On energy-momentum and spin/helicity of quark and gluon fields

Columbia; Friedrich W. Hehl (Cologne; Mo)

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On energy-momentum and spin/helicity of quark and gluon fields

Friedrich W. Hehl (Cologne, Columbia, MO)

General Relativity and Quantum Cosmology · Submitted 2 Feb 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim (iv) Within the viable EC-theory, our theses (i) and (ii) are fulfilled and, thus, we favor this gravitational theory.

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In special relativity, quantum matter can be classified according to mass-energy and spin. The corresponding field-theoretical notions are the energy-momentum-stress tensor T and the spin angular momentum tensor S. Since each object in physics carries energy and, if fermionic, also spin, the notions of T and S can be spotted in all domains of physics. We discuss the T and S currents in Special Relativity (SR), in General Relativity (GR), and in the Einstein-Cartan theory of gravity (EC). We collect our results in 4 theses: (i) The quark energy-momentum and the quark spin are described correctly by the canonical (Noether) currents T and S, respectively. (ii) The gluon energy-momentum current is described correctly by the (symmetric and gauge invariant) Minkowski type current. Its (Lorentz) spin current vanishes, S = 0. However, it carries helicity of plus or minus one. (iii) GR contradicts thesis (i), but is compatible with thesis (ii). (iv) Within the viable EC-theory, our theses (i) and (ii) are fulfilled and, thus, we favor this gravitational theory.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In special relativity, quantum matter can be classified according to mass-energy and spin.	background 1.00	0.03	0.02	asserted 0.96
s1	The corresponding field-theoretical notions are the energy-momentum-stress tensor T and the spin angular momentum tensor S.	background 1.00	0.06	0.02	asserted 1.00
s2	Since each object in physics carries energy and, if fermionic, also spin, the notions of T and S can be spotted in all domains of physics.	background 1.00	0.04	0.02	asserted 0.97
s3	We discuss the T and S currents in Special Relativity (SR), in General Relativity (GR), and in the Einstein-Cartan theory of gravity (EC).	contribution 0.93	0.63	0.03	asserted 0.89
s4	We collect our results in 4 theses: (i) The quark energy-momentum and the quark spin are described correctly by the canonical (Noether) currents T and S, respectively.	result 0.96	0.78	0.30	asserted 1.00
s5	(ii) The gluon energy-momentum current is described correctly by the (symmetric and gauge invariant) Minkowski type current.	result 1.00	0.77	0.21	asserted 1.00
s6	Its (Lorentz) spin current vanishes, S = 0.	result 1.00	0.60	0.07	asserted 1.00
s7	However, it carries helicity of plus or minus one.	result 0.98	0.57	0.08	asserted 1.00
s8	(iii) GR contradicts thesis (i), but is compatible with thesis (ii).	result 0.91	0.57	0.13	asserted 1.00
s9	(iv) Within the viable EC-theory, our theses (i) and (ii) are fulfilled and, thus, we favor this gravitational theory.	interpretation 0.87	0.74	0.79	asserted 0.71

What kind of paper the classifier reports this is: theoretical result 0.75 · evidence from proof or derivation 0.61.

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Original abstract

In special relativity, quantum matter can be classified according to mass-energy and spin. The corresponding field-theoretical notions are the energy-momentum-stress tensor T and the spin angular momentum tensor S. Since each object in physics carries energy and, if fermionic, also spin, the notions of T and S can be spotted in all domains of physics. We discuss the T and S currents in Special Relativity (SR), in General Relativity (GR), and in the Einstein-Cartan theory of gravity (EC). We collect our results in 4 theses: (i) The quark energy-momentum and the quark spin are described correctly by the canonical (Noether) currents T and S, respectively. (ii) The gluon energy-momentum current is described correctly by the (symmetric and gauge invariant) Minkowski type current. Its (Lorentz) spin current vanishes, S = 0. However, it carries helicity of plus or minus one. (iii) GR contradicts thesis (i), but is compatible with thesis (ii). (iv) Within the viable EC-theory, our theses (i) and (ii) are fulfilled and, thus, we favor this gravitational theory.

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9 arXiv papers cite this in 15 sentences

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Papers citing it · 13 sentences without a confident label

Cites it as background 2 papers

The affine connection $Γ^ k_i j$ in the ECSK theory of gravity is not symmetric and has the antisymmetric part, the torsion tensor $S^k_kij=(Γ^ k_i j-Γ^ k_j i)/2$ [ref] .

Universe in a black hole in Einstein$-$Cartan gravity · Einstein-Cartan-Sciama-Kibble theory of gravity · 0.99
In relativistic theories with spinful matter there are two possible definitions of the stress-energy tensor [ref] .

Physical stress, mass, and energy for non-relativistic matter · Introduction · 0.97

What it cites · 11 sentences without a confident label

Cites as background 3 papers

A short outline and the classical papers of the subject can be found in Blagojević and Hehl [ref] , see also the review paper [ref] .

On the Gauge Aspects of Gravity · Introduction · 0.99
Recently, in this context, the problem has been addressed of the appropriate energy-momentum and spin tensors of quark and gluon fields, see the review paper of Leader and Lorcé [ref] .

The angular momentum controversy: What's it all about and does it matter? · Introduction · 0.99
On the gravitational side, there took some developments place that are not without implications for the understanding of the energy-momentum and the spin distribution of matter fields, see also the thermodynamic considerations of Becattini & Tinti [ref] .

Thermodynamical inequivalence of quantum stress-energy and spin tensors · Introduction · 0.88

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