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Modified Laplace transformation method is applied to N component $\phi^4$theory and the finite temperature problem in the massless limit is re-examinedin the large N limit. We perform perturbation expansion of the dressed thermalmass in the massive case to several orders and try the massless approximationwith the help of modified Laplace transformation. The contribution withfractional power of the coupling constant is recovered from the truncatedmassive series. The use of inverse Laplace transformation with respect to themass square is crucial in evaluating the coefficients of fractional powerterms.Comment: 16pages, Latex, typographical errors are correcte

MODIFIED LAPLACE TRANSFORMATION METHOD AT FINITE TEMPERATURE: APPLICATION TO INFRARED PROBLEMS OF N COMPONENT ϕ4 THEORY

MODIFIED LAPLACE TRANSFORMATION METHOD AT FINITE TEMPERATURE: APPLICATION TO INFRARED PROBLEMS OF N COMPONENT ϕ⁴ THEORY