Pressure-Energy Equations of State of the Nucleon

TL;DR

This paper derives pressure-energy equations of state for the nucleon from gravitational form factors, revealing fundamental relations involving QCD confinement, superconductors, and cosmology.

Contribution

It introduces a unified framework for pressure-energy relations in nucleons, linking QCD, superconductivity, and cosmological models.

Findings

Static pressure equals minus the trace part of energy density.

Dynamic pressure from traceless stress tensor is proportional to energy density.

Pressure-energy relations are consistent across QCD, superconductors, and cosmology.

Abstract

The pressure-energy equations of state in the nucleon are derived from the gravitational form factors, which parameterize matrix elements of the energy-momentum tensor (EMT), together with EMT conservation. There are two distinct components in the pressure and energy densities. The static pressure distribution arising from the Lorentz trace part of the EMT, as manifested in the spatial stress 1/3 $T^{ii}$, is equal to minus the corresponding trace part of the energy density. This relation may be interpreted as resulting from the depletion of the gluon and quark condensates through the stress-volume relation. This trace-anomaly and sigma-term induced pressure plays a fundamental role in the confinement dynamics of QCD. In contrast, the dynamic pressure distribution from the traceless part of the spatial stress tensor equals 1/d of the corresponding traceless part of the energy density, where d is the spatial dimension. The total pressure is balanced by these two components of the pressure. We point out that the same pressure-energy relations also hold for vortices in type-II superconductors, where the static pressure-energy relation arises from the depletion of the Cooper-pair condensate. Furthermore, these equations of state are identical to those in the $\Lambda$CDM model of cosmology, where the static pressure-energy relation arises from the cosmological constant.