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shakeel
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I am confuse about the dimension of an operator? Why we need an operator of Dim six or greater for new physics?
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.
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.
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.
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.
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.