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Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples., Comment: 11 pages, 16 figures

Equilibration of observables in closed quantum systems that are described by a unitary time evolution is a meanwhile well-established phenomenon apart from a few equally well-established exceptions. Here we report the surprising theoretical observation that integrable as well as non-integrable spin rings with nearest-neighbor or long-range isotropic Heisenberg interaction not only equilibrate but moreover also synchronize the directions of the expectation values of the individual spins. We highlight that this differs from spontaneous synchronization in quantum dissipative systems. Here, we observe mutual synchronization of local spin directions in closed systems under unitary time evolution. Contrary to dissipative systems, this synchronization is independent of whether the interaction is ferro- or antiferromagnetic. In our numerical simulations, we investigate the free induction decay (FID) of an ensemble of up to $N = 25$ quantum spins with $s = 1/2$ each by solving the time-dependent Schr\"odinger equation numerically exactly. Our findings are related to, but not fully explained by conservation laws of the system. The synchronization is very robust against for instance random fluctuations of the Heisenberg couplings and inhomogeneous magnetic fields. Synchronization is not observed with strong enough symmetry-breaking interactions such as the dipolar interaction. We also compare our results to closed-system classical spin dynamics which does not exhibit phase synchronization due to the lack of entanglement. For classical spin systems the fixed magnitude of individual spins effectively acts like additional $N$ conservation laws., Comment: 13 pages, 21 figures

Quantum tunneling of the magnetization is a phenomenon that impedes the use of small anisotropic spin systems for storage purposes even at the lowest temperatures. Phonons, usually considered for temperature dependent relaxation of magnetization over the anisotropy barrier, also contribute to magnetization tunneling for integer spin quantum numbers. Here we demonstrate that certain spin-phonon Hamiltonians are unexpectedly robust against the opening of a tunneling gap, even for strong spin-phonon coupling. The key to understanding this phenomenon is provided by an underlying supersymmetry that involves both spin and phonon degrees of freedom., Comment: 5 pages, 5 figures, supplemetary material

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system's ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with $N\longrightarrow \infty$ is investigated and completely solved.

The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general equation of motion and solve it in closed form for the case of parabolic motion. Especially the motion near the horizon and near the singularity are examined., Comment: Reprinted from: 10th International Conference on General Relativity and Gravitation, Padova (Italy) July 4 - 9, 1983. Eds.: B. Bertotti, F. de Felice, A. Pascolini, Contributed papers Vol. 1, Roma (1983) page 339-341

Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high-temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J2/J1 by comparing with susceptibility measurements on corresponding magnetic compounds., Comment: paper presented at the 'XVII. International Conference on Recent Progress in Many-Body Theories', Rostock Sept 2013, accepted for publication in J. Phys. Conf. Ser

We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we discuss is the case of a very small negative value of the parameter b in the Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de Sitter solution from L = R^2 (being a local attractor) to a power-law inflation exact solution also representing a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of the G ln G-term., Comment: several revisions included, 28 pages, J. Math. Phys. accepted

In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions., Comment: 13 pages, minor revisions, updated references, to be published PLB

We deduce a new formula for the perihelion advance of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole., Comment: 22 pages, new results added at the end of scts. 4 and 5, accepted for Phys. Rev. D

For the lagrangian L = G ln G where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedman models using a statefinder parametrization. Further we show, that among all lagrangians F(G) this L is the only one not having the form G^r with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R)-theories in 2-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4., Comment: 18 pages, amended version, accepted by Phys. Rev. D

