This is a part of the Advanced Mechanics course MA2341. These notes are partially based on the textbook “Mechanics” by L.D. Landau and E.M. Lifshitz. ∗Email: [email protected] † Correspondent fellow at Steklov Mathematical Institute, Moscow.

We show that a low-energy action for massless fluctuations around a tachyonic soliton background representing a codimension one D-brane coincides with the Dirac-Born-Infeld action. The scalar modes which describe transverse oscillations of the D-brane are translational collective coordinates of the soliton. The appearance of the DBI action is a universal feature independent of details of a tach...

In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals logL 2π . In this paper we find an exact analytic expression for the finite part of the spectral density. This function allows one to calculate finite parts of variou...

We compute the Boundary Superstring Field Theory partition function on the annulus in the presence of independent linear tachyon profiles on the two boundaries. The R-R sector is found to contribute non-trivially to the derivative terms of the space-time effective action. In the process we construct a boundary state description of D-branes in the presence of a linear tachyon. We quantize the op...

Let M n M^n be a smooth compact manifold with boundary. We show that for generic ...

We prove wavenumber-explicit bounds on the Dirichlet-to-Neumann map for the Helmholtz equation in the exterior of a bounded obstacle when one of the following three conditions holds: (i) the exterior of the obstacle is smooth and nontrapping, (ii) the obstacle is a nontrapping polygon, (iii) the obstacle is star-shaped and Lipschitz. We prove bounds on the Neumann-to-Dirichlet map when one of c...

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism ...

Within front-form dynamics and in the Breit frame where initial and final three-momenta of the system are directed along the z axis, Poincaré covariance constrains the current operator only through kinematical rotations around the z axis. Therefore, in this frame the current can be taken in the one-body form. Applications to deep inelastic structure functions in an exactly solvable model and to...