Boundary three-point function on AdS2 D-branes

Using the H3+-Liouville relation, I explicitly compute the boundary three-point function on AdS2 D-branes in H3+, and check that it exhibits the expected symmetry properties and has the correct geometrical limit. I then find a simple relation between this boundary three-point function and certain fusing matrix elements, which suggests a formal correspondence between the AdS2 D-branes and discrete representations of the symmetry group. Concluding speculations deal with the fuzzy geometry of AdS2 D-branes, strings in the Minkowskian AdS3, and the hypothetical existence of new D-branes in H3+.Comment: 27 pages, v2: significant clarifications added in sections 4.3 and

Gravitational Scattering in the ADD-model Revisited

Gravitational scattering in the ADD-model is studied and it is argued that no cut-off is needed for the exchange of virtual Kaluza--Klein modes. By introduction of a small coordinate in the extra dimensions a unique form of the Kaluza--Klein-summed propagator is found for an odd number of extra dimensions. The matrix element corresponding to this propagator can also (as opposed to the cut-offed version) be Fourier transformed to position space, giving back the extra-dimensional version of Newton's law. For an even number of extra dimensions the propagator is found by requiring that Newton's law should be recovered

Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.Comment: 12 pages and 1 figur

Generalised Factorial Moments and QCD Jets

{ In this paper we present a natural and comprehensive generalisation of the standard factorial moments (\clFq) analysis of a multiplicity distribution. The Generalised Factorial Moments are defined for all $q$ in the complex plane and, as far as the negative part of its spectrum is concerned, could be useful for the study of infrared structure of the Strong Interactions Theory of high energy interactions (LEP multiplicity distribution under the ${\cal Z}_0$). The QCD calculation of the Generalised Factorial Moments for negative $q$ is performed in the double leading log accuracy and is compared to OPAL experimental data. The role played by the infrared cut-off of the model is discussed and illustrated with a Monte Carlo calculation. }Comment: 11pages 4 figures uuencode, LATEC, INLN 94/

Generalized Bernstein--Reznikov integrals

We find a closed formula for the triple integral on spheres in $\mathbb{R}^{2n}\times\mathbb{R}^{2n}\times\mathbb{R}^{2n}$ whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein--Reznikov integral formula in the $n=1$ case. Our method also applies for linear and conformal structures

Light-Front Quantisation as an Initial-Boundary Value Problem

In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional conditions the problem of solving the field equations becomes well posed. The consequences for quantisation are studied within a Hamiltonian formulation by using the method of Faddeev and Jackiw for dealing with first-order Lagrangians. For the prototype field theory of massive scalar fields in 1+1 dimensions, we find that initial conditions for fixed light cone time {\sl and} boundary conditions in the spatial variable are sufficient to yield a consistent commutator algebra. Data on a second lightlike hyperplane are not necessary. Hamiltonian and Euler-Lagrange equations of motion become equivalent; the description of the dynamics remains canonical and simple. In this way we justify the approach of discretised light cone quantisation.Comment: 26 pages (including figure), tex, figure in latex, TPR 93-

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phy

Two-loop self-dual Euler-Heisenberg Lagrangians (II): Imaginary part and Borel analysis

We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lagrangian for a constant self-dual background. The novel feature of the two-loop result, compared to one-loop, is that the prefactor of each exponential (instanton) term in the imaginary part has itself an asymptotic expansion. We also perform a high-precision test of Borel summation techniques applied to the weak-field expansion, and find that the Borel dispersion relations reproduce the full prefactor of the leading imaginary contribution.Comment: 28 pp, 6 eps figure

On the connectedness structure of the Coulomb S -matrix

The forward direction singularity of the non-relativistic Coulomb S -matrix is examined and discussed. The relativistic Coulomb S -matrix to order α is shown to have a similar singularity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46508/1/220_2005_Article_BF01646192.pd

Metastability Driven by Soft Quantum Fluctuation Modes

The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which makes a saddle for the action, is derived in terms of Jacobian elliptic functions whose periodicity establishes the one-to-one correspondence between energy of the classical motion and temperature (inverse imaginary time) of the system. The quantum fluctuation contribution has been computed through the theory of the functional determinants for periodic boundary conditions. The decay rate shows a peculiar temperature dependence mainly due to the softening of the low lying quantum fluctuation eigenvalues. The latter are determined by solving the Lam\`{e} equation which governs the fluctuation spectrum around the time dependent classical bounce.Comment: Journal of Low Temperature Physics (2008) Publisher: Springer Netherland