Information channel capacity in the field theory estimation

The construction of the information capacity for the vector position parameter in the Minkowskian space-time is presented. This lays the statistical foundations of the kinematical term of the Lagrangian of the physical action for many field theory models, derived by the extremal physical information method of Frieden and Soffer.

💡 Research Summary

The paper establishes a rigorous information‑theoretic foundation for the kinetic term of the Lagrangian that appears in a wide class of field‑theoretic models. Starting from the premise that space‑time coordinates (x^\mu) ((\mu=0,1,2,3)) can be treated as a vector parameter (\theta^\mu) of a statistical model, the author constructs the Fisher information matrix (g_{\mu\nu}(\theta)) for the conditional probability density (p(y|\theta)). Because the underlying geometry is Minkowski with metric (\eta_{\mu\nu}= \mathrm{diag}(1,-1,-1,-1)), the Fisher matrix is not positive‑definite; its signature mirrors that of space‑time. To obtain a scalar measure of the information that can be transmitted through this “channel”, the author defines the information channel capacity
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