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Extra info for Group representations in mathematics and physics;: Battelle Seattle, 1969, Rencontres
41] Mostow, G. D. "Cohomology of Topological Groups and Solvmanifolds", Ann. , 73, 20-48 (1961). 35  O'Raifeartaigh, L. "Mass Differences and Lie Algebras of Finite Order", Phys. Rev. , 14, 575-577 (1965).  Parasyuk, O. "Horocycle Flows on Surfaces of Negative Curvature", Uspehi Mat. Nauk, 8, 125-26 (1953).  Segal, I. "An Extension of a Theorem of L. O'Raifeartaigh", J. Functional Analysis, ~, 1-21 (1967). Cohomologie Galoisienne,  Serre, J. P. Berlin, Springer (1964).  Shale, D.
T If you have not read these books it is not too late to do it, but today let us just give a mlni-description of quantum mechanics. a) To each physical system corresponds a separable complex Hilbert space ~C. ) is represented by a self adjolnt operator of c) A x> 6 ~C. is the set of possible values of A on ~C. The spectrum a. I) X where P is the Hermitian projector (Px = Px *) onto the one dimensional space X spanned by x>. Note that unit eigen vectors of Px (with eigen-value i) differ only by a scalar phase factor and describe the same state since they yield the same physical predictions.
For The Mathematician Readers Physics will be injected venient Theory H. Weyl, The in these notes as needed. to gather here some information on physical However, it seems con- constants which might be useful at any time. We will study quantum phenomena. 03 × 1023 It is the number of atoms in a mass of one gram of hydrogen. i) (mass mp) and one electron ms). 03 × 1023 unit systems, for us, will use h = (elanck constant) c = (velocity In this system and a nucleus which A = Z + N topes number. 04) -1/2 , indeed the atomic mass number, For uranium x (27)-1= of light) 2 e hc is a dimensionless Coulombs a Z Z electrons is the atomic number, Z = i; hydrogen has 3 iso(unstable, A = 238.