ISSN:
1572-9575
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider a model field theory consisting of two Nambu-Jona-Lasinio spin 1/2 fields interacting via a coupling $$f(\bar \psi _1 \gamma ^\mu \gamma ^5 \psi _1 )(\bar \psi _2 \gamma _\mu \gamma ^5 \psi _2 )$$ and which is therefore invariant under the two symmetries $$\psi _1 (x) \to e^{i\alpha _1 } \gamma ^5 \psi _1 (x)$$ and $$\psi _2 (x) \to e^{i\alpha _2 } \gamma ^5 \psi _2 (x)$$ . We look for solutions in which these symmetries are spontaneously broken by giving the fermions non-zero masses. Each of the two pairs of axial-vector vertex functions in the theory satisfy two coupled integral equations, which are solved in the ‘chain approximation’. We find that all four vertex functions have the same singularity structure, in particular a pole atq 2=0 corresponding to a massless pseudoscalar Nambu-Goldstone boson, and another pole corresponding to an axial-vector boson whose mass is cut-off dependent, but which for a certain range of values off 2 is a stable particle. By considering the coupling of the strings of nucleon-antinucleon psuedoscalar ‘bubbles’ which generate the massless Nambu-Goldstone bosons associated with fermions 1 and 2, we show explicitly that there is only one massless Nambu-Goldstone boson in the theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01808028
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