International Journal of Modern Physics A

A review of recent results on large-scale structure and galaxy formation in a model with hot dark matter and cosmic strings is given. With cosmic strings seeding perturbations, many of the arguments against hot dark matter disappear. It is shown that spherical accretion about loops leads to dark matter haloes with flat velocity rotation curves. Velocity perturbations due to wakes behind long, moving strings lead to a network of planar overdensities with a distinguished scale of slightly less than 40×40 Mpc². If the mass per unit length μ exceeds a certain bound, then the wakes become nonlinear by the present time. In this case, their thickness can be calculated.

We combine a zeta-function definition and heat-kernel series to derive Casimir energy expansions parametrizing the UV divergences in the presence of arbitrarily shaped smooth boundaries. Their terms, in the form of a geometrical object times a divergence, allow for drawing conclusions on the scale dependence and on the finiteness of the vacuum energy when limiting surfaces have been introduced. Different behaviors are found depending, among other factors, on the even or odd character of the space dimension. A number of controversial points are cleared up and some misstatements in the literature are properly rigorized.

Starting from a geometrical and polynomial first-order formalism of supergravity, linear in the Riemann curvature, we construct a higher curvature supergravity which has also a polynomial Lagrangian. Next, by means of the resulting torsion equation, we show that it is possible to obtain the second order formalism which exhibits a nonpolynomial structure. The nonpolynomial second order formalism can be confronted and related to the massless sector of effective superstring field theories. This is done in the Hamiltonian framework.

The 3-string vertex for the non-critical string theory is constructed and is shown to be BRST invariant at D < 26.

We compute the generating functional of currents in the bosonic as well as supersymmetric Wess-Zumino-Witten (WZW) model and in some of its (compact and noncompact) coset spaces. We discuss correlation functions of currents defined on a (super) Riemann surface.

Arbitrary (1, 1) and (1.0) two-dimensional nonlinear σ-models, modified by the addition of coupling terms which explicitly break supersymmetry, are studied. The geometrical meaning of these additional terms is discussed. Supergraph methods, suitably extended to include the case of broken supersymmetry, are set and employed in explicit higher-loop computations to keep track of the effect that the explicit breaking of supersymmetry has on the ultraviolet behavior of the originally supersymmetric models.

This is a critical review of the literature on many-worlds interpretations, MWI, with arguments drawn partly from earlier critiques by Bell and Stein. The essential postulates involved in various MWI are extracted, and their consistency with the evident physical world is examined. Arguments are presented against MWI proposed by Everett, Graham and DeWitt. The relevance of frequency operators to MWI is examined; it is argued that frequency operator theorems of Hartle and Farhi-Goldstone-Gutmann do not in themselves provide a probability interpretation for quantum mechanics, and thus neither support existing MWI nor would be useful in constructing new MWI. Comments are made on papers by Geroch and Deutsch that advocate MWI. It is concluded that no plausible set of axioms exists for an MWI that describes known physics.

The role of inverse scattering method is illustrated to examine the connection between the multi-soliton solutions of Korteweg-de Vries (KdV) equation and discrete eigenvalues of Schrödinger equation. The necessity of normalization of the Schrödinger wave functions, which are constructed purely from a supersymmetric consideration is pointed out.

In the frame of the Lindblad theory of open quantum systems, the spherical harmonic oscillator with opening operators linear in the coordinates and the momenta of the considered system is analyzed. Explicit expressions for the damping of the energy, angular momentum and its projection, including the coupling of the harmonic oscillator due to the environment, are obtained.

The strong coupling phase of massless Quantum Electrodynamics is studied in a gauge invariant way. The formalism is given in which the order parameter of the chiral symmetry breaking is calculated through the vacuum polarization diagrams. Applying this method, the critical coupling constant is shown to exist that is independent of the gauge parameter but is now dependent on the ratio of the two kinds of cutoff. Implication of this new parameter on the renormalization scheme in the strong coupling phase is discussed.

The work of A.K.N.S. which is based on the sl(2, R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations. This is achieved by assuming the soliton connection having values in a simple Lie, Kac-Moody, Lie superalgebras. Extensions of some of the integrable nonlinear partial differential equations are given explicitly. In particular the coupled NLS equations on various homogeneous spaces and the coupled modified KdV integro-differential equations are obtained on symmetric spaces.

We present a classical field theory of interacting loops, whose low energy limit is D=4, N=1 supergravity. In Fourier modes, the theory is obtained by gauging the infinite dimensional algebra KM (SuperPoincaré) ⊕ Virasoro, where KM indicates the Kac-Moody extension. Taylor expanding the superloop vielbein in the “internal” coordinates yields towers of D=4 fields with arbitrarily high spins. The superloop diffeomorphisms relate all the higher spin fields. The field equations are obtained by requiring the closure of the generalized supersymmetries. Two different mechanisms give rise to masses for the higher modes: (i) a Kaluza-Klein type mass generation from “internal” loop coordinates, (ii) a non-vanishing background value for the zero mode of the Virasoro gauge field.