Quantum Field Theory  

... no spooky action at a distance (Einstein)  
Early Results
 
Relativistic Quantum Mechanics  KleinGordon Equation Dirac Equation  
The Dawn of QFT  Spinors Spin Feynman Slash Notation Antimatter KleinGordon Field Dirac Field Renormalisation Grassman Variable Conformal Field Theory  
Countdown to the Standard Model
 
From a framework to a model  YangMills Theory Quantum Electrodynamics Quantum Chromodynamics Electroweak Theory Higgs Mechanism Standard Model  
SemiClassical Gravity and the Dark Age  Hawking Radiation Chandrashekhar Limit Inflation Problems with the Standard Model  
Outlook
 
Beyond the Standard Model  Beyond the Standard Model Quantum Gravity Theory of Everything  
Related
 
Related  De DonderWeyl Theory  
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Renormalisation refers to replacing infinite results of a an infinite summation with a finite number through logically sortof sensible means. A classical, intuitive example of Renormalisation is a Ramanujam Sum.
ExamplesEdit this section
Ramanujam SummmationEdit this section
Take, for example, the classical example, of the sum of all positive integers:
Clearly, thus sum diverges. However, notice that if one would use the (Wrongly, actually, to speak rigorously) definition Riemann Zeta Function that only applies to positive integers, that is,
We see that this is just . In reality, however, the zeta function is not defined this way for negative integers. If we use the actual definition of the Riemann Zeta Function to calculate this , then we see that the result is . Therefore, we renormalise this sum to .
Of course, it is obvious that this is not rigorous, however, it is very useful from a Physics point of view.
Ramanujam summation  

Ramanujan^{[1]} wrote it for the case going to infinity: where is a constant specific to the series and its analytic continuation and the limits on the integral were not specified by Ramanujan, but presumably they were as given above. Comparing both formulae and assuming that tends to 0 as tends to infinity, we see that, in a general case, for functions with no divergence at = 0: where Ramanujan assumed . By taking we normally recover the usual summation for convergent series. For functions with no divergence at , we obtain: was then proposed to use as the sum of the divergent sequence. In particular, the sum of all positive integers is where the notation indicates Ramanujan Summation.

External LinksEdit this section
 Neumaimer, Arnold. Renormalization without inﬁnities – an elementary tutorial. http://www.mat.univie.ac.at/~neum/ms/ren.pdf.
 Motl, Lubos (2014). "Sum of integers and oversold common sense". The Reference Frame. http://motls.blogspot.in/2014/01/sumofintegersandoversoldcommon.html?m=1.
ReferencesEdit this section
 ↑ Bruce C. Berndt, Ramanujan's Notebooks, Ramanujan's Theory of Divergent Series, Chapter 6, SpringerVerlag (ed.), (1939), pp. 133149.