Authors: Johan Noldus
Hamiltonians in particle interactions are subject to a number of constraints originating from locality, the cluster decomposition principle and Lorentz covariance of the scattering matrix. Moreover, it is always assumed that the Hamiltonian must be defined on a Hilbert space and be bounded from below, the latter would be a requirement following from stability of the system. In this paper we examine if these criteria are really mandatory, as it is well known that all of them taken together lead to the usual infinities of quantum field theory. In particular, we study a class of Hamiltonians unbounded from below and examine its stability. This leads us into the construction of novel statistics in three space dimensions; it is shown that for rigid strings the possibilities for statistics exceed those for standard anyons in two space dimensions
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[v1] 2015-11-04 11:47:29
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