A variational perturbation scheme for many-particle systems in the functional integral approach

A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the thermodynamic potential is established. A modified Wick's theorem is obtained for the variational perturbation expansions. This theorem allows one to carry out systematic calculations of higher order terms without worrying about the double counting problem. A model numerical calculation was carried out on a nucleon gas system interacting through the Yukawa-type potential to test the efficiency of the present method.Comment: accepted for publication in Phys. Rev.

Rayleigh-Schroedinger-Goldstone variational perturbation theory for many fermion systems

We present a Rayleigh-Schroedinger-Goldstone perturbation formalism for many fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with respect to the renormalized interaction using Goldstone's expansion. Perturbation rules for the ground state wavefunctional and energy are found. Useful commuting relations between operators and the Gaussian wavefunctional are also found, which could reduce the calculational efforts substantially. As examples, we calculate the first order correction to the Gaussian wavefunctional and the second order correction to the ground state of an electron gas system with the Yukawa-type interaction.Comment: 11pages, 1figur

A Study on Virtual Reality Storytelling by Story Authoring Tool Algorithm

The objective of this study was to examine the storytelling principles of virtual reality contents, which are recently grabbing much attention, and the patterns of their generation rules and, based on the results, to analyze the elements and structure of a storytelling method suitable for virtual reality contents. In virtual reality environment, a story is usually being generated between choices made by a user who behaves autonomously under simulated environmental factors and the environmental constraints. This corresponds to a mutually complementary role of representation and simulation, which has been hotly discussed in the field of interactive storytelling. This study was conducted based on the assumption that such a mutually complementary realization is ideal for virtual reality storytelling. A simulation-based story authoring tool is a good example that shows this mutual complementation, in that it develops a story through various algorithms which involves the interaction of agents which occur within the strata of a virtual environment. Therefore, it can be a methodology for virtual reality storytelling. The structures and elements of narratives used in virtual reality storytelling which achieve balance of representation and simulation are much similar to an algorithm strategy of a simulation-based story authoring tool. The virtual reality contents released up to now can be classified into four categories based on the two axes of representation and simulation. The study focused on contents which are layered in higher strata of both representation and simulation. In the perspective of representation strata, these contents are actively using such elements as goal, event, action, perception, internal element, outcome, and setting element, which are constituents of ‘Fabula model’, to generate time relations and cause-effect relations. And in the perspective of simulation strata, the use of the ‘Late commitment’ strategy allowed users to understand the meanings of their actions taken during the process of experimenting with various dynamic principles within the environment