By G. Barton

This article takes the coed with a heritage in undergraduate physics and arithmetic in the direction of the talents and insights wanted for graduate paintings in theoretical physics. the writer makes use of Green's features to discover the physics of potentials, diffusion, and waves. those are vital phenomena of their personal correct, yet this learn of the partial differential equations describing them additionally prepares the scholar for extra complicated functions in many-body physics and box thought. Calculations are carried via in sufficient element for self-study, and case histories illustrate the interaction among actual perception and mathematical formalism. the purpose is to strengthen the behavior of debate with the equations and the craftsmanship this fosters in tackling the matter. The booklet is predicated at the author's large instructing event.

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Additional resources for Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves (Oxford science publications)

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It is concluded that the use of relativistic particle-holeand delta-holeexcitations for the pion selfenergy increases the critical density compared with the non-relativistic result, however still leads to condensation for densities from 2 t o 4 times normal nuclear matter density. *This work is supported by national science foundation of china. 34 1. Introduction Strong attractive force of pion is believed to bring about pion condensation at a high density. It is one of important problems to clarify the critical density of the pion condensation since it may affect high density systems such as heavy-ion collisions and the interior of neutron stars.

It is t o be noted that pion condensation by no means implies a naive Bose-Einstein condensation of pions, but the softening of the longitudinal spin-isospin mode with the critical momentum k,. On the other hand, such mode is unstable and the Lindhard function has an imaginary part before the critical density pc. We can see a peculiar enhancement of the strength function a t small energy near the critical density. The pion condensed phase can be represented in terms of chiral transformation as follows: Inc)= U(Bv(kc.

Lett. B489, 280 (2000). II. j p TOSHITAKA TATSUMI Department of Physics, Kyoto University, Kyoto, Japan LIANG-GANG LIU Department of Physics, Zhongshan University, Guangzhou, China HIROYUKI MATSUURA GRIPS, Tokyo 162-0056, Japan TAISUKE NAGASAWA Department of Physics, Kyushu University KEN-ICHI MAKIN0,NOBUO NODA,HIROAKI KOUNO AND AKIRA HASEGAWA Department of Physics, Saga University, Saga 840-8502, Japan The critical density of neutral pion condensation is investigated based on the relativistic framework and compared with nonrelativistic results.

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