Note on the energy-momentum tensor for general mixed tensor-spinor fields

TL;DR

This paper proves that for general mixed tensor-spinor fields, the Belinfante's energy-momentum tensor and the metric energy-momentum tensor are equivalent, clarifying their relationship in field theory.

Contribution

It provides an explicit proof of the equivalence between two fundamental energy-momentum tensors for mixed tensor-spinor fields.

Findings

Belinfante's and metric energy-momentum tensors are equivalent for mixed tensor-spinor fields

Clarifies the relationship between different energy-momentum tensors in field theory

Supports consistent energy-momentum definitions in theories involving tensor-spinor fields

Abstract

This note provides an explicit proof of the equivalence of the Belinfante's energy-momentum tensor and the metric energy-momentum tensor for general mixed tensor-spinor fields.