Recent content by rutwig

Oh, no. All equilibrium problems are indeed differential equations, even if normally chemistry books don't say it explicitely. Indeed almost any process (physical or chemical) involving changes is rules by equations of this type. Look for example at thermodynamical problems.

The result is not entirely obvious, but compactness ensures some properties (like existence of invariant integration) that are not given otherwise. For this case, the key is that for compact (connected) groups any element is conjugate to an element in a maximal torus (analytic subgroups...

If you have worked only with compact groups, then you will not have observed this; any element is the exponentiation of some element in the Lie algebra. But for noncompact groups this is no longer true, and we have to consider a finite number of elements in the Lie algebra to recover the...

Finally, you can also use operators to construct Lie algebras. If you take hermitian conjugate operators B, B* (in an infinite dimensional space) with the rule [B,B*]=BB*-B*B you obtain the Heisenberg Lie algebra, which is the basis of all classical analysis of harmonic oscillators and gave rise...

Just a comment, you can drop the word nonabelian since any vector space is an abelian Lie algebra simply taking the zero bracket. Indeed abelian algebras play a fundamental role in the theory (see for example the Cartan subalgebras). You have also the require bi-linearity, otherwise the result...

For the so called abstract Lie algebras only the bracket [,] by itself has a meaning, but it can be proven that for any (finite dimensional) Lie algebra L we can find a vector space V such that the elements of L are linear transormations of V, so that the formulae above holds (that is, we can...

You wan a complete synthetic definition of Lie algebra? Here it is: A Lie algebra L is a pair (V,t) formed by an F-module (F being a commutative ring) and an alternated tensor t of mixed type (2,1) satisfying the Jacobi identity. A special case is F a field.

When I have a close look to the reference given I will probably give a more concise answer, but the main reason to work usually on the complex is because of the representation theory of su(2). Since it is the compact form of usual sl(2,C), all complex representations are recovered from it. Now...

Quite interesting overview. Although the facts about so(3) and su(2) are quite standard, I don't know whether other members will find it as evident as it is (basing on past experience). We will see if anyone gives some answer.

Interesting ramifications should be searched for experimentally, but it is not at all insignificant that the adequate group is not the simply connected universal cover, but some projection of it. With respect to the covering, this would indicate that the system makes no distinction of the...

The book by Cvitanovic is one of the links. There are many others, but it should be specified whether one is interested on discrete, continuous (non differentiable) or Lie groups, or even generalizations like Kac-Moody groups, supergroups, etc. Each of the topics is a world in itself.

You can find the announcement of the first measure in here: http://www.aip.org/enews/physnews/1996/split/pnu300-3.htm

Any elementary book on Lie groups will give you precise definitions and properties of the ennounced groups, with the possible exception of E(8), which corresponds to the exceptional Lie group of rank 8, of great importance in HEP, specially string theory. For an eementary treatment (that is...

Well, to the source given by selfadjoint, I enumerate the following; P. Freund, Introduction to supersymmetry, Cambridge Univ. Press if your interest on Clifford algebras concerns only its relation with supersymmetry (Hey, Tom, this is a magnific book, add it to your list) W. Greub...

The eigenvectors of the operators in QM allow you to obtain the quantum numbers of the system. If you consider for example the group SU(2), the eigenvalues of its Casimir operator on the irreducible representations allows you to obtain the quantum number. This elementary example led to the...