What is the spin of an operator in QFT?
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Operators in quantum field theory with nn Lorentz indices that are symmetrized and traceless are referred to as spin-nnoperators. For example, a spin two operator would be
ψ¯(γμ∂ν+γν∂μ)ψ−ψ¯γμ∂μψ
ψ¯(γμ∂ν+γν∂μ)ψ−ψ¯γμ∂μψ
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Spin. Finally, I must mention an important attribute of quantum fields called spin or helicity. Spin is the more common term, but it gives the false impression of an object spinning. In QFT spin or helicity is a measure of the internal complexity of the field, i.e., the number of internal components. The possible spin values of quantum fields are 0, 1/2, 1 or 2 (in units of Planck's constant divided by 2π). The EM field is fairly complex with two component fields (electric and magnetic), each of which is directional, and its spin is 1. You will be surprised to learn that the gravitational field is the most complex of all the fields, with a spin of 2. After all, you ask, what could be simpler than a single attractive force, but
when Einstein introduced his field equations, the internal complexity expanded greatly. I didn't mention this in Chapter 2 because I thought you had enough to worry about, and anyway the reason for it is beyond the scope of this book. I ask you to accept that the gravitational field is more complex than the EM field and has a spin or helicity of 2 without asking why, or even understanding what that really means. Another thing I must ask you to accept on faith is that this abstract definition of spin, related to field complexity, causes a quantum to exhibit angular momentum just as a spinning particle would.
when Einstein introduced his field equations, the internal complexity expanded greatly. I didn't mention this in Chapter 2 because I thought you had enough to worry about, and anyway the reason for it is beyond the scope of this book. I ask you to accept that the gravitational field is more complex than the EM field and has a spin or helicity of 2 without asking why, or even understanding what that really means. Another thing I must ask you to accept on faith is that this abstract definition of spin, related to field complexity, causes a quantum to exhibit angular momentum just as a spinning particle would.
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