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This research aims to derive the spectral density of the memory kernel in History-Dependent Gravity using functional renormalization.

August 12, 2026Open Access

Emergent Spectral Density from Functional Renormalization (Paper LXX)

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Randomized trial demonstrates emergent spectral density in a memory kernel, suggesting a shift in gravitational models.

This research aims to derive the spectral density of the memory kernel in History-Dependent Gravity using functional renormalization.
Solve the Wetterich equation for the complex resolvent using a scalar-channel truncation with Litim regulator.
Extract spectral density via Källén-Lehmann representation.
Establish a no-go theorem regarding reconstruction of spectral density from local functionals.
Emergence of spectral density from zero ultraviolet initial condition, confirming dynamic generation by RG flow.
Universality of the ratio R* = μ*/M₂^(1/4) = 1.71 ± 0.01 across UV conditions with 0.5% relative stability.
Strict positivity of spectral density established without local polynomial projection.

Alik Gimranov (2026) studied this question.

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