Scientists / Open questions

Yoichiro Nambu

Particle physics; spontaneous symmetry breaking

2008 Nobel Prize in Physics

20 questions

Consistency, Induced Schwinger Term, and Finite-Temperature Thermodynamics of Axial-Vector Current Condensation in Spontaneously Broken Current Algebras
Consistent infinite-component wave equations with hydrogenlike mass spectra: existence of a theory free of spacelike solutions, PCT asymmetry, spin-statistics loosening, and nonlocal currents
Uncontrolled elements of the Mukerjee–Nambu BCS collective-mode derivation of the Interacting Boson Model: diagram-dependent finite-size factor, momentum-dependent π/σ couplings, minimal fermion valence space, density-mode coupling, and particle-number projection limits
Nambu's quasi-supersymmetry of BCS-type effective Hamiltonians: origin of the factorization, rules for the superpotential, and diagrammatic derivation
Quantum completion of Nambu's two-form Hamilton–Jacobi formalism for strings and its non-abelian extension
Nucleon axial-vector form factor from threshold pion electroproduction: controlled finite-pion-mass corrections and the behavior of $G_A(Q^2)$ at multi-GeV momentum transfer
Solvability of Nambu's coupled, manifestly renormalized spectral-function equations for Green's functions of interacting quantum fields
The charmonium $\rho\pi$ puzzle and the gluonic vector meson $O$ : the dynamical origin of Zweig-Iizuka-rule violation in $J/\psi\to\rho\pi$
Nonlocal separable inverse scattering for the $^4$ He– $^4$ He interaction: extension beyond the $s$ wave and off-shell validation against a realistic local potential
Simultaneous complete factorization, gauge invariance, and realistic $W_1$ in electromagnetic dual schemes for hadrons
Exact solution of the three-dimensional Ising transfer-matrix eigenvalue problem: the quartic-form obstruction left open by Nambu's anticommuting-vector method
First-principles derivation of the confining string from QCD: Nambu's path-ordered phase-factor constraint program and its unresolved core
Explicit construction of the two-photon vertex in Nambu-Tuan's gauge-invariant theory of the magnetic-field dependence of the superconducting energy gap
The Freund–Nambu trace-coupled scalar: consistent quantization, SU(3) and spin-2 completion, and the realization of scalar-meson dominance of the trace of the energy-momentum tensor
The quantization problem of Nambu mechanics (Nambu's generalized Hamiltonian dynamics)
Open questions from the double phase representation: constant total cross sections, elastic unitarity, and singularities in the complex angular-momentum plane
Empirical status and theoretical basis of Nambu's 1952 mass quantization at multiples of the unit $\alpha^{-1}m_e$ (about 70 MeV)
Validity and well-posedness of Nambu's generalized Hartree-Fock theory of superconductivity: omitted diagrams beyond weak coupling and existence of solutions of the nonlocal Eliashberg-Nambu equations
Do higher-order spectral-function identities determine the renormalization constants $Z_2$ , $Y_2$ , and $Z_3$ in the pseudoscalar meson theory after $Z_1=0$ ?
Completing Nambu's general-order spectral representation of Green's functions: existence, canonical uniqueness, and constructive determination of the real spectral functions in interacting quantum field theory

Back to open problems

Consistency, Induced Schwinger Term, and Finite-Temperature Thermodynamics of Axial-Vector Current Condensation in Spontaneously Broken Current Algebras

Consistent infinite-component wave equations with hydrogenlike mass spectra: existence of a theory free of spacelike solutions, PCT asymmetry, spin-statistics loosening, and nonlocal currents

Uncontrolled elements of the Mukerjee–Nambu BCS collective-mode derivation of the Interacting Boson Model: diagram-dependent finite-size factor, momentum-dependent π/σ couplings, minimal fermion valence space, density-mode coupling, and particle-number projection limits

Nambu's quasi-supersymmetry of BCS-type effective Hamiltonians: origin of the factorization, rules for the superpotential, and diagrammatic derivation

Quantum completion of Nambu's two-form Hamilton–Jacobi formalism for strings and its non-abelian extension

Nucleon axial-vector form factor from threshold pion electroproduction: controlled finite-pion-mass corrections and the behavior of GA(Q2)G_A(Q^2)GA​(Q2) at multi-GeV momentum transfer

Solvability of Nambu's coupled, manifestly renormalized spectral-function equations for Green's functions of interacting quantum fields

The charmonium ρπ\rho\piρπ puzzle and the gluonic vector meson OOO: the dynamical origin of Zweig-Iizuka-rule violation in J/ψ→ρπJ/\psi\to\rho\piJ/ψ→ρπ

Nonlocal separable inverse scattering for the 4^44He–4^44He interaction: extension beyond the sss wave and off-shell validation against a realistic local potential

Simultaneous complete factorization, gauge invariance, and realistic W1W_1W1​ in electromagnetic dual schemes for hadrons

Exact solution of the three-dimensional Ising transfer-matrix eigenvalue problem: the quartic-form obstruction left open by Nambu's anticommuting-vector method

First-principles derivation of the confining string from QCD: Nambu's path-ordered phase-factor constraint program and its unresolved core

Explicit construction of the two-photon vertex in Nambu-Tuan's gauge-invariant theory of the magnetic-field dependence of the superconducting energy gap

The Freund–Nambu trace-coupled scalar: consistent quantization, SU(3) and spin-2 completion, and the realization of scalar-meson dominance of the trace of the energy-momentum tensor

The quantization problem of Nambu mechanics (Nambu's generalized Hamiltonian dynamics)

Open questions from the double phase representation: constant total cross sections, elastic unitarity, and singularities in the complex angular-momentum plane

Empirical status and theoretical basis of Nambu's 1952 mass quantization at multiples of the unit α−1me\alpha^{-1}m_eα−1me​ (about 70 MeV)

Validity and well-posedness of Nambu's generalized Hartree-Fock theory of superconductivity: omitted diagrams beyond weak coupling and existence of solutions of the nonlocal Eliashberg-Nambu equations

Do higher-order spectral-function identities determine the renormalization constants Z2Z_2Z2​, Y2Y_2Y2​, and Z3Z_3Z3​ in the pseudoscalar meson theory after Z1=0Z_1=0Z1​=0?

Completing Nambu's general-order spectral representation of Green's functions: existence, canonical uniqueness, and constructive determination of the real spectral functions in interacting quantum field theory

Nucleon axial-vector form factor from threshold pion electroproduction: controlled finite-pion-mass corrections and the behavior of $G_A(Q^2)$ at multi-GeV momentum transfer

The charmonium $\rho\pi$ puzzle and the gluonic vector meson $O$ : the dynamical origin of Zweig-Iizuka-rule violation in $J/\psi\to\rho\pi$

Nonlocal separable inverse scattering for the $^4$ He– $^4$ He interaction: extension beyond the $s$ wave and off-shell validation against a realistic local potential

Simultaneous complete factorization, gauge invariance, and realistic $W_1$ in electromagnetic dual schemes for hadrons

Empirical status and theoretical basis of Nambu's 1952 mass quantization at multiples of the unit $\alpha^{-1}m_e$ (about 70 MeV)

Do higher-order spectral-function identities determine the renormalization constants $Z_2$ , $Y_2$ , and $Z_3$ in the pseudoscalar meson theory after $Z_1=0$ ?