The Finite Temperature Effective Potential for Local Composite Operators

The generating functionals for the local composite operators, $\Phi^2(x)$ and $\Phi^4(x)$, are used to study excitations in the scalar quantum field theory with $\lambda \Phi^4$ interaction. The effective action for the composite operators is obtained as a series in the Planck constant $\hbar$, and the two- and four-particle propagators are derived. The numerical results are studied in the space-time of one dimension, when the theory is equivalent to the quantum mechanics of ...

We present a self-consistent calculation of the finite temperature effective potential for $\lambda \phi^4$ theory, using the composite operator effective potential in which an infinite series of the leading diagrams is summed up. Our calculation establishes the proper form of the leading correction to the perturbative one-loop effective potential.

The effective action for the local composite operator $\Phi^2(x)$ in the scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops. The effective potential and 2-point Green's functions for elementary and composite fields are derived. The ground state energy as well as one- and two-particle excitations are calculated for space-time dimension $n=1$, when the theory is equivalent ...

We discuss the $\phi^4$ and $\phi^6$ theory defined in a flat $D$-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature $\beta^{-1}$. To obtain non-perturbative result, the $ 1/N $ expansion is used. The method of the composite operator (CJT) for summing a large set of Feynman graphs, is developed for the finite temperature system. The ressumed effective potential and the analysis of the D=3 and D=4 cases are given.

We present a self-consistent calculation of the finite temperature effective potential for $\lambda \Phi^4$ theory in four dimensions using a composite operator effective action. We find that in a spontaneously broken theory not only the so-called daisy and superdaisy graphs contribute to the next-to-leading order thermal mass, but also resummed non-local diagrams are of the same order, thus altering the effective potential at small effective mass.

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional reduction to the bosonic zero-frequency modes. The parameters of the effective theory can be calculated as perturbation series in the running coupling constant $g^2(T)$. The free energy is separated into the contributions from the momentum sca...

We construct a non-perturbative method to investigate the phase structure of the scalar theory at finite temperature. The derivative of the effective potential with respect to the mass square is expressed in terms of the full propagator. Under a certain approximation this expression reduces to the partial differential equation for the effective potential. We numerically solve the partial differential equation and obtain the effective potential non-perturbatively. It is found ...

We present a self--consistent solution of the finite temperature gap--equation for $\lambda \Phi^4$ theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not only the so--called daisy and superdaisy graphs contribute to the resummed mass, but also resummed non--local diagrams are of the same order, thus altering the effective mass for small values of the latter.

The effective potential for the local composite operator $\phi^{2}(x)$ in $\lambda \phi^{4}$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the $\phi^4 $-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate $\langle \phi ^{2} \rangle _{0}$ has lower effective action. Due to field renormalisation, $\langle \lambda \phi ^{2} \rangle _{0}$ is renormalisatio...

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functiona...