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The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration., Comment: arXiv admin note: text overlap with arXiv:1210.2630

We discuss the BCS theory for electrons in graphene with a superimposed electrical unidirectional superlattice potential (SL). New Dirac points emerge together with van Hove singularities (VHS) linking them. We obtain a superconducting transition temperature $ T_c $ for chemical potentials close to the VHS assuming that acoustic phonon coupling should be the dominant mechanism. Pairing of two onsite electrons with one electron close to the $ {\bf K} $ and the other close to the $ -{\bf K} $ point is the most stable pair formation. The resulting order parameter is almost constant over the entire SL., Comment: 10 pages, 2 figures

While free and weakly interacting nonrelativistic particles are described by a Gross-Pitaevskii equation, which is a nonlinear self-interacting Schr\"odinger equation, the phenomena in the strong- coupling limit are governed by an effective action that is extremized by a double-fractional generalization of this equation. Its particle orbits perform L\`evy walks rather than Gaussian random walks.

We show that a triangular lattice consisting of dipolar molecules pointing orthogonal to the plane undergoes a first-order defect melting transition., Comment: 6 pages

We formulate the Collective Quantum Field Theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Fred Cooper et al. and in a lowest-order Variational Perturbation Theory (VPT). It is shown that present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second - order quantum phase transition.In contrast to a recent prediction for atomic gases by Fred Cooper et. al., we find no superfluid state with zero condensate fraction., Comment: 21 pages, revtex, 4 figures. In this version the figures have been replaced, and the text extended

While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal L\'evy walks rather than Gaussian random walks with perturbations.

A detailed analysis of electron-positron pair creation induced by a spatially nonuniform and static electric field from vacuum is presented. A typical example is provided by the Sauter potential. For this potential, we derive the analytic expressions for vacuum decay and pair production rate accounted for the entire range of spatial variations. In the limit of a sharp step, we recover the divergent result due to the singular electric field at the origin. The limit of a constant field reproduces the classical result of Euler, Heisenberg and Schwinger, if the latter is properly averaged over the width of a spatial variation. The pair production by the Sauter potential is described for different physical regimes from weak to strong fields. In all these regimes, the locally constant-field rate is shown to be the upper limit., Comment: 35 pages, 6 figures

We study the quantum phase transition in optical lattices using ordinary Bose Hubbard Hamiltonian within two loop approximation in variational perturbation theory. We have shown that this approximation can reproduce superfluid Mott insulator transition in contrast to the simple Bogoliubov or Hartee - Fock - Popov approximations. The superfluid fraction and ground state energy per particle vs input parameters of the model are studied., Comment: Extended by including comarision with Gutzwiller approach. (To be published in PRA)

We recall the successes of the Hubbard-Stratonovich Transformation (HST) of many-body theory, point out its failure to cope with competing channels of collective phenomena and show how to overcome this by Variational Perturbation Theory. That yields exponentially fast converging results, thanks to the help of a variety of {\it collective classical fields}, rather than a fluctuating {\it collective quantum field} as suggested by the HST., Comment: four pages

With the help of a simple variational procedure it is possible to convert the partial sums of order $N$ of many divergent series expansions $f(g)=\sum_{n=0}^\infty a_n g^n$ into partial sums $\sum_{n=0}^N b_n g^{- \omega n}$, where $0<\omega<1$ is a parameter that parametrizes the approach to the large-$g$ limit. The latter are partial sums of a strong-coupling expansion of $f(g)$ which converge against $f(g)$ for $g$ {\em outside} a certain divergence radius. The error decreases exponentially fast for large $N$, like $e^{-{\rm const.}\times N^{1-\omega}}$. We present a review of the method and various applications., Comment: 32 pages

