The quantum cosmology with the scalar-spinor interaction of σ model is analyzed by means of Hartle and Hawking’s method. The Wheeler-DeWitt equation is obtained and the corresponding wave function of the universe solved. The obtained asymptotic solution of the wave function indicates that in the σ model the contribution of the spinor part is notable when the scalar factor α is very small, and the expression of the solution is related to the initial conditions. When the scalar factor α is great, the contribution of the spinor part is not significant and has the same conduct as the scalar part.
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