Addendum to paper: Strong-Coupling Behavior of ϕ4\phi^4-Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]

The graphical extrapolation procedure to infinite order of variational perturbation theory in a recent calculation of critical exponents of three-dimensional $\phi^4$-theories at infinite couplings is improved by another way of plotting the results.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re257a/preprint.htm

Two fermion relativistic bound states

We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system with a general interaction potential and deduce the explicit equations in a spherical basis. The case of the Coulomb interaction is studied in detail by numerical methods, solving the eigenvalue problem for J=0, J=1, J=2 and determining the spectral curves for a varying ratio of the mass of the interacting particles. Details of the computations, together with a perturbative approach in the mass ratio and an extended description of the ground states of the Para- and Orthopositronium are given in Appendix.Comment: 26 pages, 6 figure

Effective action for fermions with anomalous magnetic moment from Foldy-Wouthuysen transformation

In this paper we calculate the effective action for neutral particles with anomalous magnetic moment in an external magnetic and electric field. We show that we can take advantage from the Foldy Wouthuysen transformation for such systems, determined in our previous works: indeed, by this transformation we have explicitly evaluated the diagonalized Hamiltonian, allowing to present a closed form for the corresponding effective action and for the partition function at finite temperature from which the thermodynamical potentials can be calculated

Optimized perturbation method for the propagation in the anharmonic oscillator potential

The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential $\lambda x^4$ is discussed for real and imaginary time. The first order results in the imaginary time formalism provide approximations to the free energy and particle density which agree well with the exact results in the whole range of temperatures.Comment: 13 pages, plain LATEX, 3 compressed and uuencoded Postscript figures, submitted to Phys.Lett.

Effective Hamiltonian with holomorphic variables

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian - depending on quantum coupling and temperature - and classical-like expressions for the averages of observables. In this work the PQSCHA is derived in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the path integral for the Weyl symbol of the density matrix, makes it possible to approach directly general Hamiltonians given in terms of bosonic creation and annihilation operators.Comment: 11 pages, no figures (2nd version: few mistakes fixed in Sects. IV-V

Effective Hamiltonian with holomorphic variables

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian. In this work the PQSCHA is reformulated in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the olomorphic path integral for the Weyl symbol of the density matrix, makes it possible to directly approach general Hamiltonians given in terms of bosonic creation and annihilation operators.Comment: Proceedings of the Conference "Path Integrals from peV to TeV - 50 Years from Feynman's paper" (Florence, August 1998) -- 2 pages, ReVTe

Optimized Perturbation Methods for the Free Energy of the Anharmonic Oscillator

Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical effective potential. The results of both methods show a quick convergence and agree well with the exact free energy in the whole range of temperatures. Postscript figures are available under request to AO email [email protected]: 8 pages, preprin

Test of variational approximation for phi4phi^4 quantum chain by Monte Carlo simulation

We report results of a Monte Carlo simulation of the $\phi^4$ quantum chain. In order to enhance the efficiency of the simulation we combine multigrid simulation techniques with a refined discretization scheme. The resulting accuracy of our data allows for a significant test of an analytical approximation based on a variational ansatz. While the variational approximation is well reproduced for a large range of parameters we find significant deviations for low temperatures and large couplings.Comment: 12 pp. Latex + 3 figures as uuencoded compressed tar file, accepted for publication in Phys. Lett.

PT-symmetric operators and metastable states of the 1D relativistic oscillators

We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed PT-symmetric operators defining infinite positive energy levels converging to the Schroedinger ones as c tends to infinity. Such energy levels and their eigenfunctions give directly a definite choice of metastable states of the problem. Precise numerical computations shows that these levels coincide with the positions of the resonances up to the order of the width. Similar results are found for the Klein-Gordon oscillators, and in this case there is an infinite number of dynamics and the eigenvalues and eigenvectors of the PT-symmetric operators give metastable states for each dynamics.Comment: 13 pages, 2 figure