Energy-Momentum Tensor and Equations of Motion of Glashow-Salam-Weinberg-Theory in Curved Space-Time

A covariant Hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of Hamiltonians accounting for specific properties and interactions of spinning bodies. The dynamics for a minimal and a specific non-minimal Hamiltonian is discussed. An independent derivation of the equations of motion from an appropriate energy–momentum tensor is provided. It is shown how to derive constants of motion, both background-independent and background-dependent ones.

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On the energy-momentum tensor at finite temperature in curved space-time

Nuclear Physics B ◽

10.1016/0550-3213(85)90465-1 ◽

1985 ◽

Vol 252 ◽

pp. 621-634 ◽

Cited By ~ 31

Author(s):

Naohito Nakazawa ◽

Takeshi Fukuyama

Keyword(s):

Finite Temperature ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Space Time ◽

Curved Space

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Proof of the uniqueness of the electromagnetic energy momentum tensor

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100045175 ◽

1969 ◽

Vol 66 (2) ◽

pp. 437-438 ◽

Cited By ~ 4

Author(s):

C. D. Collinson

Keyword(s):

General Relativity ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Space Time ◽

Electromagnetic Energy ◽

Curved Space

AbstractAn alternative to Fock's proof of the uniqueness of the electromagnetic energy momentum tensor is presented. The proof is four-dimensional and is applicable in the curved space-time of general relativity.

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Theory of Spinors in Curved Space-Time

Symmetry ◽

10.3390/sym13101931 ◽

2021 ◽

Vol 13 (10) ◽

pp. 1931

Author(s):

Ying-Qiu Gu

Keyword(s):

Clifford Algebra ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Space Time ◽

Classical Dynamics ◽

Curved Space ◽

Spinor Fields ◽

Classical Approximation ◽

Dirac Matrix ◽

Spinor Connection

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of the Dirac equation, the energy-momentum tensor of spinors and so on. To split the spinor connection into the Keller connection Υμ∈Λ1 and the pseudo-vector potential Ωμ∈Λ3 not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton’s second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields; however, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table Sabμν, which plays an important role in the interaction between spinor and gravity. From this paper we find that Clifford algebra has irreplaceable advantages in the study of geometry and physics.

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Theory of Spinors in Curved Space-Time

10.20944/preprints202003.0453.v1 ◽

2020 ◽

Author(s):

Ying-Qiu Gu

Keyword(s):

Clifford Algebra ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Space Time ◽

Classical Dynamics ◽

Curved Space ◽

Spinor Fields ◽

Classical Approximation ◽

Dirac Matrix ◽

Spinor Connection

The interaction between spinors and gravity is the most complicated and subtle interaction in the universe, which involves the basic problem to unified quantum theory and general relativity. By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of Dirac equation, the energy momentum tensor of spinors and so on. To split spinor connection into Keller connection $\Upsilon_\mu\in\Lambda^1$ and pseudo-vector potential $\Omega_\mu\in\Lambda^3$ by Clifford algebra not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Keller connection only corresponds to geometric calculations, but the potential $\Omega_\mu$ has dynamical effects, which couples with the spin of a spinor and may be the origin of the celestial magnetic field. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton's second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields. However, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table $S^{\mu\nu}_{ab}$, which plays an important role in the interaction between spinor and gravity. From this paper we find that, Clifford algebra has irreplaceable advantages in the study of geometry and physics.

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