Particle physics from quantum Riemannian geometry

• Applicant: Dr. Kaushlendra Kumar
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 515782239

Standard model of particle physics is one of the most resounding success story of theoretical physics that combines three of the four known forces of nature viz. electromagnetism, strong and weak nuclear forces. A new mathematical theory called noncommutative geometry (NCG), pioneered by Alain Connes, is able to combine the fourth force of nature called gravity with this Standard Model, albeit at a low energy limit of what is known as high energy physics. A successful combination of all of these forces at quantum scale is the holy grail of theoretical/mathematical physicists and NCG tools can prove helpful to that end as well. There is another approach to NCG given by Shahn Majid and others that is equally as powerful when compared to its predecessor. Apart from reformulating the known noncommutative models, it has also produced newer models of quantum spacetime, where the classical notion of continuum is argued to break down. My broad aim is to reformulate the Standard Model in this version of NCG and understand the resulting implications. Because this approach relies more on the symmetry principles of the theory, something that lies at the heart of theoretical and mathematical physics, it is well equipped to answer very deep questions in the Standard Model such as (a) why is there three identical generation of fundamental particles (called Fermions) in nature that are identical in all respect except for their masses and (b) how does quark-confinement — something that is responsible for stability of atomic nuclei — takes place. To answer these questions, I will make use of exciting new results in this approach towards model building and fundamental understanding vis-à-vis the Connes approach. Furthermore, I already have familiarity with the Connes—Chamseddine reformulation due to my previous works in this area, which is evident from my proven track-record, with publications in excellent journals. I firmly believe that this ambitious project can be successfully completed in two years with DFG Walter—Benjamin Fellowship. The fact that Shahn Majid himself would be my academic host at Queen Mary University of London strongly supports my claim. Not only this, but my previous works in noncommutative geometry and Yang—Mills theory (the backbone of the Standard Model) compiled in 8 separate research papers also demonstrates my suitability in carrying out this project. I find this line of mathematical physics research particularly exciting owing to its sound mathematical foundation and ability to make predictions.

• DFG Programme: WBP Fellowship
• International Connection: United Kingdom
• Host: Professor Dr. Shahn Majid