Covariant Gross-Pitaevskii-like equation for relativistic fermions

Andrew Koshelkin

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arXiv · 2607.13055

Covariant Gross-Pitaevskii-like equation for relativistic fermions

Andrew Koshelkin

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Abstract

The covariant Gross-Pitaevskii-like equation for studying systems of interacting relativistic fermions is proposed. The Lagrangian generating such an equation is derived. The considered equation is examined in studying the fermi-liquid, superconductivity and the confinement problem in QCD. The Migdal's step in the fermi-liqiud model, the excitation spectrum of superconductive fermion system are derived in the context of the proposed Gross-Pitaevskii-like equation. We show that the quark fields governing such an equation turn out to be confined in the (3+1) space time.

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Andrew Koshelkin. 2026-07-04. Covariant Gross-Pitaevskii-like equation for relativistic fermions. https://arxiv.org/abs/2607.13055

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