The structure of Green functions in quantum field theory with a general state

In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.Comment: 13 pages, 6 figure

Screening in Space: Rich and Poor Consumers in a Linear City

Unlike standard models of monopolistic screening (second-degree price discrimination), we consider a situation where consumers are heterogeneous not only vertically, in their willingness to pay, but also horizontally, in their tastes or "addresses'' a la Hotelling's Linear City. For such a screening game, a novel model is composed. We formulate the game as an optimization program, prove the existence of equilibria, develop a method to calculate equilibria, and characterize their properties. Namely, the solution structure of the resulting menu of contracts can be either a "chain of envy'' like in usual screening or a number of disconnected chains. Unlike usual screening, "almost all'' consumers get positive informational rent. Importantly, the model can be extended to oligopoly screening.The authors are grateful to Pavel Ilinov, Igor Bykadorov, Mikhail Martyanov,Pavel Molchanov for discussions and help in checking the proofs. The study was financed by the HSE University Basic Research. Program

Degenerate Landau-Zener model: Exact analytical solution

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1