Question: Who introduced a map that was used by a Nobel Prize winning physicist to work out the theory of quantum angular momentum?

Context paragraphs:
Angular momentum diagrams (quantum mechanics): In quantum mechanics and its applications to quantum many-particle systems, notably quantum chemistry, angular momentum diagrams, or more accurately from a mathematical viewpoint angular momentum graphs, are a diagrammatic method for representing angular momentum quantum states of a quantum system allowing calculations to be done symbolically.  More specifically, the arrows encode angular momentum states in bra–ket notation and include the abstract nature of the state, such as tensor products and transformation rules.

Angular momentum operator: In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum.  The angular momentum operator plays a central role in the theory of atomic physics and other quantum problems involving rotational symmetry.  In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.

Stern–Gerlach experiment: The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized.  It demonstrated that atomic-scale systems have intrinsically quantum properties, and that measurement in quantum mechanics affects the system being measured.  In the original experiment, silver atoms were sent through a non-uniform magnetic field, which deflected them before they struck a detector screen.  Other kinds of particles can be used.  If the particles have a magnetic moment related to their spin angular momentum, the magnetic field gradient deflects them from a straight path.  The screen reveals discrete points of accumulation rather than a continuous distribution, owing to the quantum nature of spin.  Historically, this experiment was decisive in convincing physicists of the reality of angular momentum quantization in all atomic-scale systems.

Photomagneton: The photomagneton is a theoretical treatment of the unitary group in quantum field theory and quantum chemistry that effectively describes the experimentally observed inverse Faraday effect.  When circularly polarized light travels through a plasma, the angular momentum associated to the circular motion of the photons induces an angular momentum in the electrons of the plasma.  This angular momentum induces an associated magnetic field.

Jordan map: In theoretical physics, the Jordan map, often also called the Jordan–Schwinger map is a map from matrices M to bilinear expressions of quantum oscillators which expedites computation of representations of Lie Algebras occurring in physics.  It was introduced by Pascual Jordan in 1935 and was utilized by Julian Schwinger in 1952 to re-work out the theory of quantum angular momentum efficiently, given that map’s ease of organizing the (symmetric) representations of su(2) in Fock space.

Rotational transition: A rotational transition is an abrupt change in angular momentum in quantum physics.  Like all other properties of a quantum particle, angular momentum is quantized, meaning it can only equal certain discrete values, which correspond to different rotational energy states.  When a particle loses angular momentum, it is said to have transitioned to a lower rotational energy state.  Likewise, when a particle gains angular momentum, a positive rotational transition is said to have occurred.

Total angular momentum quantum number: In quantum mechanics, the total angular momentum quantum number parameterises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).

Angular momentum coupling: In quantum mechanics, the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta is called angular momentum coupling.  For instance, the orbit and spin of a single particle can interact through spin–orbit interaction, in which case the complete physical picture must include spin-orbit coupling.  Or two charged particles, each with a well-defined angular momentum, may interact by Coulomb forces, in which case coupling of the two one-particle angular momenta to a total angular momentum is a useful step in the solution of the two-particle Schrödinger equation.

Beta decay transition: A Fermi transition or a Gamow–Teller transition are types of nuclear beta decay determined by changes in angular momentum or spin.  In the Fermi transition, the spins of the emitted particles are antiparallel, coupling to formula_1, so the angular momentum of the initial and final angular momentum states of the nucleus are unchanged (formula_2).  This is in contrast to a Gamow-Teller transition, where the spins of the emitted electron (positron) and antineutrino (neutrino) couple to total spin formula_3, leading to an angular momentum change formula_4 between the initial and final angular momentum states of the nucleus.

Julian Schwinger: Julian Seymour Schwinger (February 12, 1918 – July 16, 1994) was a Nobel Prize winning American theoretical physicist.  He is best known for his work on the theory of quantum electrodynamics (QED), in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order.  Schwinger was a physics professor at several universities.

Supporting paragraphs: Jordan map Julian Schwinger
Answer: Pascual Jordan