Screening Anatomy of the Heat Kernel: From One-Body Projections to Multi-Body Spectral Content

@misc{dechery2026screening,
  title = {{Screening Anatomy of the Heat Kernel: From One-Body Projections to Multi-Body Spectral Content}},
  author = {Fabien Déchery},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05841411v1},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - Screening Anatomy of the Heat Kernel: From One-Body Projections to Multi-Body Spectral Content
AU  - Fabien Déchery
PY  - 2026
DA  - 2026/10/08
PB  - HAL
UR  - https://hal.science/hal-05841411v1
AB  - The heat kernel K(τ) = Tr(e^−τ 𝒟^2) of the self-consistent chiral soliton encodes all baryon observables as spectral projections, with systematic deficits ranging from <2% (mass, Class A) to 38% (magnetic moment, Class C). We perform a spectral anatomy of these deficits in the nucleon magnetic moment, using the proper-time decomposition to map the boundary between one-body projections of K(τ) and multi-body spectral content. Seven results are established. First, the isovector magnetic form factor G_M^T=1 has a UV-dominated one-body budget (75\% UV) that rebalances to 47/53 UV/IR after inclusion of the (N_c+2)/N_c algebraic factor from collective quantization and the leading meson exchange current estimate, yielding μ_p = 2.70 n.m. (−3.3%). Second, the isoscalar magnetic form factor G_M^T=0,quark vanishes exactly through a double cancellation specific to the magnetic operator γ^0 γ^k: radial orthogonality within the same angular channel and angular orthogonality across channels. This operator selectivity distinguishes the magnetic zero (G_M^T=0 = 0, Class D) from the non-zero axial isoscalar (g_A^(0) ≈ 0.2--$0.33$), establishing that the screening structure depends on the Dirac bilinear of the insertion, not merely on isospin. Third, the vanishing of the one-body contribution provides a calibration bound: the residual μ^T=0 − μ^T=0_bos = 0.13--$0.19$ n.m. measures pure inter-sector corrections in a channel where the mean-field contribution is rigorously zero. Fourth, the proper-time spectral response δ K(τ) is computed in 3+1D via the Friedel phase-shift method and compared with the Koopman screening measure Δ K; the two quantities probe complementary content (one-body Dirac shift vs inter-sector boson-fermion correlations), with anti-correlated profiles in the 1+1D benchmark. Fifth, the self-consistent profile F^* is shown to be a stationary point of the heat kernel functional: the proper-time-weighted integral of the linear spectral susceptibility vanishes, and the leading screening beyond the one-body projection is quadratic in the bosonic fluctuations, proportional to the meson propagator G_π; the Class B and C deficits are thereby shown to be structurally irreducible at the fixed point within the mean-field framework. Sixth, the quantitative reconstruction of the bosonic fluctuations via the normal-mode expansion of the quadratic susceptibility (20 quenched modes) yields corrections that worsen the agreement with experiment (Δ g_A ≈ −12%), establishing by exclusion that the Class B and C deficits arise from inter-sector meson exchange currents, not from mean-field profile fluctuations. Seventh, the Soler 1D benchmark confirms chaotic dynamics in non-integrable soliton collisions (λ_max > 0, 14/14 cases) and establishes a three-scale spectral hierarchy γ_PR ≲ λ_max ≲ α_dyn ≪ ω^2 whose monotone ordering parallels the deficit hierarchy (Classes A--D), with the spectral modification rate governed by the mass gap; this provides a dynamical mechanism for the correlation between infrared spectral weight and deficit magnitude observed in the 3+1D soliton. The Goldberger--Treiman spectral analysis closes the Class B deficit: center-of-mass and meson exchange current corrections, mapped to zero and non-zero modes of the Koopman operator, yield g_A ≈ 1.28 --- within 1% of experiment ($1.267$) --- and cascade to τ_β ≈ 864 s (−1.6%), promoting both observables to Class A; combined with the (N_c+2)/N_c recovery for μ_p, eleven of the fourteen observables in Table S9.1 are within 5% of experiment with zero adjustable parameters. Together, these results establish a triple screening structure---isospin × operator × spectral depth---that the deficit hierarchy encodes as a diagnostic of the one-body projection of K(τ).
ER  -