Representation theory on RHS

[dextercioby]

Has it been done...? If so, any textbook on it...?

The concept of Rigged Hilbert Spaces is essential to Quantum Mechanics. Symmetries are implemented in physics by doing representation theory of some symmetry groups, almost all of them being Lie groups: Galilei group, Poincaré group, Conformal group, SO(3), SU(n),... We actually know that what really is represented is the universal covering group for each group.

So, since the natural setting for QM is a RHS, the continuous symmetries for a quantum theory need to be represented on this RHS...

Daniel.

 

[dextercioby]

Well, you know what they say: sometimes silence is an answer.

I can only conclude that representation theory on RHS has not been done yet.

Daniel.

 

[tacman]

Yes, representation theory on RHS has been studied extensively in the context of quantum mechanics. In fact, it is a fundamental concept in the field. There are many textbooks available on this topic, some of which include "Representation Theory and Quantum Mechanics" by James C. Ryan, "Introduction to the Representation Theory of Algebras" by Joseph A. Cohn, and "Lie Groups, Lie Algebras, and Representations" by Brian C. Hall. These texts cover various aspects of representation theory on RHS, including its applications in quantum mechanics and the representation of different symmetry groups. Additionally, there are also numerous research articles and papers that delve deeper into this topic. Overall, representation theory on RHS is a well-studied and important subject in the field of quantum mechanics.