Article about symmetries (math problems)

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SUMMARY

The discussion centers on understanding specific equations (2.22 and 2.36) from a physics thesis related to symmetries and scaling in potential functions. The equation involving the derivative \(\left(\frac{\partial t’}{\partial t}\right)^{\frac{1}{2}}\) is identified as a mathematical trick linked to the scaling transformation \(q \to \sqrt{\lambda} q\), which also scales the potential \(V\) by \(1/\lambda\) and time \(t\) by \(\lambda t\). Participants emphasize the importance of grasping these transformations to fully comprehend the equations presented.

PREREQUISITES
  • Understanding of mathematical derivatives and their applications in physics.
  • Familiarity with scaling transformations in potential functions.
  • Knowledge of symmetries in mathematical physics.
  • Ability to interpret equations from academic papers, particularly in physics.
NEXT STEPS
  • Research the concept of scaling transformations in classical mechanics.
  • Study mathematical tricks involving derivatives in physics contexts.
  • Explore the implications of symmetries in physical theories.
  • Read literature on potential functions and their scaling properties.
USEFUL FOR

Students and researchers in physics, mathematicians interested in symmetries, and anyone seeking to deepen their understanding of scaling transformations in mathematical equations.

Caloric
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Hi all.

When I was reading a paper (http://physics.brown.edu/physics/undergradpages/theses/SeniorThesis_tlevine1.pdf) I have had a problem. I don’t understand some equations, namely I don’t understand 2.22 and 2.36. I confused by derivative [itex]\left(\frac{\partial t’}{\partial t}\right)^{\frac{1}{2}}[/itex] in the last (2.36) equation.
It’s clear for me, that it is mathematical trick, but I don’t know it. I would be happy if you could give me an explanation or a link for some literature.


Thanks.
 
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I think you have to use the given potential and its scaling.

[itex]q \to \sqrt{\lambda} q[/itex] is equivalent to a scaling of V by 1/λ, and this corresponds to a scaling of [itex]t \to \lambda t[/itex].
+- some exponents
 
thank you, i get it
 

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