Related papers: Noether and Hilbert (metric) energy-momentum tenso…
Noether's theorems are widely praised as some of the most beautiful and useful results in physics. However, if one reads the majority of standard texts and literature on the application of Noether's first theorem to field theory, one…
Recent research has highlighted the non-uniqueness problem of energy-momentum tensors in linearized gravity; many different tensors are published in the literature, yet for particular calculations a unique expression is required. It has…
We revisit the old problem of the energy-momentum tensor in general relativistic field theories. On the basis of the general covariance we derive a simple equation for the Hilbert and Noether energy-momentum tensors for the scalar and…
Through symmetry of the action under global spacetime translations, Noether's first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [Phys. Rev. D 106, 125012 (2022)],…
Two distinct energy-momentum tensors of the theory of weak gravity and spinor quantum mechanics are analyzed with respect to their four-divergence and expectation values of energy. The first energy-momentum tensor is obtained by a…
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on…
It is shown that using Noether's Theorem explicitly employing gauge invariance for variations of the electromagnetic four-potential $A^\mu$ straightforwardly ensures that the resulting electromagnetic energy-momentum tensor is symmetric.…
We clarify the relation between canonical and metric energy-momentum tensors. In particular, we show that a natural definition arises from Noether's Theorem which directly leads to a symmetric and gauge invariant tensor for electromagnetic…
Noether's first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while…
We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of the…
In a non-commutative field theory, the energy-momentum tensor obtained from the Noether method needs not be symmetric; in a massless theory, it needs not be traceless either. In a non-commutative scalar field theory, the method yields a…
We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields…
The energy-momentum tensor of a ferromagnet derived according to the standard prescription of Noether's theorem has a major flaw: the term originating from the spin Berry phase is gauge-dependent. As a consequence, some physical quantities…
Several energy-momentum "tensors" of gravitational field are considered and compared in the lowest approximation. Each of them together with energy-momentum tensor of point-like particles satisfies the conservation laws when equations of…
We reexamine the energy-momentum tensor in classical electrodynamics from the perspective of spacetime-dependent translations, i.e., diffeomorphism invariance in flat spacetime. When energy-momentum is identified through local translations…
The search for the gravitational energy-momentum tensor is often qualified as an attempt of looking for ``the right answer to the wrong question''. This position does not seem convincing to us. We think that we have found the right answer…
In this work, we investigate the structure and properties of the canonical energy momentum tensor (EMT) across a range of field theories. We begin by developing a unified and systematic method that naturally yields the canonical EMT for…
The macroscopic energy-momentum and spin densities of relativistic spin hydrodynamics are obtained from the ensemble average of their respective microscopic definitions (quantum operators). These microscopic definitions suffer from…
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral…
The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor…