Toward a finite-dimensional formulation of quantum field theory

Vladimir Naroditsky

Guang-jiong Ni, Jianjun Xu, Wei Chen

The authors present a new formulation of the two-fluid model, the thermal coherent state for handling the relativistic quantum field theory at finite temperature. Three models in one-dimensional space, the phi 4 , sine-Gordon and the Schwinger model, are discussed.

T.M. Samols

G. Rivlis

Suzanne Lanéry

Instead of formulating the states of a Quantum Field Theory (QFT) as density matrices over a single large Hilbert space, it has been proposed by Kijowski [Kijowski, 1977] to construct them as consistent families of partial density matrices, the latter being defined over small 'building block' Hilbert spaces. In this picture, each small Hilbert space can be physically interpreted as extracting from the full theory specific degrees of freedom. This allows to reduce the quantization of a classical field theory to the quantization of finite-dimensional sub-systems, thus sidestepping some of the common ambiguities (specifically, the issues revolving around the choice of a 'vacuum state'), while obtaining robust and well-controlled quantum states spaces. The present letter provides a self-contained introduction to this formalism, detailing its motivations as well as its relations to other approaches to QFT (such as conventional Fock-like Hilbert spaces, path-integral quantization, and the algebraic formulation). At the same time, it can serve as a reading guide to the series of more in-depth articles [arXiv:1411.3589, arXiv:1411.3590, arXiv:1411.3591, arXiv:1510.01926].

Eric Laenen