I Partial derivative is terms of Kronecker delta and the Laplacian operator

Click For Summary
The discussion focuses on expressing the term T_{ij} = ∂_i ∂_j φ in terms of the Kronecker delta and the Laplacian operator, Δ = ∇². Participants clarify that there is no general simplification for ∂_i ∂_j φ without additional context or specific conditions. While special cases might allow for some relations, a universal formula is not feasible. The conversation emphasizes the limitations of expressing second derivatives in this manner. Overall, the consensus is that more information is needed to establish a meaningful connection.
Safinaz
Messages
255
Reaction score
8
TL;DR
How to write partial derivatives in terms of Kronecker delta and the Laplacian operator?
How can the following term:

## T_{ij} = \partial_i \partial_j \phi ##

to be written in terms of Kronecker delta and the Laplacian operator ## \bigtriangleup = \nabla^2 ##?

I mean is there a relation like:

## T_{ij} = \partial_i \partial_j \phi = ?? \delta_{ij} \bigtriangleup \phi.##

But what are ?? term

Any help is appreciated!
 
Last edited:
Physics news on Phys.org
It cannot.
 
Orodruin said:
It cannot.
So there is no any way to simplify ## \partial_i \partial_j \phi ## ?
 
Not really no. Not without knowing more. In some special cases, perhaps, but not as a general rule.

What is the context here?
 
Theoretical physicist C.N. Yang died at the age of 103 years on October 18, 2025. He is the Yang in Yang-Mills theory, which he and his collaborators devised in 1953, which is a generic quantum field theory that is used by scientists to study amplitudes (i.e. vector probabilities) that are foundational in all Standard Model processes and most quantum gravity theories. He also won a Nobel prize in 1957 for his work on CP violation. (I didn't see the post in General Discussions at PF on his...

Similar threads

  • · Replies 4 ·
Replies
4
Views
846
Replies
3
Views
2K
Replies
4
Views
2K
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
472
Replies
2
Views
1K
  • · Replies 10 ·
Replies
10
Views
381
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K