Help with the complex tensor notations

[raj07]

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

 

[malawi_glenn]

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 ^^

 

[sir-pinski]

Understanding complex tensor notations can be a challenging task, but it is essential for comprehending the mathematics involved in research papers. In order to interpret the equations in the attached pages, it would be helpful to have a basic understanding of tensor calculus and complex numbers. A good resource for learning these concepts is the book "Tensor Calculus Made Simple" by Taha Sochi.

In addition, it may be helpful to break down the notation and equations into smaller parts and understand each component separately. For example, in the first equation on page 1, the symbol ∇ represents the gradient operator and the subscript μ represents the index of the tensor. Understanding the meaning and properties of these symbols can help in interpreting the overall equation.

Another useful resource for understanding complex tensor notations is the website "MathWorld" by Wolfram Research. They have a section specifically dedicated to tensor calculus and provide explanations and examples of various notations.

Lastly, it is always helpful to consult with a mathematics or physics tutor who can guide you through the equations and provide a deeper understanding of the concepts involved. Additionally, reaching out to the authors of the research paper for clarification or further explanation may also be beneficial.

Overall, with patience and persistence, you can gain a better understanding of complex tensor notations and successfully interpret the mathematics in the research paper. Good luck!