The energy-momentum tensor as a second fundamental form

The Energy-Momentum tensor on $Spin^c$ manifolds

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spin^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.

The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds

On a compact surface endowed with any $\Spinc$ structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a Bär-type inequality for the eigenvalues of the Dirac operator is given. The round sphere $\mathbb{S}^2$ with its canonical $\Spinc$ structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in $\mathbb{S}^2\times \mathbb{R}$ by solutions of the generalized Killing spinor equation associated with the induced $\Spinc$ structure on $\mathbb{S}^2\times \mathbb{R}$

标准模型的能量动量张量及其在能量条件中的应用

The energy-momentum tensor of the Standard Model with applications to energy conditions

本文将标准模型的拉格朗日量视为几何变分问题，推导出能量动量张量，并研究广义相对论中各种能量条件的适用性。

Stress-Energy-Momentum Tensors in Constraint Field Theories

One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum Hamiltonian formalism which provides the adequate description of constraint field systems. The goal is that, for different solutions of the same constraint field model, one should choose different stress-energy-momentum tensors in general. Gauge theory illustrates this result. Th…

Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is …

On electromagnetism and generalized energy-momentum tensor of the electromagnetic field in spaces with Finsler geometry

By using variational calculus and exterior derivative formalism, we proposed in two previous joint papers with S. Siparov a new geometric approach for electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge invariance. Also, for flat pseudo-Finsler spaces, we define a generalized energy-momentum tensor (consisting of two blocks), as the symmetrized Noether current corresponding to the invariance of the field Lagrangian with respect to spacetime translations. In curved spaces, one of…