TY - JOUR

T1 - Quantum origin of (Newtonian) mass and Galilean relativity symmetry

AU - Kong, Otto C.W.

N1 - Publisher Copyright:
© 2023 The Physical Society of the Republic of China (Taiwan)

PY - 2023/6

Y1 - 2023/6

N2 - The Galilei group has been taken as the fundamental symmetry for ‘nonrelativistic’ physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the full picture here, emphasizing aspects that are different from the more familiar picture. The analysis involves a more careful treatment of the relation between the exact mathematics and its physical application in the dynamical theories, and a more serious full implementation of the mathematical logic than what is usually available in the physics literature. The article summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant and the notion of center of mass as dictated by the symmetry, that is particularly also to be seen as the Heisenberg–Weyl symmetry inside it. Another result is the necessary exclusion of the time translational symmetry. The time translational symmetry in the Galilei group plays no role in the formulation of the dynamical theory and does not correspond to the physical time in any nontrivial setting.

AB - The Galilei group has been taken as the fundamental symmetry for ‘nonrelativistic’ physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the full picture here, emphasizing aspects that are different from the more familiar picture. The analysis involves a more careful treatment of the relation between the exact mathematics and its physical application in the dynamical theories, and a more serious full implementation of the mathematical logic than what is usually available in the physics literature. The article summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant and the notion of center of mass as dictated by the symmetry, that is particularly also to be seen as the Heisenberg–Weyl symmetry inside it. Another result is the necessary exclusion of the time translational symmetry. The time translational symmetry in the Galilei group plays no role in the formulation of the dynamical theory and does not correspond to the physical time in any nontrivial setting.

KW - (Quantum) relativity symmetry

KW - Casimir invariants

KW - Composite systems as symmetry representations

KW - Particle mass

UR - http://www.scopus.com/inward/record.url?scp=85154038260&partnerID=8YFLogxK

U2 - 10.1016/j.cjph.2023.01.008

DO - 10.1016/j.cjph.2023.01.008

M3 - 期刊論文

AN - SCOPUS:85154038260

SN - 0577-9073

VL - 83

SP - 337

EP - 345

JO - Chinese Journal of Physics

JF - Chinese Journal of Physics

ER -