Wen-Fa Lu

Gaussian effective potential and Coleman's normal-ordering prescription: the functional integral formalism

For a class of systems, the potential of whose bosonic Hamiltonian has a Fourier representation in the sense of tempered distributions, we calculate the Gaussian effective potential within the framework of the functional integral formalism. We show that Colemans normal-ordering prescription can be formally generalized to the functional integral formalism.

The Scattering phase shifts in the sine-Gordon and sinh-Gordon field theories

Abstract Scattering two-particle states of the sine-Gordon and sinh-Gordon models in D + 1 dimensions are investigated for all values of the coupling constant with the Gaussian wave-functional approach. In 1 + 1 and 2 + 1 dimensions, the phase shifts of the scattering states are obtained. We find that the phase shifts are positive for the sine-Gordon field theory and negative for the sinh-Gordon field theory. In the higher dimensions, the phase shifts vanish, which is coincident with the triviality of the two field theories.

(1+1)-dimensional massive sine-Gordon field theory and the Gaussian wave-functional approach

The ground, one- and two-particle states of (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of model parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that a two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. In addition, for the bosonic equivalent to the massive Schwinger model, the masses of the one-boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.

A variational expansion for the free energy of a bosonic system

In this paper, a variational perturbation scheme for nonrelativistic many-fermion systems is generalized to a bosonic system. By calculating the free energy of an anharmonic oscillator model, we investigated this variational expansion scheme for its efficiency. Using the modified Feynman rules for the diagrams, we obtained the analytical expression of the free energy up to the fourth order. Our numerical results at various orders are compared with the exact and other relevant results.

Thermalized displaced and squeezed number states in the coordinate representation

Within the framework of thermofield dynamics, the wavefunctions of the thermalized displaced number and squeezed number states are given in the coordinate representation. Furthermore, the time evolution of these wavefunctions is considered by introducing a thermal coordinate representation, and we also calculate the corresponding probability densities, average values and variances of the position coordinate, some special cases of which are consistent with results in the literature.Within the framework of thermofield dynamics, the wavefunctions of the thermalized displaced number and squeezed number states are given in the coordinate representation. Furthermore, the time evolution of these wavefunctions is considered by introducing a thermal coordinate representation, and we also calculate the corresponding probability densities, average values and variances of position coordinate, which are consistent with results in the literature.

Optimized Rayleigh–Schrödinger expansion of the effective potential

Abstract An optimized Rayleigh–Schrodinger expansion scheme of solving the functional Schrodinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory whose potential function has a Fourier representation in a sense of tempered distributions, we obtain the effective potential up to the second order, and show that the first-order result is just the Gaussian effective potential. Its application to the λφ 4 field theory yields the same post-Gaussian effective potential as obtained in the functional integral formalism.

Sine-Gordon expectation values of exponential fields with variational perturbation theory

Abstract In this Letter, expectation values of exponential fields in the 2-dimensional Euclidean sine-Gordon field theory are calculated with variational perturbation approach up to the second order. Our numerical analysis indicates that for not large values of the exponential-field parameter a , our results agree very well with the exact formula conjectured by Lukyanov and Zamolodchikov [Nucl. Phys. B 493 (1997) 571].

Sine-Gordon effective potential beyond Gaussian approximation

Abstract Combining an optimized expansion scheme in the spirit of the background field method with the Colemans normal-ordering renormalization prescription, we calculate the effective potential of sine-Gordon field theory beyond the Gaussian approximation. The first-order result is just the sine-Gordon Gaussian effective potential (GEP). For the range of the coupling β2⩽3.4π (an approximate value), a calculation with Mathematica indicates that the approximated effective potential up to the second order is finite without any further renormalization procedure and tends to improve the GEP more substantially while β2 increases from zero to β2⩽3.4π.

The multistate Rayleigh–Ritz variational method with the principle of minimal sensitivity for anharmonic oscillators

A theoretical scheme to employ the principle of minimal sensitivity for choosing the optimal values of nonlinear parameters is proposed for the multistate Rayleigh–Ritz variational method. Anharmonic oscillators are particularly considered in this paper. Applications of the present scheme to the one-dimensional Morse and two double-well potentials indicate that it provides much more accurate and faster convergent approximations to the exact energy eigenvalues than several schemes existing in the literatures.

Thermalized displaced squeezed thermal states

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have different correlations with the squeezing and coherence components. Moreover, different from the properties of the position, the average value and variance of the particle number operator as well as the second-order correlation function are time independent.