If the Einstein-Hilbert action ${\cal L}_{\rm EH}\propto R$ is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field $h^\alpha{}_\mu$, and the gauge field of local Lorentz transformations, the spin connection $A_{\mu \alpha}{}^ \beta $, there exists a new gauge symmetry which permits reshuffling the torsion, partially or totally, into the Cartan curvature term of the Einstein tensor, and back, via a {\em new multivalued gauge transformation\/}. Torsion can be chosen at will by an arbitrary gauge fixing functional. There exist many equivalent ways of specifing the theory, for instance Einstein's traditional way where ${\cal L}_{\rm EH}$ is expressed completely in terms of the metric $g_{\mu \nu}=h^ \alpha {}_\mu h_ \alpha {}_ \nu $, and the torsion is zero, or Einstein's teleparallel formulation, where ${\cal L}_{\rm EH}$ is expressed in terms of the torsion tensor, or an infinity of intermediate ways. As far as the gravitational field in the far-zone of a celestial object is concerned, matter composed of spinning particles can be replaced by matter with only orbital angular momentum, without changing the long-distance forces, no matter which of the various new gauge representations is used., Comment: Improved version, 5 pages and 5 figures

To comply with the equivalence principle, fields in curved spacetime can be quantized only in the neighborhood of each point, where one can construct a freely falling M i n k o w s k i frame with z e r o curvature. In each such frame, the geometric forces of gravity can be replaced by a selfinteracting spin-2 field, as proposed by Feynman in 1962. At a n y fixed distance $R$ from a black hole, the vacuum in each freely falling volume element acts like a thermal bath of all particles with Unruh temperature T_U=\hbar GM/2\pi c R^2. At the horizon R=2GM/c^2, the falling vacua show the Hawking temperature T_H=\hbar c^3/8\pi GMk_B., Comment: 2 pages, extended and corrected

At ultralow temperatures, polymers exhibit quantum behavior, which is calculated here for the second and fourth moments of the end-to-end distribution in the large-stiffness regime. The result should be measurable for polymers in wide optical traps.

We derive the exact rate of pair production of oppositely charged scalar particles by a smooth potential proportional to tanh kz in three dimensions. As a check we recover from this the known results for an infinitely sharp step as well as for a uniform electric field., Comment: Removed the labels and improved the paper

We calculate analytically the phase diagram of a two-dimensional square crystal and its wrapped version with defects under external homogeneous stress as a function of temperature using a simple elastic lattice model that allows for defect formation. The temperature dependence turns out to be very weak. The results are relevant for recent stress experiments on carbon nanotubes. Under increasing stress, we find a crossover regime which we identify with a cracking transition that is almost independent of temperature. Furthermore, we find an almost stress-independent melting point. In addition, we derive an enhanced ductility with relative strains before cracking between 200-400%, in agreement with carbon nanotube experiments. The specific values depend on the Poisson ratio and the angle between the external force and the crystal axes. We give arguments that the results for carbon nanotubes are not much different to the wrapped square crystal., Comment: 12 pages, 6 eps figures, section VI added discussing the modifications of our model when applied to tubes

We use a simple elastic Hamiltonian for the vortex lattice in a weak impurity background which includes defects in the form of integer-valued fields to calculate the free energy of a vortex lattice in the deep H_{c2} region. The phase diagram in this regime is obtained by applying the variational approach of M{\'e}zard and Parisi developed for random manifolds. We find a first-order line between the Bragg-glass and vortex-glass phase as a continuation of the melting line. In the liquid phase, we obtain an almost vertical third-order glass transition line near the critical temperature in the H-T plane. Furthermore, we find an almost vertical second-order phase transition line in the Bragg-glass as well as the vortex-glass phases which crosses the first-order Bragg-glass, vortex-glass transition line. We calculate the jump of the temperature derivate of the induction field across this second-order line as well as the entropy and magnetic field jumps across the first-order line., Comment: 19 pages, 5 figures, a discussion is added at the end of section VI relating our results with the results of Refs. 4, 10, typos corrected, version published in PRB

