arXiv subjects
Publications and source records attributed to J. W. van Holten.
The dynamics of cosmic scalar fields with flat potential is studied. Their contribution to the expansion rate of the universe is analyzed, and their behaviour in a simple model of phase transitions is discussed.
BRST-methods provide elegant and powerful tools for the construction and analysis of constrained systems, including models of particles, strings and fields. These lectures provide an elementary introduction to the ideas, illustrated with some important physical applications.
In general relativity, only relative acceleration has an observer-independend meaning: curvature and non-gravitational forces determine the rate at which world lines of test bodies diverge or converge. We derive the equations governing both in the conventional geometric formalism as well as using the background field method. This allows us to generalize the results to test bodies with charge and/or spin. The application of the equations to the motion of particles in a central field results in an elegant, fully relativistic version of the Ptolemaean epicycle scheme.
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after diagonalization describes just a collection of harmonic oscillators, with two characteristic frequencies. The new geodesic obtained by adding this solution to the circular one, describes not only the linear approximation of Kepler's laws, but gives also the right value of the perihelion advance (in the limit of almost circular orbits). We derive also the equations for higher-order deviations and show how these equations lead to better approximations, including the non-linear effects. The approximate orbital solutions are then inserted into the quadrupole formula to estimate the gravitational radiation from non-circular orbits.
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite number of degrees of freedom to one with infinitely many degrees of freedom. In some two-dimensional fluid mechanics models a duality transformation between the velocity potential and the stream function can be performed relating sources and sinks in one model to vortices in the other. The particle mechanics counterpart of the dual theory is reconstructed. In the quantum theory the strength of sources and sinks, as well as vorticity are quantized; for the duality between theories to be preserved these quantization conditions must be related.
We present a covariant and supersymmetric theory of relativistic hydrodynamics in four-dimensional Minkowski space.
We examine the motion of charged particles in gravitational and electro-magnetic background fields. We study in particular the deviation of world lines, describing the relative acceleration between particles on different space-time trajectories. Two special cases of background fields are considered in detail: (a) pp-waves, a combination of gravitational and electro-magnetic polarized plane waves travelling in the same direction; (b) the Reissner-Nordstrøm solution. We perform a non-trivial check by computing the precession of the periastron for a charged particle in the Reissner-Nordstrøm geometry both directly by solving the geodesic equation, and using the world-line deviation equation. The results agree to the order of approximation considered.
This paper discusses a procedure for the consistent coupling of gauge- and matter superfields to supersymmetric sigma-models on symmetric coset spaces of Kaehler type. We exhibit the finite isometry transformations and the corresponding Kaehler transformations. These lead to the construction of a generalized type of Killing potentials. In certain cases a charge quantization condition needs to be imposed to guarantee the global existence of a line bundle on a coset space. The results are applied to the explicit construction of sigma-models on cosets SO(2N)/U(N). Only a finite number of these models can consistently incorporate matter in representations descending from the spinorial representations of SO(2N). We investigate in detail some aspects of the vacuum structure of the gauged SO(10)/U(5) theory, with surprising results: the fully gauged minimal anomaly-free model is shown be singular, as the kinetic terms of the quasi-Goldstone fermions vanish in the vacuum. Gauging only the linear isometry group SU(5)xU(1), or one of its subgroups, can give a physically well-behaved theory. With gauged U(1) this requires the Fayet-Iliopoulos term to take values in a specific limited range.
We present measurements of mechanical vibrations induced by 0.6 GeV electrons impinging on cylindrical and spherical aluminium resonators. To monitor the amplitude of the resonator's vibrational modes we used piezoelectric ceramic sensors, calibrated by standard accelerometers. Calculations using the thermo-acoustic conversion model, agree well with the experimental data, as demonstrated by the specific variation of the excitation strengths with the absorbed energy, and with the traversing particles' track positions. For the first longitudinal mode of the cylindrical resonator we measured a conversion factor of 7.4 +- 1.4 nm/J, confirming the model value of 10 nm/J. Also, for the spherical resonator, we found the model values for the L=2 and L=1 mode amplitudes to be consistent with our measurement. We thus have confirmed the applicability of the model, and we note that calculations based on the model have shown that next generation resonant mass gravitational wave detectors can only be expected to reach their intended ultra high sensitivity if they will be shielded by an appreciable amount of rock, where a veto detector can reduce the background of remaining impinging cosmic rays effectively.
