The covariant definition of spin in relativistic quantum field theory

Hilgevoord, Jan; Kerf, E.A. De

doi:10.1016/0031-8914(65)90141-2

Cited by 39 publications

(26 citation statements)

References 4 publications

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“…It yields a symmetric energy-momentum current Σ αβ . The spin tensor of Hilgevoord et al [28,29], which was constructed outside of the framework of Lagrangian formalism, coincides with our convective spin current 2 τ (c) αβ .…”

Section: Relocalization Of Energy-momentum and Spinsupporting

confidence: 68%

See 1 more Smart Citation

On the Structure of the Energy-Momentum and the Spin Currents in Dirac’s Electron Theory

Hehl¹,

Macı́as²,

Mielke³

et al. 1999

On Einstein’s Path

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We consider a classical Dirac field in flat Minkowski spacetime. We perform a Gordon decomposition of its canonical energy-momentum and spin currents, respectively. Thereby we find for each of these currents a convective and a polarization piece. The polarization pieces can be expressed as exterior covariant derivatives of the two-formsMα and M αβ = −M βα , respectively. In analogy to the magnetic moment in electrodynamics, we identify these two-forms as gravitational moments connected with the translation group and the Lorentz group, respectively. We point out the relation between the Gordon decomposition of the energy-momentum current and its Belinfante-Rosenfeld symmetrization. In the non-relativistic limit, the translational gravitational moment of the Dirac field is found to be proportional to the spin covector of the electron. File schuecking7. tex, 1997-06-03

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Section: Relocalization Of Energy-momentum and Spinsupporting

confidence: 68%

“…Probably the latter requirement has to be given up. One could start with the convective currents (29) and (35) as well. But we will leave that for future consideration.…”

Section: Trivial Lagrangians and Relocalizationmentioning

confidence: 99%

On the Structure of the Energy-Momentum and the Spin Currents in Dirac’s Electron Theory

Hehl¹,

Macı́as²,

Mielke³

et al. 1999

On Einstein’s Path

View full text Add to dashboard Cite

show abstract

“…In this section we show a different decomposition between spin and orbital angular momentum first propsed by Hilgevoord and Wouthuysen (HW) such that the global spin transforms properly as a tensor under Lorentz transformations, unlike the canonical one [9][10][11]. The idea is based on the fact that the Dirac spinor is also a solution of the Klein-Gordon equation.…”

Section: Hilgevoord-wouthuysen Currentsmentioning

confidence: 99%

Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics

Speranza

Weickgenannt

2021

Eur. Phys. J. A

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The relativistic treatment of spin is a fundamental subject which has an old history. In various physical contexts it is necessary to separate the relativistic total angular momentum into an orbital and spin contribution. However, such decomposition is affected by ambiguities since one can always redefine the orbital and spin part through the so-called pseudo-gauge transformations. We analyze this problem in detail by discussing the most common choices of energy-momentum and spin tensors with an emphasis on their physical implications, and study the spin vector which is a pseudo-gauge invariant operator. We review the angular momentum decomposition as a crucial ingredient for the formulation of relativistic spin hydrodynamics and quantum kinetic theory with a focus on relativistic nuclear collisions, where spin physics has recently attracted significant attention. Furthermore, we point out the connection between pseudo-gauge transformations and the different definitions of the relativistic center of inertia. Finally, we consider the Einstein–Cartan theory, an extension of conventional general relativity, which allows for a natural definition of the spin tensor.

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“…Such different choices of conserved energy-momentum tensor is also known as pseudo-gauge choices and the tensor Φµνλ is called the pseudo-gauge parameter. To study the pseudo-gauge dependence of quantum statistical fluctuation of energy we consider the canonical version of the energy-momentum tensor for spin-half particle along with the Belinfante-Rosenfeld (BR) energy-momentum tensor [16,17,18], the de Groot-van Leeuwen-van Weert (GLW) energy-momentum tensor [19], and the Hilgevoord-Wouthuysen (HW) energy-momentum tensor [20,21]. Note that in the context of hyperon polarization as observed in the heavy-ion collision experiments,…”

Section: Introductionmentioning

confidence: 99%

Quantum statistical fluctuation of energy and its novel pseudo-gauge dependence

Das

2022

Preprint

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We discuss the quantum statistical fluctuations of energy in subsystems of hot relativistic gas for both spin-zero and spin half particles. We explicitly show the system size dependence of the quantum statistical fluctuation of energy. Our results show that with decreasing system size quantum statistical fluctuations increase substantially. As the consistency of the framework, we also argue that the quantum statistical fluctuations give rise to the known result for statistical fluctuation of energy in the canonical ensemble if we consider the size of the subsystem to be sufficiently large. For a spin-half particle quantum fluctuations show some interesting novel features. We show that within a small sub-system quantum statistical fluctuation of energy for spin half particles depends on the various pseudo-gauge choices of the energy-momentum tensor. Interestingly, for sufficiently large subsystems quantum fluctuations obtained for different pseudo-gauge choices converge and we recover the canonical-ensemble formula known for statistical fluctuations of energy. Our calculation is very general and can be applied to any branch of physics whenever one deals with a thermal system. As a practical application, we argue that our results can be used to determine a coarsegraining scale to introduce the concept of classical energy density or fluid element relevant for the strongly interacting matter, in particular for small systems produced in heavy-ion collisions.

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The covariant definition of spin in relativistic quantum field theory

Cited by 39 publications

References 4 publications

On the Structure of the Energy-Momentum and the Spin Currents in Dirac’s Electron Theory

On the Structure of the Energy-Momentum and the Spin Currents in Dirac’s Electron Theory

Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics

Quantum statistical fluctuation of energy and its novel pseudo-gauge dependence

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