Path Integrals in Wolfram Mathematica

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Discussion Overview

The discussion centers around the use of Wolfram Mathematica for computing path integrals in SU(2) and SU(3) pure Yang-Mills fields, particularly through the saddle point method. Participants explore the necessity and appropriateness of using computational tools for this analytical method.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses a need for guidance on using Mathematica to compute path integrals, citing a lack of programming experience.
  • Another participant questions the necessity of using Mathematica for the saddle point method, suggesting it is primarily an analytical approach.
  • A later reply indicates that the participant's mentor recommended Mathematica due to the complexity of the integrals involved, particularly with non-linear plane waves and gauge fields in SU(3).

Areas of Agreement / Disagreement

There is no consensus on whether Mathematica is necessary for the saddle point method, with some participants questioning its use while others support it based on the complexity of the integrals.

Contextual Notes

Participants have not resolved the question of the necessity of computational tools for analytical methods, and there are differing opinions on the complexity of the integrals involved.

Mitya
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Hello everyone ! I am new to this site so I 'd better say hello to you all !

I am finishing my BR in physics and part of this ending is to deliver a thesis .

Long story short I must compute path-integrals in SU(2) and SU(3) pure yang-mills fields . Problem is that i was never very good with mathematica or computers in general , whilst i had excellent marks in my lessons (i think not one of them demanded using a computer except from computational physics and our professor back then didnt demand pure programming but ony pseudo) .

Anyway I would be hugely thankful , if someone would guide me to what I should see or read , to be able to compute some path integrals via the saddle point method .

Thank you so much .
 
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Why do you want to use Mathematica for that?
 
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Mitya said:
Anyway I would be hugely thankful , if someone would guide me to what I should see or read , to be able to compute some path integrals via the saddle point method .
The saddle point method is an analytical (not a numerical) method, so I'm not sure that you really need a computer for that.
 
Hello thanks for the answers !

My mentor advised me to use Mathematica to proceed , as the integral is much complicated . I use non linear plane waves as solutions of the EoMs and the gauge fields especially is SU3 are too complicated for me to integrate them yet , i think .

I surely trust him , he must have a reason to tell me to do so .

Thanks !
 

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