Help with the complex tensor notations

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i have attached two pages from a research paper.can someone interpret the mathematics in them or provide link that will help me in understanding the papers.i need help with the complex tensor notations involved.
the full paper can be downloaded from url given below:

http://www.google.co.in/url?sa=t&source=web&ct=res&cd=1&url=http%3A%2F%2Figitur-archive.library.uu.nl%2Fphys%2F2005-0622-155106%2FQuantum_theory_of_gravitation.pdf&ei=iBJbSvueEYyPkQXZwfzTBQ&usg=AFQjCNEqtBtRvoMKOJk4Gk2EDliH4CZBvQ&sig2=KBQZSSFO4az265cwjaLWtQ
 

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This is just usual tensor notation, nothing hard or complex here...

search this forum for "Tensors without tears" https://www.physicsforums.com/showthread.php?t=240285&highlight=tensors

search this forum for Quantum Field Theory: https://www.physicsforums.com/showthread.php?t=227115&highlight=quantum+field http://www.physics.ucsb.edu/~mark/qft.html (Try before you buy! Click here to download a pdf file of a prepublication draft of the text)

search this forum for General Relativity: https://www.physicsforums.com/showthread.php?t=101428&highlight=tensors Without a pretty strong background in General Relativity and Quantum field theory, it's going to be REALLY difficult for you to understand these class notes though =/

have fun good luck

BTW thanks for the link, looks like a good course given by one of the masters of QFT ^^
 
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