Reparameterization Invariance in Heavy Particle Effective Field Theories

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In a low energy effective theory, the fields of heavy particles with mass m and total momentum p depend on both a velocity v and a residual momentum k such that p =mv +k. However, there is some arbitrariness in such a description because one may also use a slightly different velocity with a compensating change in the residual momentum. This non-uniqueness is the origin of an invariance under such a reparameterization which imposes non-trivial constraints on the theory. The implications of this invariance for effective theories of heavy spin-0, 1/2, and 1 fields is investigated.