'Symmetrisation Notation' - What is it?

  • Thread starter Thread starter InsertName
  • Start date Start date
  • Tags Tags
    Notation
Click For Summary
Symmetrisation notation refers to a method of expressing terms in equations where indices are totally symmetrized. In the context of the equation from Hobson, Efstathiou, and Lasenby, the notation ∂_{(\mu} h^{\rho}_{\nu)} indicates that the indices within the parentheses are treated symmetrically. This means that the derivative can be expressed as a combination of terms, such as ∂(μhρν) = ½(∂μhρν + ∂νhρμ). The discussion highlights the confusion around this notation and its application in the text. Understanding symmetrisation is essential for correctly interpreting the equations in the referenced material.
InsertName
Messages
26
Reaction score
0
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

\partial_{(\mu} h^{\rho}_{\nu)}.

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 :)
 
Physics news on Phys.org
The indices within the parentheses are understood to be totally symmetrized. So

∂(μhρν) = ½(∂μhρν + ∂νhρμ)
 
Thanks Bill_K!
 

Thread 'Am I understanding the concept of proper frame of reference?'

MOVING CLOCKS In this section, we show that clocks moving at high speeds run slowly. We construct a clock, called a light clock, using a stick of proper lenght ##L_0##, and two mirrors. The two mirrors face each other, and a pulse of light bounces back and forth betweem them. Each time the light pulse strikes one of the mirrors, say the lower mirror, the clock is said to tick. Between successive ticks the light pulse travels a distance ##2L_0## in the proper reference of frame of the clock...
View full post »

Similar threads

Undergrad SR: GA Multivector vs. Tensor notation, Maxwell's equations
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Ricci notations and visualisation
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Is Covariant Derivative Notation Misleading in Vector Calculus?
  • · Replies 124 ·
5
Replies
124
Views
9K
Undergrad Maxwell's Eqs. & Tensor Notation
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Strange index notation for linear transformation matrix
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Clarifying SR Notation for Advanced Mechanics Course
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Green's theorem in tensor (GR) notation
  • · Replies 19 ·
Replies
19
Views
4K
Graduate Re-writing the geodesic deviation eqn in matrix notation (3d only)
  • · Replies 0 ·
Replies
0
Views
1K
Graduate Weyl transformation of connection and curvature tensors
  • · Replies 4 ·
Replies
4
Views
5K
High School A few questions about the covariant derivative
  • · Replies 7 ·
Replies
7
Views
3K