Galilei Group and Nonrelativistic Quantum Mechanics

Journal Article · Sat Jun 01 04:00:00 EDT 1963 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1724319· OSTI ID:4688921

Levy-Leblond, Jean-Marc

The Galilei group and its representations are studied. The Galilei group presents a certain number of essential differences with respect to the Poincare group. As Bargmann showed, its physical representations, explicitly constructed, are not true representations but only up-toa-factor ones. Consequently, in nonrelativistic quantum mechanics, the mass has a very special role, and in fact, gives rise to a superselection rule that prevents the existence of unstable particles. The internal energy of a nonrelativistic system is known to be an arbitrary parameter; this is shown to come also from Galiiean invariance, because of a nontrivial concept of equivalence between physical representations. On the contrary, the behavior of an elementary system with respect to rotations, is very similar to the relativistic case. It is shown in particular, how the number of polarization states reduces to two for the zero- mass case. Finally, the two-particle system, where the orbital angular momenta quite naturally introduce themselves through the decomposition of the tensor product of two physical representations, is studied. (auth)

• Research Organization: Laboratoire de Physique Theorique et Hautes Energies, Orsay, France
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-031132
• OSTI ID: 4688921
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 4; ISSN JMAPAQ; ISSN 0022-2488
• Publisher: American Institute of Physics (AIP)
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANGULAR MOMENTUM
DECOMPOSITION
ENERGY
GALILEI GROUP
MASS
MATHEMATICS
MOMENTUM
ORBITS
PARTICLES
PHYSICS
POLARIZATION
QUANTUM MECHANICS
ROTATION
TENSORS
VECTORS