Relativistic Theory Of Infinite Statistics Fields

The usual quantum theory is based on Bose-Einstein statistics or Fermi-Dirac statis-tics. However, recent research suggest that there exist particles obeying other statistics, such as para-bosons and para-Fermions. In greater than two space dimensions, there is one new consistent statistics in which all representations of the symmetric group can occur. This is infinite statistics, which is also called quantum Boltzmann statistics. Unlike the usual statistics, the infinite statistics has a nonlocality property, which is an important char-acter of quantum gravity, so it may help us to study new physics. Recently, infinite statistics has been applied to many subjects, such as black hole statistics, dark energy quanta, large N matrix theory and holography principle.Unfortunately, the validity of relativistic quantum field theory obeying infinite statis-tics is still in doubt. This theory can also have relativistic kinematics. The CPT theorem and cluster decomposition are still hold for free fields. However there are two difficulties for infinite statistics to have consistent relativistic theory. For one thing, it is hard to check the Lorentz invariance without locality. For the other thing, by requiring that energies of systems that are widely spacelike separated should be additive, the conservation of statis-tics forbids infinite statistics. In this paper we introduce the general property of infinite statistics and its current research situation. We also prove the existence of interaction rela-tivistic field theory obeying infinite statistics by solving the two difficulties above. First, we prove that the interaction density satisfies a weak locality condition, which is sufficient for Lorentz invariance of the S-matrix. By applying the condition that the energies are additive for product states, we showed this theory obeys conservation of statistics with selected form of interaction Hamiltonian. We also give some consistency analysis of this theory such as CPT conservation and Feynman rules. We find that the vector-spinor interaction should produce CPT violation, while the Feynman rules of infinite statistics field are partly sim- ilar to conventional Feynman rules, so some traditional methods such as renormalization analysis can be extended to our new theory.In this paper, we also introduce another work that a static, spherically symmetric black hole in D-dimensional spacetime can be in equilibrium with some special kind of matter. We study the property of such black holes and matter. We find that these hairy black holes can live only in some special dimensional spacetime. This work is listed in the appendix.