We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates. We find that the field mode which in perturbation theory has a ghostlike kinetic term, turns into a t
achyon when nonlinear interaction is accounted for. The kinetic term and potential for this mode have opposite signs. Solutions of nonlinear classical equations of motion develop a singularity in finite time determined by the initial conditions.
We describe an effective theory of a scalar field, motivated by some features expected in the low energy theory of gluodynamics in 3+1 dimensions. The theory describes two propagating massless particles in a certain limit, which we identify with the
Abelian QED limit, and has classical string solutions in the general case. The string solutions are somewhat unusual as they are multiply degenerate due to spontaneous breaking of diffeomorphism invariance. Nevertheless all solutions yield identical electric field and have the same string tension.
We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator. We also point out that the normalizable vacuum state
(in the sense defined below) of this model can be understood as spontaneous breaking of the emergent conformal symmetry. We provide an example of an interacting system that couples the particle and ghost degrees of freedom and nevertheless remains unitary on both classical and quantum level.
We present a general, model independent argument demonstrating that gluons produced in high energy hadronic collision are necessarily correlated in rapidity and also in the emission angle. The strength of the correlation depends on the process and on
the structure/model of the colliding particles. In particular we argue that it is strongly affected (and underestimated) by factorized approximations frequently used to quantify the effect.
We investigate the relation between the eigenvalues and eigenfunctions of the BFKL and JIMWLK/KLWMIJ Hamiltonians. We show that the eigenvalues of the BFKL Hamiltonians are also {it exact} eigenvalues of the KLWMIJ (and JIMWLK) Hamiltonian, albeit co
rresponding to possibly non normalizable eigenfunctions. The question whether a given eigenfunction of BFKL corresponds to a normalizable eigenfunction of KLWMIJ is rather complicated, except in some obvious cases, and requires independent investigation. As an example to illustrate this relation we concentrate on the color octet exchange in the framework of KLWMIJ Hamiltonian. We show that it corresponds to the reggeized gluon exchange of BFKL, and find first correction to the BFKL wave function, which has the meaning of the impact factor for shadowing correction to the reggeized gluon. We also show that the bootstrap condition in the KLWMIJ framework is satisfied automatically and does not carry any additional information to that contained in the second quantized structure of the KLWMIJ Hamiltonian. This is an example of how the bootstrap condition inherent in the t-channel unitarity, arises in the s-channel picture.
The high energy evolution equations that describe the evolution of hadronic amplitudes with energy are derived assuming eikonal interaction of the evolved hadronic wave function with the target. In this note we remark that this derivation allows a di
fferent interpretation, whereby the hadronic wave function is not evolved, but instead the evolution acts on the S - matrix operator. In this approach, analogous to the Heisenberg picture of Quantum mechanics, the scattering is not eikonal and additional boost provides for radiation of more gluons in the final state.
