Subject: RPA and second quantization

From: sergiusz kwasniewski <[email-masked]>
Date: Tue, 24 Aug 1999 13:19:09 +0200 (MET DST)

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.

I would appreciate all helpful hints.

Thanks in advance,

S. Kwasniewski

		     _________________________________________________

			Sergiusz Kwasniewski
			LUC SBG/TS
			Universitaire Campus Gebouw D
			3590 Diepenbeek
			BELGIUM
			tel(direct): 011/268315
			fax	   : 011/268301
			email      : [email-masked]
		     _________________________________________________

---

From: "Susan R. Atlas" <[email-masked]>
Date: Tue, 24 Aug 1999 08:33:15 -0600

Dear Sergiusz:
Try D. Pines and P. Nozieres beautiful book, The Theory of Quantum Liquids
(W. A. Benjamin, Menlo Park, CA, 1966). Also Bohm's book on quantum mechanics
has a nice treatment of second quantization (don't recall the exact title, but
I can get it for you if you can't find it).
  - Susan

--

 _/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
 _/                                                                      _/
 _/   Susan R. Atlas                                                     _/
 _/   Department of Physics and Astronomy                                _/
 _/   The University of New Mexico                                       _/
 _/   800 Yale NE                    email:  [email-masked] _/
 _/   Albuquerque, NM 87131          Phone:  (505) 277-1509              _/
 _/                                                                      _/
 _/   http://www.phys.unm.edu/CompMaterials                              _/
 _/                                                                      _/
 _/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/

---

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

> but I don't seem to find the connection between the theory and the name it

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