Interpolating conformal algebra in (3+1) dimensions between the instant form and the light-front form of relativistic dynamics
Abstract
We extend the interpolation of the Poincaré algebra between instant form dynamics (IFD) and light-front dynamics (LFD) to the conformal algebra in (3+1) dimensions. Building upon our recent formulation of the interpolating conformal algebra in (1+1) dimensions, we propose an interpolation method for the conformal group SO(4,2). A central feature of this work is classifying the $15$ conformal generators into kinematic and dynamic categories as a function of the interpolation angle (0 ≤ δ≤ π/4). We show that among the five additional generators beyond the Poincaré group, the dilatation generator remains strictly kinematic across the entire interpolation region. We also find that in the exact light-front limit (δ= π/4), one additional generator from the Special Conformal Transformations (SCT) becomes kinematic in (1+1) but dynamical in (3+1). This behavior shows the advantage of LFD in maximizing kinematic generators and minimizing dynamical complexity. To support this algebraic framework, we construct a 6 × 6 interpolating projective spacetime matrix representation. We detail the explicit transformations of the interpolating time under all $15$ generators, providing a systematic view of conformal symmetry across the relativistic dynamics.
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BibTeX
@misc{ravikumar2026interpolating,
title = {{Interpolating conformal algebra in $(3+1)$ dimensions between the instant form and the light-front form of relativistic dynamics}},
author = {Hariprashad Ravikumar and Chueng-Ryong Ji},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36297},
eprint = {2609.36297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36297},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interpolating conformal algebra in (3+1) dimensions between the instant form and the light-front form of relativistic dynamics
AU - Hariprashad Ravikumar
AU - Chueng-Ryong Ji
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36297
UR - https://arxiv.org/abs/2609.36297
AB - We extend the interpolation of the Poincaré algebra between instant form dynamics (IFD) and light-front dynamics (LFD) to the conformal algebra in (3+1) dimensions. Building upon our recent formulation of the interpolating conformal algebra in (1+1) dimensions, we propose an interpolation method for the conformal group SO(4,2). A central feature of this work is classifying the $15$ conformal generators into kinematic and dynamic categories as a function of the interpolation angle (0 ≤ δ≤ π/4). We show that among the five additional generators beyond the Poincaré group, the dilatation generator remains strictly kinematic across the entire interpolation region. We also find that in the exact light-front limit (δ= π/4), one additional generator from the Special Conformal Transformations (SCT) becomes kinematic in (1+1) but dynamical in (3+1). This behavior shows the advantage of LFD in maximizing kinematic generators and minimizing dynamical complexity. To support this algebraic framework, we construct a 6 × 6 interpolating projective spacetime matrix representation. We detail the explicit transformations of the interpolating time under all $15$ generators, providing a systematic view of conformal symmetry across the relativistic dynamics.
ER -