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I present explicit examples of generalizations in relativistic quantummechanics. First of all, I discuss the generalized spin-1/2 equations forneutrinos. They have been obtained by means of the Gersten-Sakurai method forderivations of arbitrary-spin relativistic equations. Possible physicalconsequences are discussed. Next, it is easy to check that both Dirac algebraicequation $Det (\hat p - m) =0$ and $Det (\hat p + m) =0$ for $u-$ and $v-$4-spinors have solutions with $p_0= \pm E_p =\pm \sqrt{{\bf p}^2 +m^2}$. Thesame is true for higher-spin equations. Meanwhile, every book considers theequality $p_0=E_p$ for both $u-$ and $v-$ spinors of the $(1/2,0)\oplus(0,1/2))$ representation only, thus applying the Dirac-Feynman-Stueckelbergprocedure for elimination of the negative-energy solutions. The recent work byZiino (and, independently, the articles of several others) show that the Fockspace can be doubled. We re-consider this possibility on the quantum fieldlevel for $S=1/2$ particles. The third example is: we postulate thenon-commutativity of 4-momenta, and we derive the mass splitting in the Diracequation. Some applications are discussed.

Solutions in the (1/2,0)+(0,1/2) Representation of the Lorentz Group