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I am studying QFT from A First Book of QFT. It is a very well-written book. However, due to some personal reasons, I cannot buy the printed book at this moment. So I borrowed this book from a person (who, in turn, borrowed it from his university library), and scanned it. Everything is fine except the notation at some places, due to the low scan resolution.
The authors write at the beginning of the book that ##p## means a 4-vector, p means a 3-vector, and ##\mathbf{p}## means the magnitude of the 3-vector.
With this in place, for the Fourier decomposition of the Dirac field, the authors write:
Here, the integration variable is ##p## (the four-vector), the arguments of the creation and annihilation operators for the particle and antiparticle (##f_s## and ##\hat{f_s ^\dagger}##) and the spinors (##u_s## and ##v_s##) is p, the 3-vector.
In the expression in the exponent, is it the 4-vectors or the 3-vectors that are being dotted?
A similar problem occurs for photon fields:
Again, is the argument in the exponent the 4-vectors or 3-vectors?
Unfortunately, at this moment I can no longer access the print book. It will be very helpful if someone clarifies the notation.
The authors write at the beginning of the book that ##p## means a 4-vector, p means a 3-vector, and ##\mathbf{p}## means the magnitude of the 3-vector.
With this in place, for the Fourier decomposition of the Dirac field, the authors write:
Here, the integration variable is ##p## (the four-vector), the arguments of the creation and annihilation operators for the particle and antiparticle (##f_s## and ##\hat{f_s ^\dagger}##) and the spinors (##u_s## and ##v_s##) is p, the 3-vector.
In the expression in the exponent, is it the 4-vectors or the 3-vectors that are being dotted?
A similar problem occurs for photon fields:
Again, is the argument in the exponent the 4-vectors or 3-vectors?
Unfortunately, at this moment I can no longer access the print book. It will be very helpful if someone clarifies the notation.