We calculate the perihelion precession delta for nearly circular orbits in a central potential V(r). Differently from other approaches to this problem, we do not assume that the potential is close to the Newtonian one. The main idea in the deduction is to apply the underlying symmetries of the system to show that delta must be a function of r V''(r)/V'(r), and to use the transformation behaviour of delta in a rotating system of reference. This is equivalent to say, that the effective potential can be written in a one-parameter set of possibilities as sum of centrifugal potential and potential of the central force. We get a universal formula for delta. It has to be read as follows: a circular orbit at this value r exists and is stable if and only if this delta is a well-defined real; and if this is the case, then the angular difference from one perihelion to the next one for nearly circular orbits at this r is exactly 2 pi + delta. Then we show how to apply this result to examples of recent interest like modified Newtonian gravity and linearized fourth-order gravity. In the second part of the paper, we generalize this universal formula to static spherically symmetric space-times. For the Schwarzschild black hole with mass parameter m > 0 it leads to a surprisingly unknown formula. It represents a strict result and is applicable for all values r > 6m and is in good agreement with the fact that stable circular orbits exist for r > 6m only., Comment: updated version by inclusion of curved space-times and new references, 26 pages, no figure

Numerically exact investigations of interacting spin systems provide a major tool for an understanding of their magnetic properties. For medium size systems the approximate Lanczos diagonalization is the most common method. In this article we suggest two improvements: efficient basis coding in subspaces and simple restructuring for openMP parallelization., Comment: 9 pages, 2 figues, submitted to Journal of Computational Physics

A new 5D thick brane solution is presented. We conjecture that the deduced thick brane is a plane defect in a bulk gauge condensate., Comment: 3 pages, 3 fig's, talk given at the Marcel Grossmann-11 conference

Strongly frustrated antiferromagnets such as the magnetic molecule {Mo72Fe30}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M=Ns-n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T=0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined., Comment: 4 pages, submitted to the proceedings of the Yamada Conference LX on Research in High Magnetic Fields, August 16-19, 2006 Sendai, Japan

The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented., Comment: 51 pages, LaTeX, no figure, lecture for 42nd Karpacz Winter School 6.-11.2.06, references 99-109 and related comments are added

We comment on the paper [1] by Albert Einstein from 1918 to Willem De Sitter's solution [2] of the Einstein field equation from today's point of view. To this end, we start by describing the geometry of the De Sitter space-time and present its importance for the inflationary cosmological model., Comment: 19 pages, LaTeX, in German language, submitted for publication, English language title: Einstein's papers in relation to modern cosmology

We present the history of fourth order metric theories of gravitation from its beginning in 1918 until 1988., Comment: 13 pages, LaTeX

We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by J. L. Synge in 1950 to its clarification., Comment: 2 pages, LaTeX, submitted for publication; 2 references, one Note, and an Acknowledgement are added

We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized., Comment: 202 pages, Latex

We present gravitoelectromagnetism and other decompositions of the Riemann tensor from the differential-geometrical point of view., Comment: 6 pages, no figure, LaTeX, submitted for publication

Superthin and superlong solutions in 5D Kaluza-Klein gravity are considered. It is shown that they can be cosidered as a hybrid between Einstein's and string paradigmes., Comment: 3 pages, talk given at the MG-10 conference

We propose a solvable model of a one-dimensional harmonic oscillator quantum gas of two sorts of particles, fermions or bosons, which allows to describe the formation of pairs due to a suitable pair interaction. These pairs we call "pseudo-bosons" since the system can be approximated by an ideal bose gas for low temperatures. We illustrate this fact by considering the specific heat and the entropy function for N=8 pairs. The model can also be evaluated in the thermodynamic limit if the harmonic oscillator potential is suitable scaled.

For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagom\'e and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small they can be distributed randomly over the lattice. Increasing the number of localized magnons their distribution over the lattice becomes more and more regular and finally the magnons condensate in a crystal-like state. The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect., Comment: 6 pages and 2 figures included; uses IOP style files, paper presented on the HFM2003 conference

We investigate general properties of spatial 1-dimensional bright photorefractive solitons and suggest various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r.

