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The parton distribution functions (PDFs) are momentum distributions sorted by flavor. The Fourier transforms of them give you the position distributions. You can get similar, though sometimes less specific (i.e. no flavor information) from the form-factors or structure functions. See also: What is an intuitive picture of the motion of nucleons? for the ...

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A free quark wavefunction does not exist. Instead, inside nucleons quarks are relativistic and asymptotically free, which means that they only behave like individual particles for sufficiently large momentum/energy transfer. Imagine a classical solid state analog: if you apply a very small, slowly acting force to a single atom of a crystal, the force will ...

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I) An axial (vector) symmetry transformation acts opposite (the same) under the left-handed and right-handed parts of a Dirac spinor, cf. chiral symmetry. II) The full symmetry group is the product group $G=SU(3)_F\times SO(3,1)$. The quark $q$ transforms in the representation $\underline{3} \otimes \underline{4}$, i.e. under the fundamental ...

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A Dirac spinor, as your $q$ is, has four components, corresponding to one left-handed and one right-handed Weyl (two-component) spinor, $$q = q_L + q_R.$$ $\gamma_5$ is the $4\times4$ matrix that is $1$ on the right-handed part and $-1$ on the left-handed part. The expression $$q\mapsto q' = \exp(i\Phi_a \lambda^a /2 \gamma_5)q$$ means q_{R(L)} \mapsto ...

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