21 research outputs found
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 , whose
non-perturbative behaviour is inferred partly from renormalization group
properties, and from analytic continuation in properties. The resulting
ansatz can be optimized, and in the chiral limit we estimate the
dynamical contribution to the "constituent" masses of the light quarks
; the pion decay constant and the quark condensate .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.