Dimensions of an operator

In summary, the conversation is discussing the use of dimension 6 or greater operators in physics. These operators are traditionally not considered due to being non-renormalizable, but recent understanding of the renormalization group suggests they should be included when searching for new physics. However, there are also other methods, such as supersymmetric extensions of the standard model, that can incorporate new physics without the use of these higher dimensional operators. It would be helpful for the person asking the question to provide more information about their understanding of physics, specifically quantum field theory, in order for a better answer to be given.
  • #1
shakeel
23
0
I am confuse about the dimension of an operator? Why we need an operator of Dim six or greater for new physics?
 
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  • #2
It's a little unclear how/what you don't understand.

Dimension 6 or greater operators are non renormalizable, so traditionally we don't write them down. But experience with the renormalization group tells us that we should consider those terms as well, so sometimes when we look for "new physics" we do it by considering higher dimensional operators. However, I believe this isn't necessary for new physics, for example supersymmetric extensions of the standard model contain new renormalizable terms, so these terms are of dimension 4 but aren't in the standard model.

Maybe you can elaborate a little bit more about what you know about physics (specifically quantum field theory)?
 

1. What are dimensions of an operator?

The dimensions of an operator refer to the number of independent parameters required to fully describe the operator. This is also known as the number of degrees of freedom of the operator.

2. How are dimensions of an operator determined?

The dimensions of an operator are determined by the number and type of input and output variables it operates on. For example, a linear operator that takes three input variables and produces two output variables will have dimensions of 3x2.

3. Can an operator have infinite dimensions?

Yes, some operators can have infinite dimensions. This is often the case for operators that operate on continuous or infinite-dimensional spaces, such as differential operators or integral operators.

4. What is the significance of dimensions of an operator?

The dimensions of an operator can provide important information about the properties and behavior of the operator. For example, the dimensions can determine whether the operator is invertible, whether it can be composed with other operators, and what types of transformations it can perform.

5. How do dimensions of an operator relate to the dimensionality of a system?

The dimensions of an operator and the dimensionality of a system are closely related. The dimensions of an operator indicate the number of variables that are required to describe the system and the dimensionality of the system is determined by the number of independent variables that are required to fully characterize the system. In many cases, the dimensions of an operator and the dimensionality of a system will be the same.

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