Two complex fields + interaction, conserved current?

In summary, we discussed the properties of two complex fields, f_1 and f_2, which are solutions of the D'Alembert or wave operator in three space dimensions. We also explored the behavior of the Lagrangian when the difference of f_1 and f_2 is subtracted from the square of their magnitude. It was found that the Lagrangian remains unchanged if both f_1 and f_2 undergo a global phase change of exp(i*theta). This implies a conserved current. Additionally, we looked at solutions of the form f_1 = f_2 and f_1 = -f_2, which represent mass-less and massive waves, respectively. We also questioned if demanding local phase
  • #1
Spinnor
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Say we have two complex fields, f_1 and f_2 which each are solutions of the D'Alembert operator or the wave operator in three space dimensions. Say we subtract the square of the magnitude of the difference of f_1 and f_2 from the Lagrangian for the fields f_1 and f_2. In that case the Lagrangian is unchanged if both f_1 and f_2 each under go a global phase change of exp(i*theta)? If so does that imply a conserved current?

Assume solutions of the form f_1 = f_2 and f_1 = - f_2 , such waves are mass-less and massive respectively?

Can we demand local phase invariance and get some type of interaction?

Thanks for any help!
 
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  • #2
@Spinnor did you find any more insight on this topic?
 

1. What are two complex fields and how do they interact?

Two complex fields refer to two fields in physics that are described by complex numbers. These fields can interact with each other through a conserved current, which is a mathematical expression that describes the conservation of a physical quantity.

2. What is a conserved current in the context of two complex fields?

A conserved current is a mathematical expression that describes the conservation of a physical quantity, such as energy or momentum. In the context of two complex fields, a conserved current describes the interaction between these fields and how they preserve certain physical quantities.

3. How is the conservation of energy and momentum related to two complex fields and their interaction?

The conservation of energy and momentum is related to two complex fields and their interaction through the conserved current. This mathematical expression describes how the energy and momentum of the fields are conserved during their interaction, ensuring that these important physical quantities are not lost or created.

4. Can you provide an example of two complex fields and their conserved current in action?

One example of two complex fields and their conserved current in action is in the theory of electroweak interactions. The two complex fields in this theory are the Higgs field and the gauge field, and their interaction is described by a conserved current called the Noether current. This current ensures that the energy and momentum of the fields are conserved during electroweak interactions.

5. How does the concept of two complex fields + interaction, conserved current relate to other areas of physics?

The concept of two complex fields + interaction, conserved current is a fundamental principle in many areas of physics, including quantum field theory and particle physics. It is also used in other fields such as condensed matter physics and cosmology. The idea of conserved currents can be applied to various physical systems to understand how they interact and conserve important physical quantities.

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