What is ↔ mean? in commutation relation?

Thread starter rar0308
Start date Jun 12, 2013
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Commutation Mean Relation

In summary, a commutation relation is a mathematical statement used in physics to describe how two quantities or operators interact with each other. The symbol "↔" represents the operation of commutation, which is similar to regular algebra. It is used to understand the behavior of a system and derive properties and equations. Examples include the Heisenberg uncertainty principle and the relationship between angular momentum and position in quantum mechanics. Commutation relations are crucial in quantum mechanics for understanding subatomic particle behavior and play a central role in its mathematical formalism.

Jun 12, 2013

rar0308

I found this in Srednicki's QFTbook.
I don't know what ↔ means.
Help me, please

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Jun 12, 2013

Timo

Presumably "the same term as before, but with the two indices exchanged". It should be deductible from the context, though.

Jun 12, 2013

rar0308

Like this?

Jun 12, 2013

Bill_K

Science Advisor

Insights Author

Yes, like that. (Except you forgot the i.) This is Eq (34.4) in Srednicki.

What is a commutation relation?

A commutation relation is a mathematical statement that describes how two quantities or operators in a physical system interact with each other. It is used to understand the behavior and properties of a system.

What do the symbols "↔" mean in a commutation relation?

The symbol "↔" in a commutation relation represents the mathematical operation of commutation, which is a way to measure the extent to which two operators commute or do not commute with each other. It is similar to multiplication and division in regular algebra.

How is a commutation relation used in physics?

In physics, a commutation relation is used to describe the relationship between two physical quantities or operators that do not commute with each other. It helps to understand the behavior of a physical system and can be used to derive various properties and equations.

What are some examples of commutation relations?

Some examples of commutation relations in physics include the Heisenberg uncertainty principle, which describes the relationship between the position and momentum of a particle, and the commutation relation between the angular momentum and the position of a particle in quantum mechanics.

How is a commutation relation related to quantum mechanics?

In quantum mechanics, commutation relations are crucial for understanding the behavior of particles at the subatomic level. They are used to describe the relationship between different operators, such as position and momentum, and they play a central role in the mathematical formalism of quantum mechanics.