Integrals over Products of Distributions and Coordinate Independence of Zero-Temperature Path Integrals

In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac delta-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in $1 - \epsilon$ dimensions. Our rules yield the same results as the much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval.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/33

Coordinate Independence of of Quantum-Mechanical Path Integrals

We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the form dot q^2 q^n, which give rise to highly singular Feynman integrals. The new rules ensure the invariance of perturbatively defined path integrals under coordinate transformations.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/305

Universality Principle for Orbital Angular Momentum and Spin in Gravity with Torsion

We argue that compatibility with elementary particle physics requires gravitational theories with torsion to be unable to distinguish between orbital angular momentum and spin. An important consequence of this principle is that spinless particles must move along autoparallel trajectories, not along geodesics.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_re27

Covariant Effective Action for Quantum Particle with Coordinate-Dependent Mass

Using a covariant background field method we calculate the one-loop quantum effective action for a particle with coordinate-dependent mass moving slowly through a one-dimensional configuration space. The procedure can easily be extended to any desired loop order.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/31

Critical dynamics, duality, and the exact dynamic exponent in extreme type II superconductors

The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by $z=3/2$. This result does not rely on the widely used models of critical dynamics. Instead, it is shown that $z=3/2$ follows from the duality between the extreme type II superconductor and a model with a critically fluctuating gauge field. Our result is in agreement with Monte Carlo simulations.Comment: 7 pages, no figures; version accepted for publication in PR

Observing Quantum Tunneling in Perturbation Series

We apply Borel resummation method to the conventional perturbation series of ground state energy in a metastable potential, $V(x)=x^2/2-gx^4/4$. We observe numerically that the discontinuity of Borel transform reproduces the imaginary part of energy eigenvalue, i.e., total decay width due to the quantum tunneling. The agreement with the exact numerical value is remarkable in the whole tunneling regime 0.Comment: 12 pages, 2 figures. Phyzzx, Tables.tex, The final version to appear in Phys. Lett.

Variational Perturbation Theory for Markov Processes

We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.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/33

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.Comment: Corrected typos. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm

Towards a Simulation of Quantum Computers by Classical Systems

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the Schroedinger equation of a harmonic oscillator. In this way we derive the discrete oscillator spectrum from classical dynamics. The model is then generalized to an arbitrary potential. This opens up the possibility of efficiently simulating quantum computers with the help of classical systems.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/kleiner_re324/preprint.htm

Superconducting transition in disordered granular superconductors in magnetic fields

Motivated by a recent argument that the superconducting (SC) transition field of three-dimensional (3D) disordered superconductors with granular structure in a nonzero magnetic field should lie above $H_{c2}(0)$ in low $T$ limit, the glass transition (or, in 2D, crossover) curve $H_g(T)$ of disordered quantum Josephson junction arrays is examined by incorporating SC fluctuations. It is found that the glass transition or crossover in the granular materials can be described on the same footing as the vortex-glass (VG) transition in amorphous-like (i.e., nongranular) materials. In most of 3D granular systems, the vanishing of resistivity upon cooling should occur even above $H_{c2}(0)$, while the corresponding sharp drop of the resistivity in 2D case may appear only below $H_{c2}$ as a result of an enhanced quantum fluctuation.Comment: Accepted for publication in Phys. Rev. B. The content of sec.3 in v.2 was removed from here and presented more extensively in a separate paper (cond-mat/0606522) where the argument of nonsuperconducting vortex-glass in cond-mat/0512432 is shown to be fals