Interaction scalar field invariance

In summary, the conversation is about solving a question related to improved current conservation using the Euler-Lagrange equations. The problem involves a photo and the solution is found in another photo. The individual is initially unsure how to approach the question but is able to solve it with the help of others. However, upon reviewing their work, they realize there is a mistake in the sign of the current, which they are able to correct.
  • #1
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The problem:

http://www.gobigbang.nl/cft/cft.jpg

An attempt of the solution:

http://www.gobigbang.nl/cft/DSCN2722.JPG

My problem is question c. I don't have a clue how to see that the improved current is conserved... Can anyone help me?

Update
I managed to solve the question by using the Euler-Lagrange equations, up to a minus sign... can anyone see the minus sign mistake?

http://www.gobigbang.nl/cft/DSCN2724.JPG

Found it: actually if you change the sign of the current J or the term F, everything comes out nicely... So somewhere in those terms should be a mistake in the minus sign...
 
Last edited:
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  • #2
Update 2Thanks to the answers here, I was able to find the mistake. It is indeed in the sign of the current (J): it should have been J instead of -J.
 

What is an interaction scalar field invariance?

An interaction scalar field invariance refers to a property of a physical system in which the underlying equations or laws of motion remain unchanged under a certain transformation or change in variables. In other words, the system is invariant under the transformation of the scalar field that governs its interactions.

How is interaction scalar field invariance related to symmetry?

Interaction scalar field invariance is closely connected to symmetry in physics. In fact, symmetry is often used as a tool to identify and understand the underlying invariances in a physical system. Symmetry can help determine which transformations or changes in variables will leave the equations of motion unchanged and thus reveal the invariances of the system.

Why is interaction scalar field invariance important in physics?

Interaction scalar field invariance is important because it is a fundamental principle that helps us understand and describe the behavior of physical systems. It allows us to identify the underlying symmetries in a system and use them to simplify and solve complex problems. Additionally, invariance principles often lead to the discovery of new physical laws and relationships.

What are some examples of systems that exhibit interaction scalar field invariance?

One well-known example is the electromagnetic field, which is invariant under changes in the gauge potential. Another example is the strong nuclear force, which is invariant under changes in color charge. Additionally, many physical theories, such as general relativity and quantum field theory, are based on principles of symmetry and invariance.

How does interaction scalar field invariance impact the development of new scientific theories?

Interaction scalar field invariance plays a crucial role in the development of new scientific theories. It allows scientists to identify the underlying symmetries in a system and use them to make predictions and test new theories. In fact, many of the most successful theories in physics, such as the Standard Model, are based on principles of invariance and symmetry.

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