# Declare a Commutation Relationship in FeynCalc

In summary, the conversation is about a person who is new to using the FeynCalc extension in Mathematica for QFT. They encountered a problem involving a condition that relates two tensors with different indices, resulting in a value when commuted. The person is unsure how to express this relationship and is unsure of the capabilities of the program in handling it. They mention searching for solutions and receiving advice to focus on other tools. The homework equation is Peskin&Schroeder 3.1.

## Homework Statement

I am a rookie to the QFT extension in Mathematica called FeynCalc, and tried to use that into solving some quiz. Soon I met a problem upon some condition presented in a problem which declares an relation of two same tensor with different indices results in some value when commuted. I don't know how to express such relationship nor how intelligent the program is in dealing with that.

## Homework Equations

Thai problem is Peskin&Schroeder 3.1.

## The Attempt at a Solution

Searched the document and examples, no practical suggestions found yet.

Got the response from my kind of tutor that such operation ain't the focus of FeynCalc and I shall focus on other tools.

## 1. What is a commutation relationship in FeynCalc?

A commutation relationship in FeynCalc is a mathematical expression that describes the way two operators, such as momentum and position, interact with each other. It is used to calculate the outcome of a quantum mechanical system.

## 2. How do I declare a commutation relationship in FeynCalc?

To declare a commutation relationship in FeynCalc, you use the "DeclareCommutator" function and specify the two operators and their corresponding commutation relationship. For example, DeclareCommutator[x, p] = I*hbar.

## 3. What is the purpose of declaring a commutation relationship in FeynCalc?

Declaring a commutation relationship in FeynCalc allows you to perform calculations on quantum mechanical systems, such as calculating expectation values and transition probabilities. It also helps ensure that the calculations are mathematically accurate.

## 4. Can I declare a custom commutation relationship in FeynCalc?

Yes, you can declare a custom commutation relationship in FeynCalc by using the "DeclareCommutator" function and specifying the desired operators and commutation relationship. This allows for more flexibility in calculations for specific systems.

## 5. Are there any limitations to declaring a commutation relationship in FeynCalc?

One limitation of declaring a commutation relationship in FeynCalc is that it can only handle operators that are linear in the fields and their derivatives. Additionally, FeynCalc may have trouble handling certain mathematical expressions involving commutators, so it is important to check the results carefully.

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