SIUC Physics Seminar
School of Physics and Applied Physics, Southern Illinois University--Carbondale
2026 March 20 Friday 4:00 PM:
Physics Seminar in Neckers 440
Title: Hyperbolic angular momentum
Speaker: Jackson Lewis
Affiliation: Southern Illinois University--Carbondale
Abstract:
In this work we investigate the structure of angular momentum through
the oscillator realization introduced by Schwinger, in which the generators
of the \(su(2)\) algebra arise from pairs of harmonic oscillator ladder operators.
Within this framework an additional set of operators appears naturally
which satisfies the \(su(1,1)\) algebra, a structure which Schwinger refers
to as hyperbolic angular momentum. We first present a graphical visualization
of the Schwinger oscillator basis that clarifies and illustrates the action
of both the standard angular momentum ladder operators and the hyperbolic operators.
In this picture the usual \(su(2)\) ladder operators move within a fixed irreducible
representation of angular momentum, while the \(su(1,1)\) ladder operators move between
these irreducible representations of angular momentum and within a fixed
irreducible representation of hyperbolic angular momentum. As an application of
this structure, we present Schwinger's algebraic derivation of the allowed
values of the total angular momentum in the coupling of two spin systems,
obtaining the bounds without appealing to the usual dimension-counting argument.
Biography:
Jackson Lewis is a second year M.S. student in mathematics and physics at SIU.
Before that, he received a B.S. in mathematics from Austin Peay State University
in Clarksville, TN. At SIU, Jackson's research falls into the broad area of
mathematical physics, focusing on algebraic studies of quantum mechanics and
representation theory. Jackson is also the founder of the SIU Quantum Gravity Study Group,
where faculty and students of the math and physics departments meet to discuss
the mathematics and physics relevant to the covariant formulation of Loop Quantum Gravity.
Last updated on
by K V Shajesh
(kvshajesh@gmail.com).