Linked Questions
18 questions linked to/from Why is the stress-energy tensor symmetric?
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How to symmetrize the canonical stress-energy tensor? [duplicate]
Given the Lagrangian density for a real scalar field $\mathcal{L}(\phi, \partial_\mu \phi)$, we obtain from Noether's theorem the canonical stress-energy tensor
$$ T^{\mu\nu} = \frac{\partial \mathcal{...
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Energy-Momentum Tensor in QFT vs. GR
What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
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Why is the (non-relativistic) stress tensor linear and symmetric?
From Wikipedia:
"[...] the stress vector $T$ across a surface will always be a linear function of the surface's normal vector $n$, the unit-length vector that is perpendicular to it. [...] The ...
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When is stress-energy tensor defined as variation of action with respect to metric conserved?
In General Relativity Einstein's equation implies that stress-energy tensor on its RHS is conserved (has vanishing divergence), due to the Bianchi identity. Considering variational principles leading ...
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Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?
So, suppose I have an action of the type:
$$
S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu \...
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Pass to globally conserved currents from locally conserved currents in curved spacetime
Let us begin with a Lagrangian of the form
$$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$
where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
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Lack of symmetry of the canonical stress-energy tensor
Why in the general case of classical field theory canonical stress-energy tensor doesn't have symmetry of the permutation of the indices?
For explanation, let's have a "derivation" of an expression ...
user8817
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Symmetry of the $3\times 3$ Cauchy Stress Tensor [duplicate]
When presenting the stress tensor (say in a non-relativistic context), it is shown to be a tensor in the sense that it is a linear vector transformation: it operates on a vector $n$ (the normal to a ...
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In a theory with spinor fields, what general condition on the action ensures that the stress-energy tensor can be made symmetric?
In general relativity, the stress-energy tensor is normally defined by
$$
T^{ab}\equiv \frac{2}{\sqrt{|g|}}\,\frac{\delta S_m}{\delta g_{ab}},
\tag{1}
$$
where $S_m$ is the "matter" action (...
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Is conservation of energy-momentum tensor a consequence of diffeomorphism or isometry?
So far I have seen two distinct ways to derived the conservation law
$$\nabla_{a}T^{ab}=0$$,
one from diffeomorphism of the action, the other one uses variation principle with the metric fixed. Both ...
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Why is the Maxwell Stress Tensor symmetric?
What is the physical meaning of the Maxwell Stress tensor symmetry?
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Showing symmetry of the stress tensor by applying divergence theorem to $\int\int_{\delta V(t)} \vec{x}\times \vec{t} dS$ [duplicate]
I'm currently working through the symmetry of the stress tensor, in relation to viscous flow. I am looking at this by examining the conservation of angular momentum equation for a material volume $V(t)...
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Why do we need to symmetrize the stress-energy tensor?
An elementary definition of the stress-energy tensor $T_{\mu\nu}$ in terms of the Lagrangian for flat spacetime is $$T^{\mu\nu}=\frac{\partial \mathcal{L}}{\partial(\partial_\mu\phi)}(\partial^\nu\phi)...
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Symmetric energy-momentum tensor
In field theory, there's no guarantee that the energy-momentum tensor resulting from Noether's theorem is symmetric. The usual trick to construct a symmetric tensor is to add to the original energy-...
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Is Belinfante–Rosenfeld stress–energy tensor used to derive momentum?
Momentum is usually defined in QFT as:
$$P^i = \int d^3x T^{0i}$$
where $T^{uv}$ refers to energy-momentum tensor, and I believe $P$ refers to linear momentum. In fermionic field, canonical energy-...
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