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Dirac propagator in Non-Abelian Theory

Hints: P&S is considering the free fermion propagator in eq. (16.4), i.e. the cubic $\bar{\psi} A\psi$ interaction term does not contribute. In the Lagrangian density (16.1) there are implicitly ...
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Question about the parity violation of weak interaction Lagrangian

$$ \gamma^0 P_L \gamma^0 = P_R, \\ \gamma^0 P_R \gamma^0 = P_L, $$ $$ P: \qquad \psi(x) \longrightarrow \gamma^0 \psi(-x) ~~~~\leadsto \\ P: \qquad \psi(x)^\dagger \longrightarrow \psi(-x)^\dagger ...
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Soldering Spinors in cylindrical coordinate

It seems that the answer is yes and we can write the soldering in deferent coordinate system.
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The mathematics of different particle rotations

Consider a point in space, and the effect a rotation would have on that point. Because the point has no internal structure (in other words, it is characterized entirely by its spatial location), a ...
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What is the idea behind 2-spinor calculus?

May I suggest a somewhat intuitive way to try to answer the question, inspired by the late Sir Michael Atiyah's view that "spinors are the square root of geometry". Atiyah argues in his ...
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What is the correct way of looking at the Dirac field?

To add to what hft said, $\hat \psi$ is valued in a tensor product of operator densities and the spinor bundle. If you want to get an operator, you need to pair it with a smooth section of the dual ...
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What is the correct way of looking at the Dirac field?

I agree that both are operators but $\hat{\psi}$ is more than an operator. It is also a matrix. What is the correct way to think about $\hat{\psi}$ so as to distinguish it from $\hat{\phi}$? For ...
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What is the idea behind 2-spinor calculus?

A $2$-spinor $\psi\in V\cong\mathbb{C}^2$ is here a (left) Weyl spinor, so Penrose & Rindler are e.g. exploring the fact that the complexified Minkowski spacetime $\mathbb{C}^{1,3}\cong V\otimes \...
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What does it mean by spin 1/2 or spin 2 field?

Relativistic fields are classified by how they transform under the Lorentz group. This means they are classified by representations of the universal cover of the Lorentz group ${\rm SL}(2,\mathbb{C})$....
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What does it mean by spin 1/2 or spin 2 field?

In geometrical view, spin $s$ particle returns its original state when it is rotated as $2\pi / s$. For example, spin $1/2$ has minus sign with rotating as $2\pi$, but it returns original state with ...
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