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1answer
44 views

How to find the Hamiltonian density for electromagnetic field? And, how to solve the stress tensor for electromagnetic field? [closed]

How to find the Hamiltonian density for electromagnetic field? And, how to solve the stress tensor for electromagnetic field?
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1answer
63 views

Derivation of Maxwell stress tensor from EM Lagrangian

From Noether's theorem applied to fields we can get the general expression for the stress-energy-momentum tensor for some fields: $$T^{\mu}_{\;\nu} = \sum_{i} (\frac{\partial \mathcal{L}}{\partial ...
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1answer
157 views

Total Momentum From a Standing Electromagnetic Wave

How does one show the momentum imparted to a perfect conducting resonance cavity (boundary) of any shape by a classical standing electromagnetic wave inside is zero? It should be by conservation of ...
1
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0answers
61 views

Constructing conserved current given the lagrangian

Consider the following Lagrangian for a massive vector field $A_{\mu}$ in Euclidean space time: $$\mathcal L = \frac{1}{4} F^{\alpha \beta}F_{\alpha \beta} + \frac{1}{2}m^2 A^{\alpha}A_{\alpha}$$ ...
1
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1answer
46 views

Homogeneity and isotropy of stress energy tensor

Given the energy momentum tensor in E&M: $T_{\mu\nu} = -F_{\mu\alpha} g^{\alpha \beta} F_{\beta \nu} +\frac{1}{4} g_{\mu \nu} F_{\sigma \alpha} g^{\alpha \beta} F_{\beta \rho} g^{\rho \sigma}$ I ...
5
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1answer
234 views

Maxwell's Stress Tensor

What really is the Maxwell Stress Tensor? I understand that it's derived from $$\mathbf {F} = \int _V ( \mathbf E + \mathbf v \times \mathbf B )\rho \ d \tau$$ Griffiths describes this as "total EM ...
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3answers
81 views

How can the electromagnetic stress energy tensor be restricted to flat space-time

The Wikipedia article describing the electromagnetic stress energy tensor seems to suggest that this tensor can only be defined in flat space-time. How is it possible to define an electromagnetic ...
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1answer
82 views

Canonical Stress Tensor for the Free Electromagnetic Field

I have the followwing Lagrangian for the free electromagnetic field, $$\mathcal{L} = -\frac{1}{4} F^{\mu \nu}F_{\mu \nu},$$ and the canonical stress tensor is, $$T^{\alpha \beta}=\frac{\partial ...
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0answers
57 views

“+” and “-” sign in Maxwell Stress tensor

I have trouble in determining the "+" and "-" sign of momentum per unit time, per unit area of the following question. Why in the second part, $d\vec{a}$ is pointing in the $ -\vec{z} $ direction? I ...
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votes
2answers
438 views

Is the Maxwell Stress Tensor Coordinate Dependent?

I am wondering if the Maxwell stress tensor, defined as $$T_{ij} = \epsilon_0 (E_iE_j-\frac{1}{2}\delta_{ij}E^2) + \frac{1}{\mu_0}(B_iB_j-\frac{1}{2}\delta_{ij}B^2) $$ is coordinate dependent. I ...
1
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1answer
104 views

A question about electromagnetic stress-energy tensor

This is what we know as electromagnetic stress-energy tensor $T^{\mu\nu}$. Now I want to know what is its direct relation with $\rho$, charge density? $\rho\,?=T^{\mu\nu}$, $\frac ...
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1answer
352 views

Why is the Maxwell Stress Tensor symmetric?

What is the physical meaning of the Maxwell Stress tensor symmetry?
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0answers
148 views

Solving the equation of relativistic motion

How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
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votes
3answers
1k views

Action principle for the Electromagnetism and Gravity

Here is the formula for the stress energy tensor: $$ T_{\mu\nu} = - {2\over\sqrt{ |\det g| }}{\delta S_{EM}\over \delta g^{\mu\nu}} $$ (This follows from varying the total action $S ...