Lagrangian field theories and energy-momentum tensors

Muñoz, Gerardo

doi:10.1119/1.18336

Cited by 18 publications

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“…Gauge invariance of the EMT can either be achieved by exploiting this invariance of the Lagrangian in the course of the derivation of the EMT or by exploiting it upon improving the canonical EMT. The first approach is discussed in detail in reference [39] (see also [37,38,40,50]) and we will present here the second procedure which is inspired by the first one, but which has not been considered in the literature to the best of our knowledge. As we will see, the latter approach can also be used to determine in a neat and straightforward manner the improved EMT for massive Abelian vector fields, i.e.…”

Section: Improvement Procedures For Constructing a Gauge Invariant Emtmentioning

confidence: 99%

The energy–momentum tensor(s) in classical gauge theories

et al. 2016

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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 and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. The relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed. Plan of the paper:In the present note we focus, for classical YM (Yang-Mills) theories in ndimensional Minkowski space, on the EMT (energy-momentum tensor, also referred to as stressenergy tensor or stress tensor for short): the components T µν of the EMT can be interpreted as follows, e.g. see reference [12]. T 00 represents the energy density, T 0i the i-momentum density (or energy flux density) and T ij the i-momentum flux density in the j-direction. Regarding the field theoretical system as a collection of particles, we can also interpret T ii ≡ p as the pressure and (T ij ) with i = j as the shear stress. In particular, we will study here the so-called canonical EMT whose components T µν can represent the conserved current densities which are associated (by virtue of Noether's first theorem) to the invariance of the action under spacetime translations. The corresponding conserved charges P ν ≡ R n−1 d n−1 x T 0ν can define the total energy and momentum of the physical system.As is well known (for instance for Maxwell's theory), the tensor T µν can is neither symmetric nor gauge invariant in general and thereby needs to be "improved". This is traditionally realized by the "symmetrization procedure of Belinfante" [13,14] which relies on the spin angular momentum density, but this method does not work straightforwardly in the case where matter fields are minimally coupled to a gauge field [15]. After a short introduction to the subject and problematics in subsection 2.1, we will show in subsection 2.2 that the improvement can be realized in a simple manner for pure gauge fields or for interacting gauge and matter fields by taking into account the local gauge invariance 1 . A conceptually quite different approach consists of coupling the gauge and matter fields to gravity and deducing the so-called Einstein-Hilbert EMT in Minkowski space from the metric EMT on curved space. This approach is outlined for YM theories in section 3 and it is readily shown that the different results in Minkowski space coincide with each other. Concerning the latter point we should mention that more general and abstract approaches have been considered in the literature (we refer in particular to the systematic study [17] based on the earlier work [18]), but we hope that the elementary discussion of the different aspects presented here is useful both as a short introduction to, and as an overview of, the subject. While our paper is devoted to the classical theory, we conclude with some remarks...

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Section: Improvement Procedures For Constructing a Gauge Invariant Emtmentioning

confidence: 99%

The energy–momentum tensor(s) in classical gauge theories

et al. 2016

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“…This state of affairs proves the existence of a problem that should be settled. This dilemma is described in the quotation taken from [3] which is presented in the second paragraph of the Introduction section of this work. The novelty of this work is the proof that demonstrates that as a matter of fact the original tensor (5) is already symmetric provided the analysis is restricted to radiation fields.…”

Section: Discussionmentioning

confidence: 99%

A Consistent Construction of the Electromagnetic Energy-Momentum Tensor

Comay¹

2018

OALib

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This work discusses the problem of the apparently non-symmetric form of the electromagnetic fields' energy-momentum tensor, which is obtained from the variational principle. The analysis treats differently radiation fields and bound fields. This distinction has a solid experimental basis where the hydrogen atom proves that radiation fields and bound fields have a different spin and a different parity. A direct calculation proves that in the case of radiation fields, the variational principle yields the well known symmetric energy momentum tensor and the problem does not exist.

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“…Contrary to popular belief, it is possible to derive a symmetric and gauge invariant EMT via the "canonical" technique of the Noether current without resorting to Belinfante's symmetrization technique, as shown in refs. [49][50][51][52]. Since the antisymmetric part of the EMT does not contribute to the forward limit in which we are interested, we will use the symmetric form, i.e.…”

Section: Definitionsmentioning

confidence: 99%

Mass sum rules of the electron in quantum electrodynamics

Rodini

Metz

Pasquini

2020

J. High Energ. Phys.

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Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this aim we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon.

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Lagrangian field theories and energy-momentum tensors

Abstract: Invariant projection of the energymomentum tensors for field theories in spaces with affine connection and metric

Cited by 18 publications

References 0 publications

The energy–momentum tensor(s) in classical gauge theories

The energy–momentum tensor(s) in classical gauge theories

A Consistent Construction of the Electromagnetic Energy-Momentum Tensor

Mass sum rules of the electron in quantum electrodynamics

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