Temperature fluctuations in the normal direction of planar crystals such as graphene are quite violent and may be expected to influence strongly their melting properties. In particular, they will modify the Lindemann melting criterium. We calculate this modification in a self-consistent Born approximation. The result is applied to graphene and its wrapped version represented by single-walled carbon nanotubes (SWNTs). It is found that the out-of-plane fluctuations dominate over the in-plane fluctuations. This makes strong restrictions to possible Lindemann parameters. Astonishing we find that these large out-of-plane fluctuations have only a small influence upon the melting temperature., Comment: 6 pages, 1 figure, typos corrected, version published in PRB

We show that the recent observation of the time modulation of two-body weak decays of heavy ions reveals the mass content of the electron neutrinos via interference patterns in the recoiling ion wave function. From the modulation period we derive the difference of the square masses $ \Delta m^2\approx 22.5\times 10^{-5}$ eV${}^2$, which is about 2.8 times larger than that derived from a combined analysis of KamLAND and solar neutrino oscillation experiments. It is, however, compatible with a data regime to which the KamLAND analysis attributes a smaller probability. The experimental results imply that the neutrino mixing matrix violates unitarity by about 10%., Comment: 11 pages. Paper improved and title made more specific

At ultralow temperatures, polymers exhibit quantum behavior, which is calculated here for the moments and of the end-to-end distribution in the large-stiffness regime. The result should be measurable for polymers in wide optical traps., Comment: 4 pages

The theory presented is based on a simple Hamiltonian for a vortex lattice in a weak impurity background which includes linear elasticity and plasticity, the latter in the form of integer valued fields accounting for defects. Within a quadratic approximation in the impurity potential, we find a first-order Bragg-glass, vortex-glass transition line showing a reentrant behavior for superconductors with a melting line near $ H_{c2} $. Going beyond the quadratic approximation by using the variational approach of M\'ezard and Parisi established for random manifolds, we obtain a phase diagram containing a third-order glass transition line. The glass transition line separates the vortex glass and the vortex liquid. Furthermore, we find a unified first-order line consisting of the melting transition between the Bragg glass and the vortex liquid phase as well as a disorder induced first-order line between the Bragg glass and the vortex glass phase. The reentrant behavior of this line within the quadratic approach mentioned above vanished. We calculate the entropy and magnetic induction jumps over the first-order line., Comment: 26 pages, 6 figures, typos corrected, An error in Section VI C. (replica symmetric solution in the fluid phase) is corrected leading to changes in the phase diagram in Section IX. Erratum sent to Phys. Rev. B

The minute fluctuations of of S&P 500 and NASDAQ 100 indices display Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a {\em market temperature} for either sign. With increasing time the sharp Boltzmann peak broadens into a Gaussian whose volatility $ \sigma $ measured in $1/ \sqrt{{\rm min}}$ is related to the temperature $T$ by $T= \sigma / \sqrt{2}$. Plots over the years 1990--2006 show that the arrival of the 2000 crash was preceded by an increase in market temperature, suggesting that this increase can be used as a warning signal for crashes. A plot of the Dow Jones temperature over 78 years reveals a remarkable stability through many historical turmoils, interrupted only by short heat bursts near the crashes., Comment: Published version

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogolubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent., Comment: Latex file, 22 pages, 2 figures

We set up a melting model for vortex lattices in high-temperature superconductors based on the continuum elasticity theory. The model is Gaussian and includes defect fluctuations by means of a discrete-valued vortex gauge field. We derive the melting temperature of the lattice and predict the size of the Lindemann number. Our result agrees well with experiments for $ {\rm YBa}_2 {\rm Cu}_3 {\rm O}_{7-\delta} $, and with modifications also for $ {\rm Bi}_2 {\rm Sr}_2 {\rm Ca} {\rm Cu}_2 {\rm O}_8 $ . We calculate the jumps in the entropy and the magnetic induction at the melting transition., Comment: 7 pages, 2 figures, typos corrected, Extended final version published in PRB

