How Are Yang-Mills Theory and Gauge Theory Related?

[scariari]

what do these terms have to do with each other?

yang mills
gauge theory
't hooft
instanton

 

[humanino]

Yang and Mills generalized the concept of gauge theory in the case of non-cummutative symmetry
't Hooft (and Veltman) proved the renormalizability

Instanton is a term coined by 't Hooft. See [thread=34636]this thread[/thread] or [thread=55628]this one[/thread] or [thread=38964]this more compete one[/thread]

 

[R0man]

Yang-Mills theory and gauge theory are closely related concepts in theoretical physics. They both refer to mathematical frameworks used to describe the behavior of fundamental forces in nature, specifically the strong and weak nuclear forces.

Gauge theory is a mathematical approach that describes the interactions between particles and their associated fields. It is based on the idea that the fundamental forces in nature are mediated by carrier particles, known as gauge bosons. These bosons have a specific "charge" associated with them, and their interactions with particles are governed by mathematical equations known as gauge transformations.

Yang-Mills theory, named after physicists Chen Ning Yang and Robert Mills, is a specific type of gauge theory that focuses on the strong nuclear force, which is responsible for binding particles together in the atomic nucleus. It describes the strong force in terms of a quantum field theory, using mathematical equations that involve the properties of particles such as quarks and gluons.

The 't Hooft instanton is a mathematical solution that arises in Yang-Mills theory. It describes a localized, non-perturbative fluctuation in the strong force field that can have important consequences for particle interactions. This solution was proposed by Dutch physicist Gerard 't Hooft in the 1970s and has been a key tool in understanding the behavior of the strong force.

In summary, Yang-Mills theory and gauge theory are closely intertwined concepts that are essential for understanding the fundamental forces in nature. The 't Hooft instanton is a mathematical solution that arises within Yang-Mills theory and has important implications for particle interactions.