An introduction to thermal physics schroeder pdf free download

We have given accurate results for the high and low-density electron gas in Chap. In the Hartree approximationДЄlthough the Dyson equation is in principle exact, one still has to evaluate sigma, and this is in general not possible except in some approximation. Since all diagrams are either proper diagrams or their repetition. Then one can sum over all repetitions of sigma (в€‘ k, П‰) to getДysonвЂ™s equation yields an exact expression for the propagator, It is common to defineДЄs the sum over all proper self-energy parts. An irreducible or proper self-energy part is a part that cannot be further reduced into unconnected self-energy parts. The bubbles of the Hartree method are an example. The self-energy part of a diagram is a diagram that has no incoming or outgoing parts and can be inserted into a particle line. To state DysonвЂ™s equation we need a couple of definitions. DysonвЂ™s equation can be regarded as a generalization of the partial sum technique used in the Hartree and HartreeвЂ“Fock approximations. This is the starting point for many approximations both diagrammatic, and algebraic. The random-phase approximation can also be obtained by a partial summation of diagrams, and it is equivalent to the Lindhard theory of screening.ДЎ1 Reproduced with permission from Mattuck RD, A Guide to Feynman Diagrams in the Many-Body Problem, 2nd edn, (4.76) p. Which is just what we got for the HartreeвЂ“Fock approximation (see (3.50)).

О•k вЂІ = Оµk + в€‘ l (occ.) ( Vklkl в€’ Vlkkl ) , О© в€’ Оµk в€’ в€‘ l (occ.) ( Vklkl в€’ Vlkkl ) + i ОґДЇrom this we identify the elementary energy excitations as Doing the partial sum of forward scattering and exchange scattering one has (Mattuck 11):ДЄssociating propagators with the terms in the diagram gives Where a particle not only strikes a particle in l and creates an instantaneous hole, but is exchanged with it.

It is actually very simple to go from here to the HartreeвЂ“Fock approximation вЂ“ all we have to do is to include the exchange terms in the interactions. Which is exactly the same as the Hartree approximation (see (3.21)) since

An introduction to thermal physics schroeder pdf free download