The paper presents a study of gluon distribution functions for very large nuclei at small transverse momentum. The authors show that these functions can be computed as correlation functions of an ultraviolet finite two-dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in α_s. The gluon distribution function is proportional to 1/x, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum. The authors argue that in a limited range of transverse momentum, for small values of Bjorken x, quark and gluon distribution functions for very large nuclei can be evaluated as the solution of a weakly coupled many-body theory. This result relies on light cone quantization. When a parameter μ² is much larger than the QCD scale Λ_QCD², the strong coupling α_s(μ²) is small. For x << A^{-1/3}, valence quarks can be replaced by delta functions of charge along the light cone. The gluon distribution function is computed to lowest order in weak coupling to be proportional to 1/(x q_t²). The physical picture is that the Weizsacker-Williams distribution is generated by random fluctuations in the charge per unit area. The approximation of small x guarantees that the central region gluons see a source of valence quarks much smaller than a typical gluon wavelength. This is the deeply screened region, where Lipatov enhancements of the gluon distribution function are expected to modify the Bjorken x dependence of the distribution function. The problem is to compute the distribution function of gluons in the presence of static sources of color charge localized along the light cone and uniform in transverse space. The external current due to the source is represented as a delta function along the light cone. The nucleus can be broken into regions of transverse spatial extent such that the number of valence quarks in each region is large. This allows the sources of charge to be treated as classical. The authors show that the correlation function which gives the gluon distribution function can be expressed as a two-dimensional Euclidean correlation function of an ultraviolet finite field theory. Summing to all orders in α_s²μ² modifies the q_t distribution function. However, to all orders in this expansion, the gluon distribution function is proportional to 1/x. The problem is therefore a simple one: If we want to compute a ground state correlation function, we can do it by the path integral that is equivalent to integrating the path integral for fixed charge around a Gaussian fluctuating charge at each point in space. The approximation that we may treat the source as classical is only true in the limit where the spatial regions we are looking at have a large number of quarks in them. The authors assume that this is also the case in this paper.The paper presents a study of gluon distribution functions for very large nuclei at small transverse momentum. The authors show that these functions can be computed as correlation functions of an ultraviolet finite two-dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in α_s. The gluon distribution function is proportional to 1/x, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum. The authors argue that in a limited range of transverse momentum, for small values of Bjorken x, quark and gluon distribution functions for very large nuclei can be evaluated as the solution of a weakly coupled many-body theory. This result relies on light cone quantization. When a parameter μ² is much larger than the QCD scale Λ_QCD², the strong coupling α_s(μ²) is small. For x << A^{-1/3}, valence quarks can be replaced by delta functions of charge along the light cone. The gluon distribution function is computed to lowest order in weak coupling to be proportional to 1/(x q_t²). The physical picture is that the Weizsacker-Williams distribution is generated by random fluctuations in the charge per unit area. The approximation of small x guarantees that the central region gluons see a source of valence quarks much smaller than a typical gluon wavelength. This is the deeply screened region, where Lipatov enhancements of the gluon distribution function are expected to modify the Bjorken x dependence of the distribution function. The problem is to compute the distribution function of gluons in the presence of static sources of color charge localized along the light cone and uniform in transverse space. The external current due to the source is represented as a delta function along the light cone. The nucleus can be broken into regions of transverse spatial extent such that the number of valence quarks in each region is large. This allows the sources of charge to be treated as classical. The authors show that the correlation function which gives the gluon distribution function can be expressed as a two-dimensional Euclidean correlation function of an ultraviolet finite field theory. Summing to all orders in α_s²μ² modifies the q_t distribution function. However, to all orders in this expansion, the gluon distribution function is proportional to 1/x. The problem is therefore a simple one: If we want to compute a ground state correlation function, we can do it by the path integral that is equivalent to integrating the path integral for fixed charge around a Gaussian fluctuating charge at each point in space. The approximation that we may treat the source as classical is only true in the limit where the spatial regions we are looking at have a large number of quarks in them. The authors assume that this is also the case in this paper.