Scientists / Open questions

Julian Schwinger

Quantum field theory; quantum electrodynamics

1965 Nobel Prize in Physics

22 questions

Completing Schwinger's 1962 radiation-gauge construction of non-Abelian gauge fields: explicit evaluation of the short-distance correction functions and proof of the trace rearrangement theorem
Impulsive energy decay at a displaced lattice atom: robustness of Schwinger's 1990 phonon-dynamics predictions beyond the separable, narrow-band model
Large-coupling behavior of Schwinger's asymptotic functions for the photon propagation function: the spectral weight function, the phase function, the Gell-Mann-Low function, and the mapping between them
Dynamical, gauge-invariant mass generation for vector gauge fields in realistic four-dimensional theories: the open core of Schwinger's 1962 'Gauge Invariance and Mass' question
Finiteness of the bare charge in quantum electrodynamics: the strong-coupling asymptotics of the photon spectral weight function and the Gell-Mann-Low function
Schwinger's source-theoretic double spectral account of deep inelastic scattering: anomalous negative- $M_-^2$ spectral support, the $h_2$ cutoff ansatz, the $M_0$ mass-scale hypothesis, and the modified scaling variable $\omega_S$
Schwinger pair production in general strong time-dependent electromagnetic fields: exact nonperturbative rate and self-consistent backreaction
Schwinger's $\nu\to\infty$ problem for unitary operator bases: characterizing the physically meaningful states and operators admitting a uniform continuous-spectrum limit
The unresolved mathematical foundations of Schwinger's Euclidean quantum electrodynamics: rigorous existence of the interacting theory (canonical eigenstates, indefinite-metric Lorentz-gauge operator formulation, and the functional-integral measure)
Spin-coherence restoration after Stern–Gerlach splitting: the deferred quantum-field account of the apparatus and the fundamental limits on field-gradient reproducibility
Microscopic foundations of the Lifshitz Casimir formalism for real materials: the atomic-scale cutoff in Casimir surface energies (surface tension and latent heat)
Rigorous spatial point-splitting evaluation of the Casimir self-stress on a perfectly conducting spherical shell
Determine the sharp constant in the Cwikel-Lieb-Rozenblum bound on the number of bound states of a three-dimensional Schrodinger operator
Completing the large- $Z$ expansion of the neutral atom's total binding energy: the oscillatory fourth term and the definitive relativistic supplement
Completing the strong-coupling theory of the charged scalar mesotron field: intermediate coupling, recoil and gauge invariance, spin, and the unfinished canonical-transformation treatment (Schwinger, 1970)
Equal-time commutation relations of the current and stress tensor in interacting quantum field theory: completing Schwinger's 1963 program (Schwinger terms and the no-time-derivative assumptions)
Dyon-dyon scattering: closed-form summation of the nonrelativistic partial-wave series and the relativistic quantum scattering theory of magnetically charged particles
Completing the source-theoretic Casimir effect: first-principles finite-temperature propagation functions and transient boundary effects
Quantum consistency of the canonical gravitational field: well-defined energy and boost generators and the anomaly-free closure of Schwinger's 1963 tetrad constraint algebra
Exact nonperturbative one-loop QED effective action for arbitrarily space-time varying external electromagnetic fields
The all-orders infrared problem for charged-particle scattering in quantum electrodynamics: infrared-finite observables beyond Schwinger's 1949 second-order radiative corrections
Completing the physical foundations of Schwinger's algebra of microscopic measurement: a dynamics that reproduces the measurement symbolism, and the matter-antimatter meaning of complex numbers

Back to open problems

Completing Schwinger's 1962 radiation-gauge construction of non-Abelian gauge fields: explicit evaluation of the short-distance correction functions and proof of the trace rearrangement theorem

Impulsive energy decay at a displaced lattice atom: robustness of Schwinger's 1990 phonon-dynamics predictions beyond the separable, narrow-band model

Large-coupling behavior of Schwinger's asymptotic functions for the photon propagation function: the spectral weight function, the phase function, the Gell-Mann-Low function, and the mapping between them

Dynamical, gauge-invariant mass generation for vector gauge fields in realistic four-dimensional theories: the open core of Schwinger's 1962 'Gauge Invariance and Mass' question

Finiteness of the bare charge in quantum electrodynamics: the strong-coupling asymptotics of the photon spectral weight function and the Gell-Mann-Low function

Schwinger's source-theoretic double spectral account of deep inelastic scattering: anomalous negative-M−2M_-^2M−2​ spectral support, the h2h_2h2​ cutoff ansatz, the M0M_0M0​ mass-scale hypothesis, and the modified scaling variable ωS\omega_SωS​

Schwinger pair production in general strong time-dependent electromagnetic fields: exact nonperturbative rate and self-consistent backreaction

Schwinger's ν→∞\nu\to\inftyν→∞ problem for unitary operator bases: characterizing the physically meaningful states and operators admitting a uniform continuous-spectrum limit

The unresolved mathematical foundations of Schwinger's Euclidean quantum electrodynamics: rigorous existence of the interacting theory (canonical eigenstates, indefinite-metric Lorentz-gauge operator formulation, and the functional-integral measure)

Spin-coherence restoration after Stern–Gerlach splitting: the deferred quantum-field account of the apparatus and the fundamental limits on field-gradient reproducibility

Microscopic foundations of the Lifshitz Casimir formalism for real materials: the atomic-scale cutoff in Casimir surface energies (surface tension and latent heat)

Rigorous spatial point-splitting evaluation of the Casimir self-stress on a perfectly conducting spherical shell

Determine the sharp constant in the Cwikel-Lieb-Rozenblum bound on the number of bound states of a three-dimensional Schrodinger operator

Completing the large-ZZZ expansion of the neutral atom's total binding energy: the oscillatory fourth term and the definitive relativistic supplement

Completing the strong-coupling theory of the charged scalar mesotron field: intermediate coupling, recoil and gauge invariance, spin, and the unfinished canonical-transformation treatment (Schwinger, 1970)

Equal-time commutation relations of the current and stress tensor in interacting quantum field theory: completing Schwinger's 1963 program (Schwinger terms and the no-time-derivative assumptions)

Dyon-dyon scattering: closed-form summation of the nonrelativistic partial-wave series and the relativistic quantum scattering theory of magnetically charged particles

Completing the source-theoretic Casimir effect: first-principles finite-temperature propagation functions and transient boundary effects

Quantum consistency of the canonical gravitational field: well-defined energy and boost generators and the anomaly-free closure of Schwinger's 1963 tetrad constraint algebra

Exact nonperturbative one-loop QED effective action for arbitrarily space-time varying external electromagnetic fields

The all-orders infrared problem for charged-particle scattering in quantum electrodynamics: infrared-finite observables beyond Schwinger's 1949 second-order radiative corrections

Completing the physical foundations of Schwinger's algebra of microscopic measurement: a dynamics that reproduces the measurement symbolism, and the matter-antimatter meaning of complex numbers

Schwinger's source-theoretic double spectral account of deep inelastic scattering: anomalous negative- $M_-^2$ spectral support, the $h_2$ cutoff ansatz, the $M_0$ mass-scale hypothesis, and the modified scaling variable $\omega_S$

Schwinger's $\nu\to\infty$ problem for unitary operator bases: characterizing the physically meaningful states and operators admitting a uniform continuous-spectrum limit

Completing the large- $Z$ expansion of the neutral atom's total binding energy: the oscillatory fourth term and the definitive relativistic supplement