretical results to the study of the many electron problem. The practical consequences appeared to be negligible, but everyone felt that to be in the mainstream one had to learn about it. Yet there were no good texts from which one could learn group theory. It was a frustrating experience, worthy of the name of a pest. I had what I can only describe as a feeling of outrage at the turn which the subject had taken… As soon as this [Slaters] paper became known, it was obvious that a great many other physicists were as disgusted as I had been with the grouptheoretical approach to the problem. As I heard later, there were remarks made such as “Slater has slain the ‘Gruppenpest’”. I believe that no other piece of work I have done was so universally popular.
Gruppenpest, a word of German origin, which has also entered into English to mean "the plague of group theory" and group theorists (mathematicians) who were applying abstract algebra to physics and quantum mechanics in the midtwentieth century.


inferencereview.com inferencereview.com

If nothing else, Woit’s book allows its readers a sense of vicarious sympathy for physicists of the early twentieth century forced to face the facts and learn some group theory. The term gruppenpest has entered the literature, the spontaneous outburst, one gathers, of John Slater, the chair of MIT’s Department of Physics.
