On Energy Differences in Many Body Systems

Given two nearby lying states of a m a n y b o d y system, each one involving m a n y one-par t ic le contributions, it would be very inconvenient to express the difference of the energies of these states as a difference of absolute energy values. Small errors in the absolute values could drast ical ly change the d i f ference. In cases where the energies are inf in i te , their difference makes no sense at all. At this point Dyson [1] p roposed the " N e w T a m m D a n c o f f f o r m a l i s m " ( N T D ) . He m o d i f i e d an approximat ion p rocedure of T a m m [2] and D a n c o f f [3], the mathemat ica l content of it be ing an app rox i mative de te rmina t ion of the e igenvalues of a Schrödinger equat ion by the m e t h o d of R i t z -Ga le rk in [4], In the f r amework of sol id-state physics N T D has been discussed by Wahl and coworkers [5. 6. 7], In the spirit of Dyson we here take N T D as an idea to look for a convenient re fe rence state with respect to which energy d i f fe rences should be calculated. In high energy physics the po la r i zab le vacuum is such a reference s tate ( " D i r a c sea") . Referring to it avoids the inf in i te self -energy of this state. In solid-state physics, for e x a m p l e in the case of a semiconductor , the comple te ly fil led valence band can serve as a reference state ( " F e r m i sea") . Excitations with respect to the valence b a n d