The degenerate vacuum and the infinite component wave equation

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In the field theoretical viewpoint, an infinite component wave equation, which is of first order in p '"' is derived for the one-particle wave function. The mass formulas are as follows : m=JJ.o(J +~) for the simplified Heisenberg nwdel, m= ±JJ.o(J +D for the original Heisenberg model, where J denotes the intrinsic spin of one-particle states. For this purpose, we have relaxed the requirement for the vacuum in the following way: Instead of the existence of the invari­ ant vacuum, we assume that the vacuum corresponds to an irreducible unitary representation of Poincare group with P'"=O. That is, we allow the existence of the infinitely degenerate vacuum.

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