'Symmetrisation Notation' - What is it?

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In summary, symmetrisation notation is a mathematical notation used in physics to describe the symmetry properties of a system or equation. It is commonly used in quantum mechanics and statistical mechanics and allows for a concise and precise representation of symmetries. While it has benefits such as easier manipulation of equations, it may also be complex and require a strong understanding of mathematics and physics. It can be applied to various systems and equations, but its usefulness may vary depending on the specific system being studied.
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I'm reading Hobson, Efstathiou and Lasenby, where on page 490, some notation is used that I am not familiar with.

In the rather long equation (17.62), some terms contain things like

[itex] \partial_{(\mu} h^{\rho}_{\nu)} [/itex].

The author(s) then says "where we have made use of the symmetrisation notation discussed in Chapter 4."

I've tried looking in Chapter 4 but it's not at all clear what is going on, so I came here :)
 
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  • #2
The indices within the parentheses are understood to be totally symmetrized. So

hρν) = ½(∂μhρν + ∂νhρμ)
 
  • #3
Thanks Bill_K!
 

1. What is symmetrisation notation?

Symmetrisation notation is a mathematical notation used to describe symmetries in a system or equation. It is commonly used in quantum mechanics and statistical mechanics to represent the symmetry of a wave function or a probability distribution.

2. How is symmetrisation notation used in physics?

In physics, symmetrisation notation is used to describe the symmetry properties of a physical system or equation. It is particularly useful in quantum mechanics, where it is used to describe the symmetry properties of wave functions, and in statistical mechanics, where it is used to describe the symmetry of probability distributions.

3. What are the benefits of using symmetrisation notation?

The main benefit of using symmetrisation notation is that it allows for a concise and mathematically precise description of symmetries in a system. It also allows for easier manipulation of equations and calculations involving symmetries.

4. Are there any drawbacks to using symmetrisation notation?

One potential drawback of symmetrisation notation is that it can be more complex and difficult to understand for those who are not familiar with it. It also requires a strong understanding of mathematics and physics to use effectively.

5. Can symmetrisation notation be applied to any system or equation?

Symmetrisation notation can be applied to many different systems and equations in physics, such as quantum systems, statistical systems, and even classical systems. However, it may not always be necessary or useful depending on the specific system being studied.

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