The existence of Killing-Yano tensors on space-times can be probed by spinning particles. Specifically, Dirac particles possess new fermionic constants of motion corresponding to non-standard supersymmetries on the particle worldline. A geometrical duality connects space-times with Killing-Yano structure, but without torsion, to other space-times with Killing-Yano structure and torsion. A relation between the indices of the Dirac operators on the dual space-times allows to express the index on the space-time with torsion in terms of that of the space-time without torsion.
A consistent N=1 supersymmetric $σ$-model can be constructed, given a Kähler manifold by adding chiral matter multiplets. Their scalar components are covariant tensors on the underlying Kähler manifold. The Kähler U(1)-charges can be adjusted such that the anomalies cancel, using the holomorphic functions in which the Kähler potential transforms. The arbitrariness of the U(1)-charges of matter multiplets is related to their Weyl-weights in superconformal gravity, before it is reduced to supergravity. The covariance of the Kähler potential forces the superpotential to be covariant as well. This relates the cut-off, the Planck scale and the matter charges to each other. A non-vanishing VEV of the covariant superpotential breaks the Kähler U(1) spontaneously. If this VEV vanishes, the gravitino is massless and depending on the above mentioned parameters there may be additional internal symmetry breaking. The separation of the different representations of chiral multiplets can be achieved by covariantizations of derivatives and fermions. Using non-holomorphic transformations, the full Kähler metric can be block-diagonalized and the necessary covariantizations come out naturally. Various aspects are illustrated by applying them to Grassmannian coset models. In particular a consistent model of coset $SU(5)/SU(2)\times U(1) \times SU(3)$ with the field content of the standard model is constructed. The phenomenology of this model is analyzed.
We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the variations of the kinetic energy of the particle during passage of the waves. We also explicitly compute the change in the orbit due to a wave with constant curvature.
These notes address the planar gravitational wave solutions of general relativity in empty space-time, and analyze the motion of test particles in the gravitational wave field. Next we consider related solutions of the Einstein equations for the gravitational field accompanied by long-range wave fields of scalar, spinor and vector type, corresponding to particles of spin s=(0,1/2,1). The motion of test masses in the combined gravitational and scalar, spinor or vector wave fields is discussed.
Generalized matter couplings to four-dimensional supersymmetric sigma models on general Kaehler manifolds are presented, preserving all holomorphic symmetries. Our generalization allows assignment of arbitrary U(1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted gamma_5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of a chiral scalar multiplet, the U(1) symmetry is broken spontaneously, generating a mass for the U(1) vector multiplet via the supersymmetric Higgs effect. As an example we discuss the case of the homogeneous coset space E6/SO(10) x U(1).
In this paper we consider classical point particles in full interaction with an arbitrary number of dynamical scalar and (abelian) vector fields. It is shown that the requirement of stability ---vanishing self-force--- is sufficient to remove the well-known inconsistencies of the classical theory: the divergent self-energy, as well as the failure of Lorentz-covariance of the energy-momentum when including the contributions of the fields. As a result, in these models the mass of a point particle becomes finitely computable. It is shown how these models are connected to quantum field theory via the path-integral representation of the propagator.
The spinorial local world-line $κ$-symmetry of the covariant Brink-Schwarz formulation of the 4-$D$ superparticle is abelian in an off-shell phase-space formulation. The result is shown to generalize to the extended spinorial transformations of the spinning superparticle.
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like those of black holes are discussed. Their properties are investigated by studying the geodesic structure of the corresponding space-times, as representing the motion of point-like test particles. The interaction between gravitational, electro-magnetic and scalar fields is also considered.
The world-line path-integral representation of fermion propagators is discussed. Particular attention is paid to the representation of $γ_5$, which is connected to the realization of manifest world-line supersymmetry.