Finite-temperature effects on the Gaussian effective potential

We derive the finite-temperature Gaussian effective potential (FTGEP) from first principles, resolving some confusions arising in earlier treatments. The advantages of the FTGEP approach over the conventional loop expansion, even for high temperatures, are illustrated in a quantum-mechanical example. Results are presented for ${\phi }^6$ theory in two and three dimensions and for the ‘‘autonomous’’ version of λ${\phi }^4$ theory in four dimensions.