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Hagen Kleinert

Publications and source records attributed to Hagen Kleinert.

82 records · Page 5Linked to original sources
arXiv1998

Smearing Formula for Higher-Order Effective Classical Potentials

In the variational approach to quantum statistics, a smearing formula describes efficiently the consequences of quantum fluctuations upon an interaction potential. The result is an effective classical potential from which the partition function can be obtained by a simple integral. In this work, the smearing formula is extended to higher orders in the variational perturbation theory. An application to the singular Coulomb potential exhibits the same fast convergence with increasing orders that has been observed in previous variational perturbation expansions of the anharmonic oscillator with quartic potential.

quant-ph↗
arXiv1998

Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor

The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force changes geodesic into autoparallel trajectories, which are a direct manifestation of inertia. The geometric origin of the torsion force is a closure failure of parallelograms. The torsion force changes the covariant conservation law of the energy-momentum tensor whose new form is derived.

gr-qc↗
arXiv1997

Supersymmetry in Stochastic Processes with Higher-Order Time Derivatives

A supersymmetric path integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the Langevin equation with inertia studied by Kramers, where N=2. The supersymmetric action contains N fermion fields with first-order time derivatives whose path integral is evaluated for fermionless asymptotic states.

quant-ph↗
arXiv1997

Comment on "Continuum dual theory of the transition in 3D lattice superconductor"

A recent paper by Herbut in J. Phys. A: Math. Gen. {\bf 29}, 1 (1996) is shown to contain an internal inconsistency which invalidates the principal conclusion of the paper that the magnetic penetration depth diverges with an XY-exponent rather than a mean-field exponent, as predicted some time ago by Kiometzis, Kleinert, and Schakel (KKS).

cond-mat↗
arXiv1997

Proper Dirac Quantization of Free Particle on D-Dimensional Sphere

We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first class in Dirac's classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere. A quantization of Dirac's modified Poisson brackets for second-class constraints is also possible and unique, but must be rejected since the resulting energy spectrum is physically incorrect.

quant-ph↗
arXiv1996

Convergence Behavior of Variational Perturbation Expansions

Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we explain the physical origin of the empirically observed convergence behavior which is exponentially fast with superimposed oscillations.

quant-ph↗
arXiv1996

New Universality Class in the Superconductive Phase Transition

The superconductive phase transition in the Ginzburg-Landau theory (or Coulomb-Higgs phase transition of scalar QED in 3D) is discussed in a dual formulation which focuses on the magnetic rather than the electric excitations of the system. Renormalization group analysis of the dual formulation reveals the transition to be of second order and of a new universality class. Whereas coherence length and specific heat have XY-model exponents, the magnetic penetration depth shows mean-field behavior. Experimental evidence for these predictions is discussed.

supr-con↗
arXiv1995

Critical Exponents of the Superconducting Phase Transition

We study the critical exponents of the superconducting phase transition in the context of renormalization group theory starting from a dual formulation of the Ginzburg-Landau theory. The dual formulation describes a loop gas of Abrikosov flux tubes which proliferate when the critical temperature is approached from below. In contrast to the Ginzburg-Landau theory, it has a spontaneously broken global symmetry and possesses an infrared stable fixed point. The exponents coincide with those of a superfluid with reversed temperature axis.

cond-mat↗