Motivated by recent experimental progress in the critical regime of high-$T_c$ superconductors we show how the tricritical point in a superconductor can be derived from the Ginzburg-Landau theory as a consequence of vortex fluctuations. Our derivation explains why usual renormalization group arguments always produce a first-order transition, in contrast to experimental evidence and Monte Carlo simulations., Comment: 4 pages,1 figure

We set up a harmonic lattice model for 2D defect melting which, in contrast to earlier simple-cubic models, lives on a triangular lattice. Integer-valued plastic defect gauge fields allow for the thermal generation of dislocations and disclinations. The model produces universal formulas for the melting temperature expressed in terms of the elastic constants, which are different from those derived for square lattices. They determine a Lindemann-like parameter for two-dimensional melting. In contrast to the square crystal which underwent a first-order melting transition, the triangular model melts in two steps. Our results are applied to the melting of Lennard-Jones and electron lattices., Comment: 13 pages, 5 eps figures, section VI modified

't Hooft's derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al.. It is shown how the key element of this procedure - the loss of information constraint - can be implemented by means of Faddeev-Jackiw's treatment of constrained systems. It is argued that the emergent quantum systems are identical with systems obtained in [Phys.Rev. A 71 (2005) 052507] through Dirac-Bergmann's analysis. We illustrate our approach with two simple examples - free particle and linear harmonic oscillator. Potential Liouville anomalies are shown to be absent., Comment: 11 pages, RevTeX, revised version with minor changes, accepted to Annals of Physics

The wormlike chain model of stiff polymers is a nonlinear $\sigma$-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only for periodic and Dirichlet boundary conditions. We modify this theory appropriately and show how to perform a systematic large-stiffness expansions for all physically interesting quantities in powers of $L/\xi$, where $L$ is the length and $\xi$ the persistence length of the polymer. This requires special procedures for regularizing highly divergent Feynman integrals which we have developed in previous work. We show that by adding to the unperturbed action a correction term ${\cal A}^{\rm corr}$, we can calculate all Feynman diagrams with Green functions satisfying Neumann boundary conditions. Our expansions yield, order by order, properly normalized end-to-end distribution function in arbitrary dimensions $d$, its even and odd moments, and the two-point correlation function.

A cosmological model with a gravitational Lagrangian $L_g(R)\propto R+A R^n$ is set up to account for the presently observed re-acceleration of the universe. The evolution equation for the scale factor $a$ of the universe is analyzed in detail for the two parameters $n=2$ and $n=4/3$, which were preferred by previous studies of the early universe. The initial conditions are specified at a red-shift parameter $z\approx 0$. The fit to the observable data fixes the free parameter $A$. The analysis shows that the model with $n=2$ agrees better with present data. Then, if we set $w(q)=-1$ at $z=0$, corresponding to the deceleration parameter $q\approx -1/2$, we find that at $z\approx 0.5$, $w(q)$ has evolved to $w\approx -0.72$, corresponding to $q\approx 0$. At $z\approx 1$ we find $w\approx 0$ corresponding to $q\approx 1/2$. These results are compared with the flat Friedmann model with cold matter and Lambda-term (LCDM model) for the same initial conditions at $z\approx 0$. The other choice of the model with $n=4/3$ allows for big crunch. However this possibility is eliminated by the fit of $A$ to the present data., Comment: 8 pages, 1 figure, added reference, corrected the title of the figure

In a Ginzburg-Landau theory with $n$ fields, the anomalous dimension of the gauge-invariant nonlocal order parameter defined by the long-distance limit of Dirac's gauge-invariant two-point function is calculated. The result is exact for all $n$ to first order in $\epsilon \equiv 4-d$, and for all $d\in (2,4)$ to first order in $1/n$, and coincides with the previously calculated gauge-dependent exponent in the Landau gauge., Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper http://www.physik.fu-berlin.de/~kleinert/356

