Modern Physics Letters A

Milgrom has proposed that the appearance of discrepancies between the Newtonian dynamical mass and the directly observable mass in astronomical systems could be due to a breakdown of Newtonian dynamics in the limit of low accelerations rather than the presence of unseen matter. Milgrom's hypothesis, modified Newtonian dynamics or MOND, has been remarkably successful in explaining systematic properties of spiral and elliptical galaxies and predicting in detail the observed rotation curves of spiral galaxies with only one additional parameter — a critical acceleration which is on the order of the cosmologically interesting value of cH₀. Here we review the empirical successes of this idea and discuss its possible extension to cosmology and structure formation.

A coupling-constant definition is given based on the compositeness property of some particle states with respect to the elementary states of other particles. It is applied in the context of the vector-spin-1/2-particle interaction vertices of a field theory, and the standard model. The definition reproduces Weinberg's angle in a grand-unified theory. One obtains coupling values close to the experimental ones for appropriate configurations of the standard-model vector particles, at the unification scale within grand-unified models, and at the electroweak breaking scale.

The gauge-fixed action of a "spacetime-filling" D3-brane with dilaton–axion coupling is formulated in N=1 superspace. We investigate its symmetries by paying special attention to a possible nonlinearly realized extra supersymmetry, and emphasize the need of a linear superfield coupled to an Abelian Chern–Simons superfield to represent a dilaton–axion supermultiplet in the off-shell manifestly supersymmetric approach.

It is shown that, to the lowest order in ℏ, the particle production related to the tunneling that leads to the false vacuum decay is described by the orthogonal part of fluctuation field with respect to the bounce solution. As a simple example the spatially homogeneous tunneling is considered in order to illustrate the consequences coming from such a restriction of the fluctuation field.

An exactly solvable, two-parameter implicit quantum mechanical potential is derived and characterized. With a change of variable, this potential is shown to belong to the Natanzon class, and for at least one value of the potential parameters, an explicit, rather than implicit, potential results.

We briefly introduce the concept of Euler–Lagrange cohomology groups on a symplectic manifold (ℳ²ⁿ, ω) and systematically present the general form of volume-preserving equations on the manifold from the cohomological point of view. It is shown that for every volume-preserving flow generated by these equations there is an important two-form that plays the analog role with the Hamiltonian in the Hamilton mechanics. In addition, the ordinary canonical equations with Hamiltonian H are included as a special case with the two-form . The other volume preserving systems on (ℳ²ⁿ, ω) are studied. The relations between our approach and Feng–Shang's volume-preserving systems as well as the Nambu mechanics are also explored.

We derive an exact equation for simple self non-intersecting Wilson loops in non-Abelian gauge theories with gauge fields interacting with fermions in two-dimensional Euclidean space.