Space Translation: Sidney Coleman's Lectures Problem

In summary, Space Translation is a concept in theoretical physics that explains the behavior of physical systems under changes in their spatial coordinates. It is important because it helps us understand how objects and forces behave in different positions in space, and has applications in fields such as cosmology and quantum mechanics. Sidney Coleman, a renowned theoretical physicist, has given lectures on Space Translation, focusing on its mathematical framework and physical implications. Some key concepts covered in these lectures include the translation operator, commutation relations, and the role of symmetries and conservation laws. Understanding Space Translation can also aid in our understanding of the universe, particularly in fields such as cosmology. Additionally, there are practical applications of Space Translation in areas such as quantum computing and the development of new
  • #1
direct99
9
0
Hi,

In Sidney Coleman's Lectures he talked about space translations such that

gif.latex?e%5E%7B%5Cimath%20p.a%7D%20%5Crho%20%28x%29%20e%5E%7B-%5Cimath%20p.gif


but when I expanded the exponentials
gif.latex?e%5E%7B%5Cimath%20p.gif
and
gif.latex?e%5E%7B-%5Cimath%20p.gif
and used the commutation relation of p and x, I got ρ(x+a) instead of ρ(x-a)

Does anyone see where I may of went wrong?
 
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  • #2
Which version of "Lectures" you have in mind? In the online version at

http://www.physics.emory.edu/students/tbrunson/PDF/QFT_Lecture_1.pdf

there is a plus sign (bottom pf p. 16).
 
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1. What is Space Translation and why is it important?

Space Translation is a concept in theoretical physics that describes the behavior of physical systems under changes in their spatial coordinates. It is important because it allows us to understand how objects and forces behave in different positions in space, and has applications in areas such as cosmology and quantum mechanics.

2. Who is Sidney Coleman and what are his lectures about?

Sidney Coleman was a renowned theoretical physicist who made significant contributions to quantum field theory. His lectures on Space Translation focus on the mathematical framework and physical implications of this concept, and are highly regarded in the field of theoretical physics.

3. What are some key concepts covered in Sidney Coleman's lectures on Space Translation?

Some key concepts covered in the lectures include the translation operator, which describes the change in position of a physical system, and the commutation relations that govern the behavior of physical quantities under space translations. The lectures also discuss the role of symmetries and conservation laws in space translation.

4. How can understanding Space Translation help us understand the universe?

By understanding Space Translation, we can better understand the behavior of objects and forces at different positions in the universe. This has implications in fields such as cosmology, where the study of the large-scale structure of the universe relies on our understanding of how objects behave under translations in space.

5. Are there any real-world applications of Space Translation?

Yes, Space Translation has practical applications in fields such as quantum computing, where it is used to describe the behavior of quantum systems under changes in position. It also has applications in the development of new technologies, such as precision measurements and advanced materials.

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