Quantum Charge as a Particle/Antiparticle Label
Abstract
We show that the concept of particles and antiparticles is related to the Weyl-Heisenberg group W H3. Its generators are the position operators x̂a, the momentum operators p̂a, and the central element Qsfv, which defines a subgroup U(1)sf v of W H3. We show that the wave functions have a charge relative to the group U(1)sfv equal to either q+=1/ℏ (particle ψ+) or q-=−1/ℏ (antiparticle ψ-). We call these eigenvalues of the operator Qsfv quantum charges: Qsfvψ±=q±ψ±. The wave functions ψ+ and ψ- belong to the Hilbert spaces ℋ+ and ℋ-, on which unitarily inequivalent representations πℏ and π−ℏ of the Weyl-Heisenberg group W H3 are defined. These representations are related to each other by the antilinear charge conjugation operator Ĉ, which maps ℋ+, q+ to ℋ-, q-. Charges q± are intrinsic characteristics of the wave functions ψ±, similar to spin and electric charge. The wave function possesses one of these charges, q+ or q-, prior to the specification of any equations. We show that negative probabilities/energies and the Klein paradox in Klein-Gordon and Dirac theories are consequences of the violation of U(1)sf v-invariance in these theories. Restoring this invariance separates particle and antiparticles and eliminates all paradoxes at the level of first-quantized relativistic theories.
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BibTeX
@misc{popov2026quantum,
title = {{Quantum Charge as a Particle/Antiparticle Label}},
author = {Alexander D. Popov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29791},
eprint = {2610.29791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29791},
}
RIS
TY - UNPB
TI - Quantum Charge as a Particle/Antiparticle Label
AU - Alexander D. Popov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29791
UR - https://arxiv.org/abs/2610.29791
AB - We show that the concept of particles and antiparticles is related to the Weyl-Heisenberg group W H_3. Its generators are the position operators x̂^a, the momentum operators p̂_a, and the central element Q_sfv, which defines a subgroup U(1)_sf v of W H_3. We show that the wave functions have a charge relative to the group U(1)_sfv equal to either q_+=1/ℏ (particle ψ_+) or q_-=−1/ℏ (antiparticle ψ_-). We call these eigenvalues of the operator Q_sfv quantum charges: Q_sfvψ_±^=q_±^ψ_±^. The wave functions ψ_+ and ψ_- belong to the Hilbert spaces ℋ_+ and ℋ_-, on which unitarily inequivalent representations π_ℏ and π_−ℏ of the Weyl-Heisenberg group W H_3 are defined. These representations are related to each other by the antilinear charge conjugation operator Ĉ, which maps ℋ_+, q_+ to ℋ_-, q_-. Charges q_±^ are intrinsic characteristics of the wave functions ψ_±^, similar to spin and electric charge. The wave function possesses one of these charges, q_+ or q_-, prior to the specification of any equations. We show that negative probabilities/energies and the Klein paradox in Klein-Gordon and Dirac theories are consequences of the violation of U(1)_sf v-invariance in these theories. Restoring this invariance separates particle and antiparticles and eliminates all paradoxes at the level of first-quantized relativistic theories.
ER -