5059816
Cosmological sector for localized mass and spin in 2+1 dimensional topologically massive gravity
Abstract The cosmological sector to the full non-linear topologically massive gravity (TMG) is obtained for localized sources of mass m and spin σ besides the asymptotically spinning conical flat sector previously obtained [A. Edery, M.B. Paranjape, gr-qc/9606029, to be published]. In a small region near but outside the sources, the metric resembles the spinning conical flat metric but we find that the mass m creates a negative deficit angle of 3 m as opposed to m . Furthermore, it is not possible to recover the results of pure Einstein gravity in the limit μ →∞ unlike the flat sector.
18809373
Spontaneous symmetry breaking and the renormalization of the Chern-Simons term
We calculate the one-loop perturbative correction to the coefficient of the Chern-Simons term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual U(1) symmetry, radiative corrections do not change the coefficient of the Chern-Simons term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant Chern-Simons term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the Chern-Simons term is a discontinuous function over the phase diagram of the theory.
123600595
CONFORMAL GRAVITY AND GRAVITATIONAL WAVES
We consider monochromatic, plane gravitational waves in a conformally invariant theory of general relativity. We show that the simple, standard ansatz for the metric, usually that which is taken for the linearized theory of these waves, is reducible to the metric of Minkowski spacetime via a sequence of conformal and coordinate transformations. This implies that we have in fact, exact plane wave solutions. However they are simply coordinate/conformal artifacts. As a consequence, they carry no energy.
115618345
Quantization of anomalous gauge theories: The chiral Schwinger model
We implement the proposal of Faddeev and quantize the anomalous, chiral Schwinger model. We carry out a Schrodinger representation quantization,on a circle, in the Hamiltonian formulation. We make a special emphasis to uncover the structure of the fermionic Hilbert bundle over the space of gauge fields. We find that although a unitary and consistent quantum field theory is obtained, Lorentz invariance is lost.
119355228
Recent mathematical developments in the Skyrme model
Abstract In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of the model. Then we review the instanton method which yields an analytical approximation to the minimum energy configuration in any sector of fixed baryon number, as well as an approximation to the surfaces which join together all the low energy critical points. We present some explicit results for B =2. We then describe the work done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theory. Next we turn to recent work on the dynamics of Skyrmions. We focus exclusively on the low energy interaction, specifically the gradient flow method put forward by Manton. We illustrate the method with some expository toy models. We end this review with a presentation of our own work on the semi-classical quantization of nucleon states and low energy nucleon–nucleon scattering.
12785921
Low energy Skyrmion-Skyrmion scattering.
We study the scattering of two Skyrmions at low energy and large separation. We use the method proposed by Manton for truncating the degrees of freedom of the system from infinite to a manageable finite number. This corresponds to identifying the manifold consisting of the union of the low energy critical points of the potential along with the gradient flow curves joining these together and by positing that the dynamics is restricted here. The kinetic energy provides an induced metric on this manifold while restricting the full potential energy to the manifold defines a potential. The low energy dynamics is now constrained to these finite number of degrees of freedom. For a large separation of the two Skyrmions the manifold is parametrized by the variables of the product ansatz. We find the interaction between two Skyrmions coming from the induced metric, which was independently found by Schroers. We find that the static potential is actually negligible in comparison to this interaction. Thus to lowest order, at large separation, the dynamics reduces to geodesic motion on the manifold. We consider the scattering to first order in the interaction using the perturbative method of Lagrange and find that the dynamics in themore » no spin or charge exchange sector reduces to the Kepler problem.« less
117870436
Halo bias in the excursion set approach with correlated steps
In the excursion set approach, halo abundances and clustering are closely related. This relation is exploited in many modern methods which seek to constrain cosmological parameters on the basis of the observed spatial distribution of clusters. However, to obtain analytic expressions for these quantities, most excursion-set-based predictions ignore the fact that, although different k modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a non-trivial way. We show that when the excursion set approach is extended to include such correlations, then one must be careful to account for the fact that the associated prediction for halo bias is explicitly a real-space quantity. Therefore, care must be taken while comparing the predictions of this approach with measurements in simulations, which are typically made in Fourier space. We show how to correct for this effect, and demonstrate that ignorance of this effect in recent analyses of halo bias has led to incorrect conclusions and biased constraints.