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Spin (Lorentz) connection 
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#1
Jan1513, 08:59 AM

P: 23

what is the formula of spin connection in GR ?
can we show it in term of structure coefficients ? 


#2
Jan1513, 09:25 AM

Sci Advisor
P: 906

If you want the explicit solution in terms of vielbeins, check e.g. Van Proeyen's textbook or notes on supergravity, or eqn.(2.7) of http://arxiv.org/abs/1011.1145. Section 2 of this article reviews GR as a gauge theory of the Poincare algebra.



#3
Jan1513, 09:39 AM

P: 23

Exactly i study Teleparallel gravity, that is a gauge theory for translation group,and i know how to derive spin connection in terms of vielbeins, but i want its definition in GR.



#4
Jan1513, 09:58 PM

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Spin (Lorentz) connection



#5
Jan1513, 10:35 PM

P: 23

we need spin connections, whenever we want to compare them. 


#6
Jan1613, 01:28 AM

Sci Advisor
P: 906

You use the vielbein postulate. Conceptually, you state with it that the vielbein is just an inertial coordinate transformation. Algebraically, it allows you to solve the Gamma connection in terms of the spin connection and vielbein. See again the reference I gave.



#7
Jan1613, 01:42 AM

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P: 5,443

As far as I remember tetrad formalism and spin connection are nicely explained in Nakahara's textbook.



#8
Jan1613, 04:52 PM

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P: 6,245

If you want to learn about the differential geometry of spin connections, and of teleparallelism, I suggest you look at the book "Differential Geometry for Physicists" by Fecko.



#9
Jan1713, 03:57 AM

P: 23




#10
Jan1713, 08:50 AM

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P: 6,245

Spacetimes that are compact are possibly nonphysical, as any compact spacetime admits closed timelike curves, so the above is probably a useful equivalence. 


#11
Jan1913, 04:29 AM

Sci Advisor
P: 906

Hi george, I'm not familiar with these kind of technicalities, but I will look them up. Thanks!



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