The global SU (3) invariance is broken to a subgroup H in QCD
Abstract
I show that the global SU (3) invariance is broken to a subgroup H in QCD by quantization. Here H = U 2 • ES 3 (2.8) is the trivial symmetry group of the triplet colored quark fields, the product of Symmetric Group S 3 interchanging R, G, B quark fields combined with the U (1) phase factor for each field. The reason is quite simple and obvious. The existence of quanta after quantization is incompatible with the full non-Abelian SU (3) invariance. One argues "The conservation of SU (3) quantum Noether currents implies SU (3) invariance of QCD after quantization." This is wrong. Conserved Noether currents are the necessary condition of quantum SU (3) invariance but not sufficient. H invariance implies the same SU (3) Noether currents conservation. Thus QCD as SU (3) invariant quantum field theory does not exist. The same argument applies to any quantum field theory with Lie group (gauge) symmetry which mixes multiple fields.
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BibTeX
@misc{sasaki2026global,
title = {{The global SU (3) invariance is broken to a subgroup H in QCD}},
author = {Ryu Sasaki},
howpublished = {HAL},
year = {2026},
month = jul,
url = {https://hal.science/hal-05735039v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The global SU (3) invariance is broken to a subgroup H in QCD
AU - Ryu Sasaki
PY - 2026
DA - 2026/07/28
PB - HAL
UR - https://hal.science/hal-05735039v1
AB - I show that the global SU (3) invariance is broken to a subgroup H in QCD by quantization. Here H = U 2 • ES 3 (2.8) is the trivial symmetry group of the triplet colored quark fields, the product of Symmetric Group S 3 interchanging R, G, B quark fields combined with the U (1) phase factor for each field. The reason is quite simple and obvious. The existence of quanta after quantization is incompatible with the full non-Abelian SU (3) invariance. One argues "The conservation of SU (3) quantum Noether currents implies SU (3) invariance of QCD after quantization." This is wrong. Conserved Noether currents are the necessary condition of quantum SU (3) invariance but not sufficient. H invariance implies the same SU (3) Noether currents conservation. Thus QCD as SU (3) invariant quantum field theory does not exist. The same argument applies to any quantum field theory with Lie group (gauge) symmetry which mixes multiple fields.
ER -