One gluon, two gluon: multigluon production via high energy evolution

We develop an approach for calculating the inclusive multigluon production within the JIMWLK high energy evolution. We give a formal expression of multigluon cross section in terms of a generating functional for arbitrary number of gluons $n$. In the dipole limit the expression simplifies dramatically. We recover the previously known results for single and double gluon inclusive cross section and generalize those for arbitrary multigluon amplitude in terms of Feynman diagramms of Pomeron - like objects coupled to external rapidity dependent field $s(\eta)$. We confirm the conclusion that the AGK cutting rules in general are violated in multigluon production. However we present an argument to the effect that for doubly inclusive cross section the AGK diagramms give the leading contribution at high energy, while genuine violation only occurs for triple and higher inclusive gluon production. We discuss some general properties of our expressions and suggest a line of argument to simplify the approach further.Comment: 32 pages, one reference corrected. to appear in JHE

Fermionic Operators from Bosonic Fields in 3+1 Dimensions

We present a construction of fermionic operators in 3+1 dimensions in terms of bosonic fields in the framework of $QED_4$. The basic bosonic variables are the electric fields $E_i$ and their conjugate momenta $A_i$. Our construction generalizes the analogous constuction of fermionic operators in 2+1 dimensions. Loosely speaking, a fermionic operator is represented as a product of an operator that creates a pointlike charge and an operator that creates an infinitesimal t'Hooft loop of half integer strength. We also show how the axial $U(1)$ transformations are realized in this construction.Comment: 8 pages, two figures available on request, LA-UR-94-286

SUSY 3D Georgi-Glashow model at finite temperature

We study the finite-temperature properties of the supersymmetric version of (2+1)D Georgi-Glashow model. As opposed to its nonsupersymmetric counterpart, the parity symmetry in this theory at zero temperature is spontaneously broken by the bilinear photino condensate. We find that as the temperature is raised, the deconfinement and the parity restoration occur in this model at the same point $T_c=g^2/8\pi$. The transition is continuous, but is not of the Ising type as in nonsupersymmetric Georgi-Glashow model, but rather of the Berezinsky-Kosterlitz-Thouless type as in $Z_4$-invariant spin model.Comment: 8 pages, LaTeX2e, no figure

Bosonization in 2+1 dimensions without Chern - Simons attached

We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The fermion operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify the regularization procedure involved in the definition of these operators, and calculate the fermionic bilinears and the energy - momentum tensor. The algebra of bilinears exhibits the Schwinger terms which also appear in perturbation theory. The bosonic Hamiltonian density is a local polynomial function of $A_i$ and $E_i$, and we check explicitly the Lorentz invariance of the resulting bosonic theory. Our construction is conceptually very similar to Mandelstam's construction in 1+1 dimensions, and is dissimilar from the recent bosonization attempts in 2+1 dimensions which hinge crucially on the existence of a Chern - Simons term.Comment: 12 pages, LA-UR-93-1062, some misprints and algebraic errors corrected, several comments adde

From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy

We derive the evolution of a hadronic light cone wave function with energy at weak coupling. Our derivation is valid both in the high and the low partonic density limit, and thus encompasses both the JIMWLK and the KLWMIJ evolution. The hadronic wave function is shown to evolve by the action of the Bogoliubov-type operator, which diagonalizes on the soft gluon sector the light-cone hamiltonian in the presence of an arbitrary valence charge density. We find explicitly the action of this operator on the soft as well as the valence degrees of freedom of the theory.Comment: 30 page

The Higgs field and the ultraviolet behaviour of the vortex operator in 2+1 dimensions

We calculate the change in the ultraviolet behaviour of the vortex operator due to the presence of dynamical Higgs field in both 2+1 dimensional QED and the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the presence of the Higgs field leads at the one loop level to power like correction to the propagator of the vortex operator. On the other hand, in the Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex propagator. Thus, as long as the mass of the Higgs field is much larger than the gauge coupling constant, the ultraviolet behaviour of the vortex operator in the Georgi-Glashow model is independent of the Higgs mass.Comment: 14 page

Fermions from photons: Bosonization of QED in 2+1 dimensions

We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify the regularization procedure involved in the definition of these operators, and calculate the fermionic bilinears and the energy - momentum tensor. The algebra of bilinears exhibits the Schwinger terms which also appear in perturbation theory. The bosonic Hamiltonian is a local, polynomial functional of $A_i$ and $E_i$, and we check explicitly the Lorentz invariance of the resulting bosonic theory. Our construction is conceptually very similar to Mandelstam's construction in 1+1 dimensions, and is dissimilar from the recent bosonization attempts in 2+1 dimensions, which hinge crucially on the presence of a Chern - Simons term.Comment: 30 pages, LA - UR - 93 - 200

The Yin and Yang of High Energy Chromodynamics: Scattering in Black and White

We further discuss the QCD Reggeon field theory (RFT) as it emerges from the JIMWLK/KLWMIJ evolution equation and beyond. We give an explicit expression for the calculation of scattering amplitude in terms of the eigenstates of the RFT Hamiltonian. We point out that the spectrum of RFT is doubly degenerate, the degeneracy being related to the spontaneous breaking of the Dense-Dilute Duality symmetry of RFT. The degeneracy is between the "almost white" states (the Yang sector) which contain a small number of gluons, and "almost black" states (the Yin sector). The excitations above the Yang vacuum have natural interpretation in terms of gluons. Analogously the excitations above the Yin vacuum have natural interpretation as "holes" in the black disk - points at which an incoming gluon does not scatter with unit probability. We discuss in detail the spectrum of the "parton model approximation" to the KLWMIJ evolution introduced in our previous paper, and prove that it is explicitly selfdual. This allows us to find explicitly the counterpart hole states in this approximation. We also present an argument to the effect that the end point of the evolution for any physical state cannot be a "grey disk" but must necessarily be the "black disk" Yin vacuum state. Finally, we suggest an approximation scheme for including the Pomeron loop contribution to the evolution which requires only the solution of the JIMWLK/KLWMIJ Hamiltonian.Comment: 25 pages, 1 figur