All Questions
Tagged with special-relativity tensor-calculus
63
questions with no upvoted or accepted answers
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Uses of the Angular Momentum 4-Tensor
The angular momentum 4-tensor has 6 independent components, three angular momentum components and three new guys. Some call these new guys the 'boosts', but since they are the conjugate momentum of ...
- 1,911
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Timelike, spacelike etc. for higher-order tensors
Vectors $V^\mu$ in relativity can be classified into those which are timelike, spacelike and null. A similar classification is available for tensors: A tensor
$$T^{\mu_1\mu_2...\mu_p}_{\phantom{\mu_1\...
- 591
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Counting independent components of Lorentz tensor
Say I have Lorentz tensors $A^{\mu\nu}$ and say this Lorentz tensor is symmetric under $\mu \Leftrightarrow \nu$ and there are only $p^\mu$ and $q^\mu$ as the physical Lorentz vectors involved. If so, ...
- 857
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Tetrad basis: a doubt on "Comoving" and "Static" tetrads
In the awesome paper $[1]$, Müller then gives us a plethora of spacetimes and their basic geometrical objects like the form of the line element, Christoffel symbols, Krestchmann scalars and so on. ...
- 3,085
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The connection between classical and quantum spins
I have two questions, which are connected with each other.
The first question.
In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
user8817
2
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Fundamental invariants of a Lorentz tensor
As answered in this question, an antisymmetric tensor on 4D Minkowski space has two Lorentz-invariant degrees of freedom. These are the two scalar combinations of the electromagnetic tensor (as proven ...
- 21
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How do Maxwell's equations follow from the action of Lorentz generators on field strength?
Following Warren Siegel's book on Field theory (pg. 223), one might derive the action of Lorentz generators $S_{ab}$ on an antisymmetric 2-tensor field strength $F_{cd}$ which arises for example in ...
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Help understanding Gauss' and Stoke's Theorem in Minkowski space in index notation
My professor said that it's easy to generalize to these definitions of Stoke's and Gauss' theorem from the 3 dimensional versions but didn't say much else. He threw the following on the chalk board:
$$...
- 111
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Weinberg's proof that $F^{\alpha \beta}$ is a tensor
I am interested in Weinberg's approach to proving that $F^{\alpha \beta}$ is a tensor in his book Gravitation and Cosmology. He begins by rewritting the Maxwell equations as:
$$\frac{\partial}{\...
- 157
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Find the energy-impulse tensor of a fluid of charged dust from the action principle
I have the total action given by:
$$S_{tot} = -\frac{1}{16\pi c}\int d\Omega\ F^{\mu \nu}F_{\mu \nu} + \sum_{i=1}^{N}\bigg(-\frac{q}{c}\int dx_i^\mu A_\mu - mc \int ds_i\bigg) \\= \int d\Omega\ \frac{...
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Wald General Relativity Exercice 4.5 - Derivation of Tensor Calculus Identity Relevant to "Effective Gravitational Stress Tensor"
This is a lot of text so I apologise, its hard to pose this question concisely while still being clear.
In the text, Wald derives to second order deviation from flatness an expression for the "...
- 307
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The form of QED Vertex Correction
In chapter 6 of Peskin-Schroeder's text Introduction to Quantum Field Theory it is argued that the form of vertex correction for QED can only have the following form (since we have only the constants, ...
- 648
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Momentum in capacitor field; How can an EM field have zero momentum density but non-zero momentum flux?
Consider the case of a simple, stationary parallel plate capacitor oriented with its plates lying in the x-y plane. The E-field is simply given by:
$$\vec{E} = \frac{Q}{\epsilon_0A}\hat{z} $$
with ...
- 340
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1
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Derivation of 4-current $j$ being a 4-vector in Landau-Lifschitz: Formulation with rigorous mathematical treatment?
Here on Stack exchange, there appeared the question on how to derive the 4-current actually being a Lorentz-tensor. One of the answers (How do we prove that the 4-current $j^\mu$ transforms like $x^\...
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Tensor Calculus/Vector Calculus and so on in special relativity book recommandation
I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...