Condensed matter many-body theory in relativistic covariant form

TL;DR

This paper develops a relativistic covariant many-body theory derived from QED, capturing spin, relativistic effects, and electromagnetic interactions in a gauge-invariant, causal framework.

Contribution

It introduces a covariant Lagrangian for many-body systems from QED, including relativistic and spin effects, extending traditional non-relativistic approaches.

Findings

Derivation of a gauge-invariant covariant many-body Lagrangian

Recovery of the traditional Hamiltonian as an approximation

Inclusion of relativistic and spin interactions such as spin-orbit and Lorentz force

Abstract

We present a relativistic covariant form of many-body theory. The many-body covariant Lagrangian is derived from QED by integrating out the internal non-quantized electromagnetic field. The ordinary many-body Hamiltonian is recovered as an approximation to the exact covariant theory that contains many-body terms beyond the solely electrostatic interaction, e.g. the Lorentz force among electrons, spin-spin etc. Spin and relativistic terms, e.g. spin-orbit, are also automatically accounted. Moreover, the theory is compact, gauge-invariant and respects causality.