φ4theory in 1+d dimensions at high temperature: Dimensional reduction

The ${\phi }^4$ theory in 1+d dimensions is analyzed at high temperatures in the imaginary-time formalism. General results are given for the leading high-temperature contributions to all renormalized Green’s functions. The latter are generated by a high-temperature partition function which describes another ${\phi }^4$ theory in d spatial dimensions with special mass renormalizations. The triviality/ nontriviality of the (${\phi }^4$ ${)}_{1+3}$ theory is discussed briefly.