What makes Lie Groups a crucial theory in modern dynamics and beyond?

AI Thread Summary
Lie Groups provide a rigorous foundation for modern dynamics and are essential in various fields such as physics, engineering, chemistry, and biology. The lecture notes by Vladimir G. Ivancevic and Tijana T. Ivancevic are tailored for a third-year or graduate-level course, requiring only knowledge of calculus and linear algebra. This theory is pivotal for understanding field and gauge theories, which are fundamental in contemporary scientific applications. The notes span 58 pages and include four figures to aid comprehension. Overall, Lie Groups are recognized as a crucial theoretical framework in modern dynamics and beyond.
marcus
Science Advisor
Homework Helper
Gold Member
Dearly Missed
Messages
24,753
Reaction score
794
http://arxiv.org/abs/1104.1106
Lecture Notes in Lie Groups
Vladimir G. Ivancevic, Tijana T. Ivancevic
(Submitted on 6 Apr 2011)
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. The only necessary background for comprehensive reading of these notes are calculus and linear algebra.
Comments: 58 pages, 4 figures
 
  • Like
Likes beniamino
Mathematics news on Phys.org
Thanks for posting this link.
 
:smile:Thanks !
 
These guys are pretty good. They've also got some nice notes on TQFT and De Rham–Hodge Theory that are well worth checking out.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Back
Top