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Please can someone provided me with academic literature (Journals/Books, titles & links) which discuss the current view on space time i.e. that there is not Infinitely many points of space-time?

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The premise of your question (that the current view on spacetime is that 'there are not infinitely many point of it') is questionable at best. Where did you get this idea? –  Danu Mar 17 at 12:27
    
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Is this question about a possible discreteness of space-time? –  pfnuesel Mar 17 at 12:47
    
Are you familiar with the mathematical concepts of infinity, to wit: Aleph-null, Aleph-one, etc.? –  Carl Witthoft Mar 17 at 13:27
    
Sounds like the OP is interested in lattice field theory on a $n$-torus (or some other topologically exotic space)...also see Jacobson and Foster's "Quantum field theory on a growing lattice" arXiv:hep-th/0407019 –  Alex Nelson Mar 17 at 13:51
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2 Answers 2

This is a nice introduction to Loop Quantum Theory in which both space and time are the result of weaving together fundamental quantum of space itself. http://arxiv.org/pdf/1001.1330v1.pdf. I am sending you too a page which contains several links and options for the study of this theory. http://cosmicposts.wordpress.com/loop-quantum-gravity/

Enjoy it

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I agree that loop quantum gravity is relevant, but would stress that it's not the most popular theory of quantum gravity. Also, maybe there is something to say about quantum foam? –  innisfree Mar 17 at 14:28
    
Minor comment to the post (v1): In the future please link to abstract pages rather than pdf files, e.g., arxiv.org/abs/1001.1330 –  Qmechanic Mar 17 at 18:00
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this is my paper which show that the space in some special curved spacetime is discreete by using one form of generalized uncertainty principle. This paper has been published in {Advances in High Energy Physics} http://www.hindawi.com/journals/ahep/2013/124543/

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Dear user42958: Welcome to Phys.SE. Are you in any way related to the linked article? For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself, not in attached links. –  Qmechanic Mar 20 at 17:14
    
Answers are usually reserved for more detailed responses. In the future you should leave this type of response as a comment. –  Chris Mueller Mar 20 at 17:28
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