In this talk I briefly present recent developments in the theory of the Color Glass Condensate. The duality between the dense and dilute regimes of the gluon field is discussed as well as the effective selfdual Hamiltonian which includes both Pomeron merging and Pomeron splitting. Introduction: high energy limit and the Pomeron One of the central problems in the theory of strong interactions is...

In the preceding papers (see [1, 2]), the superfluidity of the classical liquid was proved under the assumption that the parameters N and r, where N is the particle number and r it the capillary radius, tend respectively to infinity and to zero so that 1 N ≪ r R , where R is the capillary length. In the present paper, this assumption is removed. 1. We first note that solutions of the variationa...

We consider branes N in a Schwarzschild-AdS(n+2) bulk, where the stress energy tensor is dominated by the energy density of a scalar fields map φ : N → S with potential V , where S is a semiRiemannian moduli space. By transforming the field equation appropriately, we get an equivalent field equation that is smooth across the singularity r = 0, and which has smooth and uniquely determined soluti...

Schnabl recently found an analytic expression for the string field tachyon condensate using a gauge condition adapted to the conformal frame of the sliver projector. We propose that this construction is more general. The sliver is an example of a special projector, a projector such that the Virasoro operator L0 and its BPZ adjoint L0 obey the algebra [L0,L0] = s(L0 + L0), with s a positive real...

contains many of the features of the Dirac theory. The theory of spin-s free particles has been also developed by Proca [4], Kemmer [5] and Bargmann and Wigner [6]. All of these formalisms for spin-s free particles have many intrinsic contradictions and difficulties when an electromagnetic field interaction is introduced (see [7] and references therein). It should be noted that the mathematical...

A lagrangian for relativistic fluid systems with matters inside is developed using gauge principle. In the model, the gauge boson represents the fluid field in a form Aμ ≡ ǫμ φ, where ǫμ contains the fluid kinematics and φ is an auxiliary field representing the fluid distribution. This leads to a new relativistic equation of motion for fluid, but which further coincides to the classical Euler e...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

In a space-time M with a Killing vector field ξa which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of ξa gives a 3-dimensional space S. Besides the symmetry-reduced action from that of Einstein-Hilbert, an alternative action of the fields on S is also proposed which gives the same fields equations as those reduced from the vacuum Einstein equation o...

of which the second requires α > 1 to exist biologically. When α < 1 the first is stable; it is unstable when the second exist, which in such a case is stable. To get further insight we look at the isoclines, i.e., the curves where the trajectories are parallel to one of the axes. In this case the equation s′ = 0 corresponds to the curve b = (s0 − s) 1+s s and the equation b′ = 0 to straignt li...