Degenerate Systems and Mass Singularities
1964/03/23 by T. D. Lee, M. Nauenberg, Michael Nauenberg · 1,411 citations
Mathematics · Physics and Astronomy · #Degenerate energy levels #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Power series #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Quantum electrodynamics #Quantum mechanics #Series (stratigraphy) #Zero (linguistics)
paper · doi:10.1103/physrev.133.b1549
published in Physical Review 133(6B), B1549-B1562 (American Institute of Physics)
openalex publication_date 1964/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract
For a system with degenerate energies, the power series expansions of the S-matrix elements may become singular. An elementary theorem in quantum mechanics is proved which shows that under certain general conditions such singularities do not appear in the power series expansions of the transition probabilities, provided these are averaged over an appropriate ensemble of degenerate states. Application of this theorem leads to the cancellations of mass singularities and infrared divergences in quantum electrodynamics. The question of whether a charged particle can have zero mass is studied.
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