Subject: Re: CCL:RPA and second quantization

From: Tom Sundius <[email-masked]>
Date: Tue, 24 Aug 1999 18:58:38 +0300 (EET DST)

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