View Single Post
theturbanator
#1
Feb3-12, 09:57 PM
P: 7
Hi everyone,

I was just wondering if anyone had any suggestions of more-mathematically-rigorous textbooks on Lie groups and Lie algebras for (high-energy) physicists than, say, Howard Georgi's book.

I have been eying books such as "Symmetries, Lie Algebras And Representations: A Graduate Course For Physicists" by J. Fuchs and C. Schweigert and "Lie Groups, Lie Algebras, and Some of Their Applications'' by R. Gilmore; however, the problem that arises with those, and with pure mathematical books on the subject, is that their (exponential map) convention is different from that used in physics: in physics, the Lie algebra of a matrix Lie group, G, is defined to be the set of all matrices X such that exp[itX] is in G for all real numbers t, whereas in math, the Lie algebra of G is defined by exp[tX], without the i. This leads to different conventions/results throughout the entire subject (for instance, the Lie algebra of the unitary group is the space of all hermitian matrices in physics, but the space of all ANTI-hermitian matrices in math -- it is obvious why the former convention is chosen in physics).

Even though the two textbooks that I listed above are meant for physicists, they have adopted the mathematical convention (I guess that is in line with their intent to be more mathematically rigorous), so I would like to look elsewhere, if possible.

So, just to summarize (since this post has become rather long -- sorry about that!): I am looking for a mathematically-rigorous textbook on Lie groups and Lie algebras that uses physicists' conventions.

I greatly appreciate your help!
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces