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We derive an equivalent traveling wave form description for Dirac field. Inthe non-relativistic limit, such form can reduce to inverse-Galileantransformed Schrodinger-type equation. We find that, the resultingtwo-component Schrodinger-type equation from the reduction of traveling waveform description of Dirac field is different to the naive Galilean transformedSchrodinger equation. Taking into account the interactions of the system toelectromagnetic field by adding proper forms of covariant derivative, thetraveling wave form description for Pauli equation can be similarly obtained inthe non-relativistic limit. Such descriptions allow one to choose arbitraryconvenient reference frame for quantum system involving spins. UsingBargmann-Wigner formalism for field with arbitrary spin $s\geq 1/2$, whichsatisfy Dirac-type equations in all its indices, the traveling wave descriptionfor such a field can be similarly obtained from the traveling wave formdescription of Dirac field, for example, for the spin-3/2 Rarita-Schwingerfield and spin-2 gravitational field.

Traveling Wave Form Description for Dirac Field and Its Deduction To Pauli Equation Type Forms in Quantum Mechanics