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Why are gravitons tensorial? 
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#1
Dec812, 01:08 AM

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Why are gravitons tensorial spin 2 particles while Newtonian gravity is a scalar?



#2
Dec812, 01:12 AM

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Because the spacetime metric is a tensor. And spin2 comes from the fact that
(1/2,1/2) x (1/2, 1/2) = (0,0) + (1,0) + (0,1) + (1,1) so a symmetric traceless tensor is in the (1,1) representation, whose spatial part corresponds to S=2 rep. of the so(3) ~ su(2) Lie algebra of spatial rotations. EDIT: Scalar gravitational potential from Newton's theory is the g_{00} perturbation to the Minkowski metric. 


#3
Dec812, 02:14 AM

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Thank you Dick!



#4
Dec812, 10:43 AM

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Why are gravitons tensorial?
The newton potential is not a scalar under general coordinate transformations, only under the galilei group. More precisely, as soon as you make boosts quadratic in time or more, which are (time dependent) accelerations, the potential transforms inhomogeneously. You can derive this from the fact that the potential comes from the i00 component of the connection.



#5
Dec912, 02:06 PM

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I don't think there is a "why". It's just like that.
Nordstrom's second theory is a scalar relativistic theory of gravity that preceded general relativity. It satisfies the equivalence principle, and has a geometric formulation. It happens to predict the wrong perihelion precession. http://arxiv.org/abs/grqc/0611100 http://arxiv.org/abs/grqc/0405030 Also relevant is exercise 24.1c in http://www.pma.caltech.edu/Courses/p...6/0424.1.K.pdf about a scalar theory of gravity: "Explain why this prediction implies that there will be no deflection of light around the limb of the sun, which conflicts severely with experiments that were done after Einstein formulated his general theory of relativity. (There was no way, experimentally, to rule out the above theory in the epoch, ca. 1914, when Einstein was doing battle with his colleagues over whether gravity should be treated within the framework of special relativity or should be treated as a geometric extension of special relativity.)" 


#6
Dec1012, 01:07 PM

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*The graviton field is a first perturbation of the curved spacetime metric around the flat Minkowski background is conventionally called <the PauliFierz field> and obeys the same quantum dynamics as a linearized vierbein (the antisymmetric components of the linearized vierbein do not propagate) which is used in supergravity theories. 


#7
Dec1112, 02:02 AM

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What exactly do you mean by "antisymmetric components of the vierbein"? The vierbein has two different components, namely a flat and a curved one, so it doesn't really make sense to take the antisymmetric part of it; then you're already talking about the metric, isn't it? :)



#8
Dec1112, 02:12 AM

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I don't think it is appropriate to say that because of two indices on some stressenergy tensor type thing,one can say that it is spin 2.One say that with electromagnetic field the origin is charge current which has one index so it represents spin1.this is really not right.If I remember it, then in feynman lectures on gravitation it is pointed out that spin 2 is the lowest possible spin which can be chosen,and is satisfactory.



#9
Dec1112, 07:51 AM

P: 436

The question was about the difference between Newton and Einstein theories of gravity. In Newton's the gravitational potential is scalar. Why is it a tensor in Einstein's?
One simple answer might be like this: In Newton's gravity the source of gravitational interaction is mass. Mass is a scalar. To describe an interaction intensity between two scalars, we need one scalar. In Einstein's gravity the source of interaction is the whole energymomentum 4vector. To describe interaction between components of two 4vectors we need a 4tensor. Some other arguments are needed to show that the tensor must be symmetric. This is not a mathematical derivation, rather an intuitive explanation. The very same line may be answered to a question why interactions of spinors are described by gaugecovariant vector fields. 


#10
Dec1112, 02:03 PM

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