Light-Front Quantization of Field Theory

TL;DR

This paper reviews key aspects of Light-Front quantized field theory, discussing Poincaré algebra, spin operators, and the implications of non-local Hamiltonians for phenomena like spontaneous symmetry breaking and anyon dynamics.

Contribution

It introduces a non-local Hamiltonian framework on the Light-Front that captures spontaneous symmetry breaking and provides a new approach to quantizing Chern-Simons gauge theory for anyons.

Findings

Non-local Hamiltonian describes spontaneous symmetry breaking on the LF.

Instability of symmetric phase in 2D scalar theory at strong coupling.

LF Hamiltonian for Chern-Simons gauge theory enables potential construction of anyon theories.

Abstract

Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincar\`e algebra and the LF Spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons.