Conceptual problems in quantum field theory

Abstract

We review some conceptual problems in quantum field theory, with an emphasis on exact results and open problems.We review some conceptual problems in quantum field theory, with an emphasis on exact results and open problems. The review is organized as follows: 1. The Stückelberg -Bogoliubov -Shirkov -Epstein -Glaser S(g) operator. A brief review of perturbative results, including the adiabatic limit. Open problems: the infrared problem in QCD and its relation to gauge invariance. The problem of convergence and asymptotic character of the S-matrix series: the problem of large coupling. Problems with the series for (large and) small coupling: definition and triviality.2. Nonperturbative results and problems: Triviality of the S matrix and nonperturbative construction of S(g) . Open problems.

The role of positivity and causality in interactions involving higher spin

“…Of special interest is the relation of the modular conjugation J with the TCP operator which is known to be connected to the S-Matrix [69]. This is particularly useful in d = 1 + 1 integrable models whose S-matrix is known (62).…”

O Campo de Radiação Quantizado sob Vínculos Macroscópicos e a Pressão de Casimir no Calibre de Coulomb

“…Assim, nosso ponto de partidaé o procedimento cânonico usual baseado na definição do produto normal, i.e., do produto de Wick. Este programa foi realizado pela primeira vez para a densidade energia considerando o campo escalar sob o vínculo de Dirichlet [1,[4][5][6][7][8][9].…”

O Campo de Radiação Quantizado sob Vínculos Macroscópicos e a Pressão de Casimir no Calibre de Coulomb

“…Assim, nosso ponto de partida é o procedimento cânonico usual baseado na definição do produto normal, i.e., do produto de Wick. Este programa foi realizado pela primeira vez para a densidade energia considerando o campo escalar sob o vínculo de Dirichlet [1,[4][5][6][7][8][9].…”