H. Kleinert

Path integrals in quantum mechanics, statistics, and polymer physics

Elementary properties and simple solutions external sources, correlation function and perturbation theory semiclassical time displacement amplitude Feynman-Kleinert variational approach and systematic improvements path integrals with topological constraints many orbitals statistics and second quantization angular decomposition of path integrals wave functions short-time amplitude in spaces with curvature and torsion Schroedinger equation in general metric-affine spaces beyond Feynmans path integral formula for singular potentials path integral of Coulomb system further path integrals solvable by generalized Duru-Kleinert method path integrals in polymer physics polymers and particle orbits in multiply connected spaces Chern-Simons theory of entanglement, fractional quantum hall effect path integrals and tunneling path integrals and non-equilibrium quantum statistics.

The Membrane Properties of Condensing Strings

Abstract It is pointed out that near a phase transition the string action requires an extra term to control the fluctuations and it is shown that the associated coupling constant, which is dimensionless, is asymptotically free in the ultraviolet. Attention is drawn to previous studies of the same term in biophysical membranes and microemulsions.

Solution of the path integral for the H-atom

Abstract The Greens function of the H-atom is calculated by a simple reduction of Feynmans path integral to gaussian form.

Five-loop renormalization group functions of O(n)-symmetric φ4-theory and ϵ-expansions of critical exponents up to ϵ5

Abstract Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the β -function and the anomalous dimensions of the O( n )-symmetric φ 4 -theory in D =4- ϵ dimensions we present the results of a full analytic reevaluation of all diagrams. The divergences are removed by minimal subtraction and ϵ -expansions are given for the critical exponents η,ν and ω up to order ϵ 5 .

Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory

As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.

Thermal softening of curvature elasticity in membranes

Abstract Recently, there have been three determinations of the reduction of curvature elasticity due to thermal fluctuations. The results obtained by Helfrich, Peliti and Leibler, and Forster are κR=κ-(T/4π)I log(qmax/qmin), with I=1, 3, and 2 respectively. We discuss the differences between the calculations and show that, despite a careless handling of the path integration measure, Peliti and Leiblers result is correct. Forsters paper, on the other hand, has the correct measure but the wrong algebra. As a further result, the gaussian curvature constant is shown to change with temperature as [ovbar|κ]R=[ovbar|κ]+(T/4π) × 4log(qmax/qmin).

NONPERTURBATIVE XY-MODEL APPROACH TO STRONG COUPLING SUPERCONDUCTIVITY IN TWO AND THREE DIMENSIONS

For an electron gas with d-function attraction, we investigate the crossover from weak- to strong-coupling superconductivity in two and three dimensions. From mean-field theory we extract the stiffness of phase fluctuations and set up effective XY models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperatureTc as a monoto- nous function of the coupling strength both in two and three dimensions, and give analytic formulas for the merging of temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit. @S0163-1829~99!07605-5# theory to describe it. In three dimensions, crossover from BCS superconductivity to the Bose-Einstein condensation of tightly bound fermion pairs was first investigated in Ref. 2 by summing particle-particle ladder diagrams which corre- spond to Gaussian fluctuations around the mean field. In the functional integral formalism this was studied in Ref. 5. In both papers, fluctuation corrections were retained in the number equation, which was solved together with the mean- field gap equation. In this approximation, starting from a fermionic system, the gas of electron pairs was mapped in the strong-coupling limit to an ideal Bose gas, and the criti- cal temperature asymptotically becomes the temperature of the Bose-Einstein condensation of an ideal Bose gas of par- ticles with mass 2m and density n/2, where m and n are the fermion mass and density. The critical temperature T c has an artificial maximum at an intermediate coupling strength, thus approaching a limiting value in the strong-coupling limit from above. This artifact was removed in the generalized self-consistent Green-function numerical approach in Ref. 9. In this paper we shall study the properties of collective modes with help of the lowest gradient terms governing the Gaussian fluctuations around the mean-field solution. These fluctuations are most violent in the phase of the order param- eter. Phase transitions in a system with these fluctuations are well understood in two and three dimensions from extensive studies of the XY model. By setting up an equivalent XY model we are therefore able to describe very well the onset and disappearance of superconductivity in the entire cross- over regime. In this way, we shall obtain simple formulas for the critical temperature T c , which turns out to be a monoto- nously increasing function of the coupling strength and car- rier density in both two and three dimensions. In the weak- coupling limit, we give simple explicit formulas which show how the temperature of the XY-model transition converges to the transition temperature in the BCS theory.

Five-loop renormalization group functions of O(n)-symmetric φ4-theory and ϵ5: (Phys. Lett. B 272 (1991) 39)

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the

Disorder version of the Abelian Higgs model and the order of the superconductive phase transition

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Systematic corrections to the variational calculation of the effective classical potential

-function and the anomalous dimensions of the