The critical temperature T_c of an interacting Bose gas trapped in a general power-law potential V(x)=\sum_i U_i|x_i|^{p_i} is calculated with the help of variational perturbation theory. It is shown that the interaction-induced shift in T_c fulfills the relation (T_c-T_c^0)/T_c^0= D_1(eta)a + D'(eta)a^{2 eta}+ O(a^2) with T_c^0 the critical temperature of the trapped ideal gas, a the s-wave scattering length divided by the thermal wavelength at T_c, and eta=1/2+\sum_i 1/p_i the potential-shape parameter. The terms D_1(eta)a and D'(eta) a^{2 eta} describe the leading-order perturbative and nonperturbative contributions to the critical temperature, respectively. This result quantitatively shows how an increasingly inhomogeneous potential suppresses the influence of critical fluctuations. The appearance of the a^{2 eta} contribution is qualitatively explained in terms of the Ginzburg criterion., 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/352

We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by re-calculating the critical exponents of O(N)-symmetric $\vp^4$ theory. From only three-loop perturbation expansions in $4- \epsilon $ dimensions we obtain {\em analytic results for the exponents, with practically the same accuracy as those derived recently from ordinary field-theoretic variational perturbational theory to seventh order. In particular, the theory explains the best-measured exponent $\al\approx-0.0127$ of the specific heat peak in superfluid helium, found in a satellite experiment with a temperature resolution of nanoKelvin. In addition, our analytic expressions reproduce also the exactly known large-N behaviour of the exponents $ \nu $ and $ \gamma= \nu (2- \eta) $ with high precision., 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_re349/preprint.html

Assuming that at small distances space-time is equivalent to an elastic medium which is isotropic in space and time directions, we demonstrate that the quantum nematic liquid arising from this crystal by spontaneous proliferation of dislocations corresponds with a medium which is merely carrying curvature rigidity. This medium is at large distances indistinguishable from Einstein's spacetime of general relativity. It does not support torsion and possesses string-like curvature sources which in spacetime form world surfaces., Comment: 4 pages, submitted to Phys. Let. B: this is a polished version of gr-qc/0307033

We set up and solve a recursion relation for all even moments of a two-dimensional stiff polymer (Porod-Kratky wormlike chain) and determine from these moments a simple analytic expression for the end-to-end distribution at all persistence lengths., 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_re/preprint.html

We calculate the location of the quantum phase transitions of a bose gas trapped in an optical lattice as a function of effective scattering length $a_{\eff}$ and temperature $T$. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a {\em nose} in the phase diagram above the free Bose-Einstein critical temperature $T_c^{(0)}$, thus predicting the existence of a reentrant transition {\em above} $T_c^{(0)}$, where a condensate should form when {\em increasing} $a_{\eff}$. At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator., Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html

We attribute the gravitational interaction between sources of curvature to the world being a crystal which has undergone a quantum phase transition to a nematic phase by a condensation of dislocations. The model explains why spacetime has no observable torsion and predicts the existence of curvature sources in the form of world sheets, albeit with different high-energy properties than those of string models., Comment: 4 pages, no figures. 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/346

We set up recursion relations for calculating all even moments of the end-to-end distance of a Porod-Kratky wormlike chains in $D$ dimensions. From these moments we derive a simple analytic expression for the end-to-end distribution in three dimensions valid for all peristence lengths. It is in excellent agreement with Monte Carlo data for stiff chains and goes properly over into the Gaussian random-walk distributions for low stiffness., 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/345 Mathematica programs at http://www.physik.fu-berlin.de/~kleinert/b5/pgm15

We present a method for evaluating divergent non-Borel-summable series by an analytic continuation of variational perturbation theory. We demonstrate the power of the method by an application to the exactly known partition function of the anharmonic oscillator in zero spacetime dimensions. In one spacetime dimension we derive the imaginary part of the ground state energy of the anharmonic oscillator for {\em all negative values of the coupling constant $g$, including the nonanalytic tunneling regime at small-$g$. As a highlight of the theory we retrieve from the divergent perturbation expansion the action of the critical bubble and the contribution of the higher loop fluctuations around the bubble., 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/344

