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pinu
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Can some one explain what are the so called "large gauge transformations" and where do they play important role in physics? Explanations with less mathematical rigor will be greatly appreciated.
Can you please explain it in a bit detail (using required mathematical formalism).Haelfix said:Large gauge transformations are gauge transformations that cannot be continously connected to the identity element homotopically. It's hard to explain this without math here.
julian said:Yang-Mills theories are non-Abelian generalizations of Maxwell's theory. You start with a gauge group just like in Maxwell's theory, but instead of being a collection of numbers, it is a collection of matrices.
Small gauge transformation are defined with respect to group elements continuously connected with the unit matrix, as with a Taylor expansion of the exponential function about the unit matrix. If they are not `connected' to the unit matrix then they correspond to what are called large gauge transformations. Examples of `disconnected' gauge transformations occur with a non-Abelian gauge theory where you have a topologically non-trivial configuration space. Such disconnected gauge transformations do not occur with Abelian gauge theory - i.e. Maxwell's theory.
You want to look at the WKB approximation and "Instantons" (for a start) which can be used to probe the nonperturbative realm of gauge theories.
You can have a look at chapter 16 of "Quantum Field Theory" by Michio Kaku.
Large gauge transformations refer to changes in the gauge field of a physical system that are large compared to the local fluctuations of the field. These transformations are important in understanding the symmetries and dynamics of gauge theories, such as electromagnetism and the strong and weak nuclear forces.
Large gauge transformations play a crucial role in the understanding of the symmetries and dynamics of gauge theories. They can reveal hidden symmetries and provide a deeper understanding of the physical laws governing a system. They also have practical applications in fields such as quantum computing and high energy physics.
Small gauge transformations are local changes to the gauge field that do not significantly affect the overall structure of the system. Large gauge transformations, on the other hand, are global changes that have a significant impact on the system. They can lead to different physical interpretations and predictions compared to small gauge transformations.
No, large gauge transformations cannot be directly observed experimentally. This is because they do not cause any physical effects that can be measured. However, their effects on the symmetries and dynamics of a system can be observed indirectly through the behavior of particles and fields.
Gauge invariance refers to the fact that the physical laws governing a system should not depend on the choice of gauge. Large gauge transformations are related to this concept as they are global changes to the gauge field that do not affect the physical laws of the system. In other words, gauge invariance is a consequence of large gauge transformations.