A vacuum solution of the Einstein gravitational field equation is given that follows from a general ansatz but fails to follow from it if a certain symmetric matrix is assumed to be in diagonal form from the beginning., Comment: 18 pages, latex, no figures. An Acknowledgement, 4 references, and the section "Note added" are added

We suggest a general rule for the shift quantum numbers k of the relative ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even rings. Our rule is confirmed by numerical investigations and rigorous proofs for special cases, including systems with a Haldane gap. Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model., Comment: 8 pages, 2 figures, submitted to Phys. Rev. B. More information at http://www.physik.uni-osnabrueck.de/makrosysteme/

We show that the square of the Weyl tensor can be negative by giving an example., Comment: 3 pages, latex, no figures, to appear in Gen. Relat. Grav

Large spin systems as given by magnetic macromolecules or two-dimensional spin arrays rule out an exact diagonalization of the Hamiltonian. Nevertheless, it is possible to derive upper and lower bounds of the minimal energies, i.e. the smallest energies for a given total spin S. The energy bounds are derived under additional assumptions on the topology of the coupling between the spins. The upper bound follows from "n-cyclicity", which roughly means that the graph of interactions can be wrapped round a ring with n vertices. The lower bound improves earlier results and follows from "n-homogeneity", i.e. from the assumption that the set of spins can be decomposed into n subsets where the interactions inside and between spins of different subsets fulfill certain homogeneity conditions. Many Heisenberg spin systems comply with both concepts such that both bounds are available. By investigating small systems which can be numerically diagonalized we find that the upper bounds are considerably closer to the true minimal energies than the lower ones., Comment: 17 pages, 5 figures, submitted to Eur. Phys. J. B. More information at http://www.physik.uni-osnabrueck.de/makrosysteme/

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

Recently obtained results on linear energy bounds are generalized to arbitrary spin quantum numbers and coupling schemes. Thereby the class of so-called independent magnon states, for which the relative ground-state property can be rigorously established, is considerably enlarged. We still require that the matrix of exchange parameters has constant row sums, but this can be achieved by means of a suitable gauge and need not be considered as a physical restriction.

O. Waldmann has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal energies are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states., Comment: 2 pages, accepted for Europhysics Letters

Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev. D 40, (1989) 315] are corrected., Comment: 3 pages, LaTeX, reprinted from Phys. Rev. D 50 (1994) 5452

We answer the following question: Let l, m, n be arbitrary real numbers. Does there exist a 3-dimensional homogeneous Riemannian manifold whose eigenvalues of the Ricci tensor are just l, m and n ?, Comment: 2 pages, LaTeX, reprinted from Proc. Conf. Brno (1995)

We present an example that non-isometric space-times with non-vanishing curvature scalar cannot be distinguished by curvature invariants., Comment: 2 pages, LaTeX, reprinted from Abstracts Conf. GR 14 (1995)

We consider the spatially flat Friedmann model. For a(t) = t^p, especially, if p is larger or equal to 1, this is called power-law inflation. For the Lagrangian L = R^m with p = - (m - 1)(2m - 1)/(m - 2), power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field Phi in an exponential potential V(Phi) = exp(mu Phi) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we use another gauge. Finally, special solutions for the closed and open Friedmann model are found., Comment: 9 pages, LaTeX, reprinted from Astron. Nachr. 311 (1990) 165

We consider the Newtonian limit of the theory based on the Lagrangian L = R + \sum a_k R \Box^k R. The gravitational potential of a point mass turns out to be a combination of Newtonian and Yukawa terms. For sixth-order gravity the coefficients are calculated explicitly. For the general case one gets as a result: The the potential is always unbounded near the origin., Comment: 12 pages, LaTeX, reprinted from Astron. Nachr. 312 (1991) 97

The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their curvature and invariance properties are discussed. Just one of this class has the property to bring the lagrangian of General Relativity into the form of a classical particle's motion. The signature of the superspace metric depends in a non-trivial manner on the signature of the original metric, we derive the corresponding formula. Our approach is a local one: the essence is a metric in the space of all symmetric rank-two tensors, and then the space becomes a warped product of the real line with an Einstein space., Comment: 10 pages, LaTeX, reprinted from Proc. Conf. Diff. Geom. Appl., Brno, Czechoslovakia 1989, WSPC Singapore, Eds. J. Janyska, D. Krupka

