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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In theoretical physics, namely quantum field theory, the classical scaling dimension of an operator O is the power of mass of an operator determined by dimensional analysis from the Lagrangian (1 for elementary bosonic fields including the vector potentials, 3/2 for elementary fermionic fields etc.). It is also called the naïve dimension or the engineering dimension. The dimension of a product is the sum of the dimensions. For example, in four-dimensional quantum field theory, the Lagrangian must have dimension of mass to the fourth power. By a dimension of the individual terms, we mean the dimension of the corresponding operators with the coefficients removed.