Re: CCL:RPA and second quantization

[Tom Sundius <sundius -x- at -x- pcu.helsinki.fi>]

On Tue, 24 Aug 1999, sergiusz kwasniewski wrote:
 > Hi CCL'ers,
 >
 > I'm currently studying polarization propagator techniques like RPA and
 MBGF.
 > Does anyone know to what the following names are related to:
 > Random Phase and Second Quantization. I know more or less what it is about,
 > but I don't seem to find the connection between the theory and the name it
 > is given to.
 >
 These concepts have originated in physics. Second quantization deals with
 the algebra of creation and annihilation operators and connects quantum
 field theory with many-body theories. A simple introduction to second
 quantization is given in Szabo and Ostlund: Modern Quantum Chemistry
 (Dover 1996). More can be found out from books on quantum mechanics
 (for instance, Baym's Lectures on quantum mechanics).
 The random phase approximation (RPA) is, what I can see, not treated in
 Szabo's and Ostlund's book, although it gives a good introduction to
 Green's functions. RPA is an approximation to the two-body Green's function,
 and was first used by in a paper by Bohm and Pines (Phys. Rev. 92, 609 (1953))
 to describe plasma oscillations by assuming random phases. RPA is decribed
 in books on many-body theories, for instance G.E. Brown: Many-body problems,
 North-Holland, 1972 (probably there are some books on quantum chemistry that
 have it, too).
           Greetings,
            TS
 Tom Sundius
 University of Helsinki, Department of Physics    phone +358-9-191 8339
 P.O.Box 9, FIN-00014 Helsinki, Finland           fax   +358-9-191 8680