Interpolating conformal algebra in $(1+1)$ dimensions between the instant form and the light-front form of relativistic dynamics

Abstract

We present the interpolating conformal algebra between the instant form dynamics (IFD) and the light-front dynamics (LFD) in $(1+1)$ dimensions, along with a $4\times 4$ interpolating projective spacetime matrix representation. While there are six generators in the $(1+1)$ dimensional conformal algebra, the number of kinematic and dynamic generators dramatically changes in LFD, maximizing (minimizing) the number of kinematic (dynamic) generators to four (two) with respect to two (four) kinematic (dynamic) generators in IFD, as well as in any other forms of dynamics between IFD and LFD. It confirms and signifies the utility of LFD, saving substantial dynamical efforts in solving the $(1+1)$ dimensional quantum field theories. We also present $2\times 2$ Pauli matrix representation of $(1+0)$ and $(0+1)$ conformal groups, and creation/annihilation operators of quantum simple harmonic oscillator representations of $(1+0)$ dimensional conformal groups.

14 pages, 9 tables

References in corpus (8)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Light-Front Holographic QCD and Emerging Confinement
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Interpolating Scattering Amplitudes between Instant Form and Front Form of Relativistic Dynamics
• Poincare Invariant Algebra From Instant to Light-Front Quantization
• The Electromagnetic Gauge Field Interpolation between the Instant Form and the Front Form of the Hamiltonian Dynamics
• Interpolating Helicity Spinors Between the Instant Form and the Light-front Form
• Interpolating Quantum Electrodynamics between Instant and Front Forms