## A non-perturbative solution of the zero-dimensional [wave length][phi]4 field theory |

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analytically continued partition analytically extend Área de Publicações asymptotic Bender Bessel function Borel summation technique Borel summed expression Borel transform branch cut Brasileiro de Pesquisas Centro Brasileiro coefficients complex coupling constant constant complex plane coupling constant complex coupling constant plane dimensional divergent domain of validity domain Re(g essential singularity exact expression expression in terms Hamiltonian hypergeometric function imaginary instantons interaction Khuri large order Macdonald's function negative coupling negative real axis non-perturbative NOTAS DE FÍSICA order moments partition func partition function given partition function obtained partition function Z{m2 perturbative expansion perturbative methods perturbative series Pesquisas Físicas Área Publicações Rua Dr quantum field theories quartic probability distribution real A-axis real negative axis renormalons representation restricted to positive resummation Rio de Janeiro second kind series in Eq.(7 summability take m2 valid for Re(X whole complex A-plane whole complex plane whole coupling constant X^p4 model Xavier Sigaud zero zero-dimensional field theory zero-dimensional model Zinn-Justin