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove that D = 1 or D > 1, where D is the (fractal) dimension of the set of solutions which can be integrated up to t to infinity. (D > 0 was conjectured by PAGE (1984)). We discuss concepts like ``the probability of the appearance of a sufficiently long inflationary phase" and argue that it is primarily a probability measure q in the space V of solutions (and not in the space of initial conditions) which has to be applied. q is naturally defined for Bianchi-type I cosmological models because V is a compact cube. The problems with the closed Friedmann model (which led to controversial claims in the literature) will be shown to originate from the fact that V has a complicated non-compact non-Hausdorff Geroch topology: no natural definition of q can be given. We conclude: the present state of our universe can be explained by models of the type discussed, but thereby the anthropic principle cannot be fully circumvented., Comment: 20 pages, LaTeX, reprinted from Astron. Nachr. 311 (1990) 99

For a class of frustrated spin lattices including the kagome lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagome lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect., Comment: 4 pages, 4 figures, accepted by Phys.Rev.Lett

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E_{min}(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Lande interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase., Comment: 11 pages, 4 figures, submitted to Eur. Phys. J. B

The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the ``SU(2) gauge potential'' (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed., Comment: misprints are corrected

We provide exact analytical expressions for the magnetic susceptibility function in the high temperature expansion for finite Heisenberg spin systems with an arbitrary coupling matrix, arbitrary single-spin quantum number, and arbitrary number of spins. The results can be used to determine unknown exchange parameters from zero-field magnetic susceptibility measurements without diagonalizing the system Hamiltonian. We demonstrate the possibility of reconstructing the exchange parameters from simulated data for two specific model systems. We examine the accuracy and stability of the proposed method., Comment: 13 pages, 7 figures, submitted to Phys. Rev. B

We consider strings with the Nambu action as extremal surfaces in a given space-time, thus, we ignore their back reaction. Especially, we look for strings sharing one symmetry with the underlying space-time. If this is a non-null symmetry, the problem of determining the motion of the string can be dimensionally reduced. We get exact solutions for the following cases: straight and circle-like strings in a Friedmann background, straight strings in an anisotropic Kasner background, different types of strings in the metric of a gravitational wave. The solutions will be discussed., Comment: 13 pages, LaTeX, reprinted from Astron. Nachr. 310 (1989) 103

We generalize the well-known analogies between m^2 \phi^2 and R + R^2 theories to include the selfinteraction \lambda \phi^4-term for the scalar field. It turns out to be the R + R^3 Lagrangian which gives an appropriate model for it. Considering a spatially flat Friedman cosmological model, common and different properties of these models are discussed, e.g., by linearizing around a ground state the masses of the resp. spin 0-parts coincide. Finally, we prove a general conformal equivalence theorem between a Lagrangian L = L(R), L'L" \ne 0, and a minimally coupled scalar field in a general potential., Comment: 16 pages, LaTeX

For the non-tachyonic curvature squared action we show that the expanding Bianchi-type I models tend to the dust-filled Einstein-de Sitter model for t tending to infinity if the metric is averaged over the typical oscillation period. Applying a conformal equivalence between curvature squared action and a minimally coupled scalar field (which holds for all dimensions > 2) the problem is solved by discussing a massive scalar field in an anisotropic cosmological model., Comment: 9 pages, LaTeX, no figure

We discuss the consequences of the incorrectness [see the Erratum in Phys. Rev D 49, 1145 (1994)] of that paper and add two related remarks. The scope of this comment is to encourage further research on: `Which of the conformally equivalent metrics is the physical one?', Comment: 4 pages, LaTeX, published in Phys. Rev. D52, 6198 (1995)

The weak-field slow-motion limit of fourth-order gravity will be discussed., Comment: 5 pages, LaTeX

The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation plays the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of geometrodynamics., Comment: 16 pages, LaTeX, no figures

For field equations of 4th order, following from a Lagrangian `Ricci scalar plus Weyl scalar', it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = 0 and r = infinity resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme., Comment: 12 pages, LaTeX, no figure