What are the applications of Nonstandard Analysis in mathematical physics?

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Discussion Overview

The discussion centers around the applications of Nonstandard Analysis (NSA) in mathematical physics, with participants seeking resources and elaboration on different perspectives within NSA, particularly the Robinson and Nelson approaches. The scope includes theoretical applications and potential implications in mathematical physics.

Discussion Character

  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant requests links to ebooks about NSA and inquires about its applications in mathematical physics.
  • Another participant notes the difficulty in finding resources on NSA and mentions its use in differential equations, analysis of singularities, resolution methods, and bifurcation.
  • A participant asks for elaboration on the Robinson and Nelson perspectives of NSA.
  • It is explained that Robinson's work involves analysis with infinitesimals, while Nelson's Internal Set Theory (IST) is described as an extension of the Zermelo-Fraenkel axioms, including the axiom of choice.

Areas of Agreement / Disagreement

Participants express interest in both the Robinson and Nelson approaches, but there is no consensus on which perspective is more applicable or relevant to mathematical physics.

Contextual Notes

The discussion lacks specific examples of applications and does not resolve the differences between the two approaches to NSA. There are also no detailed mathematical steps or definitions provided.

Who May Find This Useful

Readers interested in Nonstandard Analysis, mathematical physics, and those seeking resources on advanced mathematical theories may find this discussion relevant.

MathematicalPhysicist
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can someone please provide a link to an ebook about nsa?

p.s
what are the application of this theory in mathematical physics?

thanks in advance.
 
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To find books about NSA is very difficult. Now, you want the Robinson point of view or the internal set theory of Nelson?
In math. physics they are used for differential equations and the analysis of singularirties, as well as resolution mmethods and bifurcation.
 
Originally posted by rutwig
Now, you want the Robinson point of view or the internal set theory of Nelson?
could you please ellaborate about them both?
 
Originally posted by loop quantum gravity
could you please ellaborate about them both?

The work of Robinson is the analysis made with infinitesimals, while the Nelson IST is an extension of the ZF-axioms (plus choice axiom).
 

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