We present a method for extracting tunnelling amplitudes from perturbation expansions which are always divergent and not Borel-summable. We show that they can be evaluated by an analytic continuation of variational perturbation theory. The power of the method is illustrated by calculating the imaginary parts of the partition function of the anharmonic oscillator in zero spacetime dimensions and of the ground state energy of the anharmonic oscillator for all negative values of the coupling constant $g$ and show that they are in excellent agreement with the exactly known values. As a highlight of the theory we recover from the divergent perturbation expansion of the tunnelling amplitude the action of the instanton and the effects of higher loop fluctuations around it., 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/342

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/341

The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -\beta V^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called effective classical potential containing the effects of all quantum fluctuations. The variable of integration is the temporal path average ${\bf x_0\equiv \beta ^{-1}\int_0^ \beta d\tau {\bf x}(\tau)$. We show how to generalize this concept to paths $q^\mu(\tau)$ in curved space with metric $g_{\mu \nu (q)$, and calculate perturbatively the high-temperature expansion of $V^{\rm eff cl(q_0)$. The requirement of independence under coordinate transformations $q^\mu(\tau)\to q'^\mu(\tau)$ introduces subtleties in the definition and treatment of the path average $q_0^\mu$, and covariance is achieved only with the help of a suitable Faddeev-Popov procedure., 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/339

Using variational perturbation theory, we calculate the shift in the critical temperature T_c up to five loops to lowest order in the scattering length a and find Delta T_c/T_c^{(0)} approx (1.14\pm0.11)an^{1/3}, where n is the particle density. Our result is lower than the latest Monte Carlo result (1.32\pm0.02)an^{1/3}., 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/320

The critical behavior of the Ginzburg-Landau model is described in a manifestly gauge-invariant manner. The gauge-invariant correlation-function exponent is computed to first order in the $4-d$ and $1/n$-expansion, and found to agree with the ordinary exponent obtained in the covariant gauge, with the parameter $\alpha=1-d$ in the gauge-fixing term $(\partial_\mu A_\mu)^2 /2 \alpha$., Comment: 4 pages, no figures

We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating products of distributions. The rules are derived using equations of motion and partial integration, while keeping track of certain minimal features stemming from the unique definition of all singular integrals in 1 - epsilon dimensions. Our rules guarantee complete agreement with much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. In contrast to our previous papers where we solved the same problem for an infinite time interval or zero temperature, we consider here the more involved case of finite-time (or non-zero temperature) amplitudes., 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/330

We speculate that the universe is filled with stars composed of electromagnetic and dilaton fields which are the sources of the powerful gamma-ray bursts impinging upon us from all directions of the universe. We calculate soliton-like solutions of these fields and show that their energy can be converted into a relativistic plasma in an explosive way. As in classical detonation theory the conversion proceeds by a relativistic self-similar solution for a spherical detonation wave which extracts the energy from the scalar field via a plasma in the wave front., 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/326

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/313

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/335

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.html

The forward--backward path integral describing a charged particle moving in a thermal bath of photons is expressed in terms of the solution of a Langevin-type of equation. Approximate methods for solving this equation are discussed., 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/323

The effective potential of scalar QED is computed analytically up to two loops in the Landau gauge. The result is given in 4-epsilon dimensions using minimal subtraction and epsilon-expansions. In three dimensions, our calculation is intended to help throw light on unsolved problems of the superconducting phase transition, where critical exponents and the position of the tricritical point have not yet found a satisfactory explanation within the renormalization group approach., 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/321

From a forward--backward path integral, we derive a master equation for the emission and absorption of gravitons by a massive quantum object in a heat bath of gravitons. Such an equation could describe collapse phenomena of dense stars. We also present a useful approximate Langevin equation for such a system., 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/319