Article about symmetries (math problems)

In summary, the speaker had a problem understanding equations 2.22 and 2.36 while reading a paper. Specifically, they were confused by the derivative in equation 2.36 and were looking for an explanation or literature on the mathematical trick involved. Another participant suggested using the given potential and its scaling to understand the equations. The speaker thanked them for the clarification.
  • #1
Caloric
3
0
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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  • #2
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
 
  • #3
thank you, i get it
 

1. What are symmetries in math?

Symmetries in math refer to transformations or operations that preserve the shape, size, or orientation of an object. These transformations can include reflections, rotations, translations, and combinations of these operations.

2. How are symmetries used in math problems?

Symmetries are used in math problems to simplify and solve complex equations or geometric constructions. They can help identify patterns, reduce the number of unknowns, and provide shortcuts for calculations.

3. What is the relationship between symmetries and equations?

Symmetries and equations are closely related as symmetries can be used to solve equations and equations can be used to describe symmetries. For example, a line of symmetry in a graph can be represented by an equation that divides the graph into two mirrored halves.

4. How do symmetries contribute to the understanding of mathematical concepts?

Symmetries play a crucial role in understanding mathematical concepts by providing a visual representation of abstract concepts. They can also aid in recognizing relationships between different mathematical ideas and help identify similarities and differences between different objects or equations.

5. Can symmetries be found in real-world applications?

Yes, symmetries can be found in various real-world applications such as architecture, design, and nature. For example, the symmetry of a butterfly's wings, the reflection symmetry of a building, or the rotational symmetry of a Ferris wheel.

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