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Generalizations of certain vectors 
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#1
Jun3010, 07:28 PM

P: 647

Hello,
I have a few questions about generalizing a few 4vectors into tensors based on physical and intuitive arguments. The first question I have is if I can form a StressEnergyMomentum tensor out of the energymomentum wave 4vector [tex]\hbar k_{\alpha}[/tex]? The formation of the stressenergy tensor in GR came out by associating the energy momentum 4vector with a 3volume. What if I preform that same association with the wave 4vector? The result I obtain is still of course a stressenergymomentum tensor when multiplied by [tex]\hbar[/tex], however by it self it is simply just a wavetensor, with the [tex]k_{0i}[/tex] components representing momentum and energy, but with the [tex]k_{ij}[/tex] components representing the flux of [tex]k[/tex] or the [tex]\frac{dk}{dt}[/tex] across [tex]dA[/tex]. Is this result generally known and unaccepted, or is it physically absurd and hence dismissed? The second part of my post hinges on the former idea, however I'll still write it for fun. the wave 4vector is commonly contracted with the coordinate 4vector. However, if the wave tensor exists, it will need to be contracted with a coordinate tensor. using dimensional analysis the spatial components of the coordinate tensor [tex]x^{\alpha\beta}[/tex], [tex]x_{ij}[/tex], are 4volumes, each containing the multiplication of two, 2surfaces. one, a spatial surface, and the other a temporal surface, with the diagonal elements being a typical 4volume from GR [tex] v=\int \sqrt{g}d^{4}x[/tex]. Pending the first part of the post, is this an acceptable generalization of the coordinate 4vector into a tensor? any help would be appreciated. 


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