Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum?

In summary, the conversation discusses the relationship between a symmetric Lagrangian and a symmetric Stress-Energy Momentum tensor. It is mentioned that a Lagrangian is a scalar with no indices, and there is a doubt about the symmetry of a stress-energy tensor's Lagrangian. The speaker then explains that a Lagrangian that is symmetric on the indices μ and ν leads to a symmetric Stress-Energy Tensor, which is also discussed.
  • #1
centry57
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Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum ?
 
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  • #2
A "symmetric energy momentum tensor" obeys [itex]T_{\mu\nu}=T_{\nu\mu}[/itex].

A Lagrangian is a scalar, with no indices.

So what does one have to do with another?
 
  • #3
I was adoubt if a symmetric stress-energy tensor 's lagrangian is symmetry .

Since [itex] {\cal L}= - \frac{1}{16\pi}F^{\mu\nu} F_{\mu\nu}[/itex] is symmetry on \mu &\nu,the corresponding Stress-Energy Tensor [itex]\Theta^{\mu}\,_{\nu} = - \frac{1}{4 \pi} F^{\mu \alpha} \partial_{\nu}A_{\alpha} + \frac{1}{16\pi} \delta^{\mu}_{\nu} F^{\alpha\beta}F_{\alpha\beta} [/itex] is also symmetry.

Is this the special one ?
 
Last edited:

What is a symmetric Lagrangian?

A symmetric Lagrangian is a mathematical expression that describes the dynamics of a system in terms of its coordinates and their derivatives. It is symmetric if it remains unchanged when the coordinates are interchanged.

What is a symmetric Stress-Energy Momentum?

A symmetric Stress-Energy Momentum is a tensor that describes the distribution of energy, momentum, and stress in a physical system. It is symmetric if the components of the tensor remain unchanged when the coordinate axes are rotated.

Why is symmetry important in a Lagrangian?

Symmetry in a Lagrangian is important because it leads to conserved quantities in a physical system, such as energy and momentum. This allows for a deeper understanding of the system's behavior and can make solving equations of motion easier.

Can a non-symmetric Lagrangian lead to a symmetric Stress-Energy Momentum?

No, a non-symmetric Lagrangian will not lead to a symmetric Stress-Energy Momentum. In order for the Stress-Energy Momentum tensor to be symmetric, the Lagrangian must also be symmetric.

What are the implications of a symmetric Lagrangian and Stress-Energy Momentum in physics?

A symmetric Lagrangian and Stress-Energy Momentum have important implications in physics, as they allow for the conservation of energy and momentum, which are fundamental principles in understanding the behavior of physical systems. They also have applications in fields such as classical mechanics, quantum field theory, and general relativity.

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