Sunday, June 9, 2019

quantum field theory - Why does the Walecka model not include pions?



The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?



Answer



I want to cite the original paper of Walecka where he awnsers your question:


From Annals of Physics 83/2 (1974) p. 491 "A theory of highly condensed matter


"The reader might object to the fact that there is no one-pion exchange tail in this interaction; however, the strong spin and isospin dependence of the potential arising from the exchange of an isovector, pseudoscalar pion implies that the contribution of the one-pion exchange potential to the bulk proerties of nuclear matter largely averages to zero"


Hope this helps


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