Fermions and the Autonomous λϕ ⁴ Theory

Abstract

By means of Gaussian effective potential method, we investigate two models with and coupling in 3+1 dimensions respectively. While the fermion effect through Yukawa coupling makes the autonomous λϕ4 theory more stable, it is shown that there are three different autonomous phases for model. The temperature dependences of these two models are similar to those in pure λϕ4 autonomous theory.

Structure Phase Transitions of the ( D + 1)-Dimensional Double sine-Gordon Field Theory

“…V, we study the similarity between the structure phase transitions of the DsG model and the symmetry restored phase transition of \<j> 4 model by the mapping relation of some special solutions of these two modelsJ 14 W with 0 -\jT and H is the Hamiltonian of the system. In this paper, we calculate the Gibbs average (5) by a very convenient method -the thermal coherent state methodi 13,15 ! It is known that the coherent state of a neutral scalar field is expressed as' 15 !…”

“…In this paper, we calculate the Gibbs average (5) by a very convenient method -the thermal coherent state methodi 13,15 ! It is known that the coherent state of a neutral scalar field is expressed as' 15 !…”

“…with E k = {i 2 + k 2 being the energy of the quasiparticle at temperature T(= 1//?). Where the mass parameter n may be taken as a variational parameter,f 15,16 ^ but however, in order to make calculation analytical, we take fi as the mass of the independent quasiparticle, i.e., of the free phonon just as some other authors did.' 13,17 ^ Now we can calculate the ensemble average of the observable O by (d)p = p(f\d\f) p (9) in place of Eq.…”

“…Using the definition of \0)p (Eq. ( 8)) and the usual commutation relations of the annihilation and creation operators, one can get' 15 '…”

The Finite Temperature Effects on the Coleman Phase Transition in Double Sine-Gordon Model

“…The Gaussian effective potential (GEP) method in quantum field theory serves as a nonperturbative tool for estimating the effective potential' 1 '. There are various equivalent methods to obtain the GEP, for instance, Gaussian wave functional ansatz' 2 ' 3 ', optimized expansion' 4 ' 6 ', coherent state effective potential method' 6 ', cacta (or superdaisy) approximation' 7 ' and so on. Similarly, the FTGEP can also be obtained by various methods, for instance, imaginary time Green function method, thermal coherent state effective potential method etc' 6 '.…”