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.Comment: 9 pages, 3 EPS figures. With a few typo errors corrected. to appear in J. Phys.

Gaussian Effective Potential and the Coleman's normal-ordering Prescription : the Functional Integral Formalism

For a class of system, 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 functional integral formalism. We show that the Coleman's normal-ordering prescription can be formally generalized to the functional integral formalism.Comment: 6 pages, revtex; With derivation details and an example added. To appear in J. Phys.

Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.Comment: 4 pages, 3 figure

Testing the Gaussian expansion method in exactly solvable matrix models

The Gaussian expansion has been developed since early 80s as a powerful analytical method, which enables nonperturbative studies of various systems using `perturbative' calculations. Recently the method has been used to suggest that 4d space-time is generated dynamically in a matrix model formulation of superstring theory. Here we clarify the nature of the method by applying it to exactly solvable one-matrix models with various kinds of potential including the ones unbounded from below and of the double-well type. We also formulate a prescription to include a linear term in the Gaussian action in a way consistent with the loop expansion, and test it in some concrete examples. We discuss a case where we obtain two distinct plateaus in the parameter space of the Gaussian action, corresponding to different large-N solutions. This clarifies the situation encountered in the dynamical determination of the space-time dimensionality in the previous works.Comment: 30 pages, 15 figures, LaTeX; added references for section

Gaussian Wavefunctional Approach in Thermofield Dynamics

The Gaussian wavefunctional approach is developed in thermofield dynamics. We manufacture thermal vacuum wavefunctional, its creation as well as annihilation operators,and accordingly thermo-particle excited states. For a (D+1)-dimensional scalar field system with an arbitrary potential whose Fourier representation exists in a sense of tempered distributions, we calculate the finite temperature Gaussian effective potential (FTGEP), one- and two-thermo-particle-state energies. The zero-temperature limit of each of them is just the corresponding result in quantum field theory, and the FTGEP can lead to the same one of each of some concrete models as calculated by the imaginary time Green function.Comment: the revised version of hep-th/9807025, with one equation being added, a few sentences rewritten, and some spelling mistakes corrected. 7 page, Revtex, no figur

Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent omega governing the approach to the strong-coupling, or scaling limit. Otherwise the procedure either does not converge at all or to the wrong limit. This invalidates all papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/34

Precision calculation of magnetization and specific heat of vortex liquids and solids in type II superconductors

A new systematic calculation of magnetization and specific heat contributions of vortex liquids and solids (not very close to the melting line) is presented. We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. The expansion is convergent in contrast to the conventional high temperature expansion which is asymptotic. In the solid phase we calculate first two orders which are already quite accurate. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.Comment: 4 pages, 3 figure

Chiral Symmetry Breaking in QCD: A Variational Approach

We develop a "variational mass" expansion approach, recently introduced in the Gross--Neveu model, to evaluate some of the order parameters of chiral symmetry breakdown in QCD. The method relies on a reorganization of the usual perturbation theory with the addition of an "arbitrary quark mass $m$, whose non-perturbative behaviour is inferred partly from renormalization group properties, and from analytic continuation in $m$ properties. The resulting ansatz can be optimized, and in the chiral limit $m \to 0$ we estimate the dynamical contribution to the "constituent" masses of the light quarks $M_{u,d,s}$; the pion decay constant $F_\pi$ and the quark condensate $< \bar q q >$.Comment: 10 pages, no figures, LaTe

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure

Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a Phi**4 model in 1+1 dimensions with a symmetric and a double well potential. We use the 2PPI formalism and go beyond the Hartree approximation by including the sunset term. In addition to the mean field phi= the 2PPI formalism uses as variational parameter a time dependent mass M**2(t) which contains all local insertions into the Green function. We compare our results to those obtained in the Hartree approximation. In the symmetric Phi**4 theory we observe that the mean field shows a stronger dissipation than the one found in the Hartree approximation. The dissipation is roughly exponential in an intermediate time region. In the theory with spontaneous symmetry breaking, i.e., with a double well potential, the field amplitude tends to zero, i.e., to the symmetric configuration. This is expected on general grounds: in 1+1 dimensional quantum field theory there is no spontaneous symmetry breaking for T >0, and so there should be none at finite energy density (microcanonical ensemble), either. Within the time range of our simulations the momentum spectra do not thermalize and display parametric resonance bands.Comment: 14 pages, 18 encapsulated postscript figures; v2 minor changes, new appendix, accepted for publication in Phys.Rev.