Effective dimension of the Universe and violation of the Pauli principle
We discuss a Modified Field theory (MOFT) in which the number of fields can vary. It is shown that in MOFT at very large distances the effective number of spatial dimensions is D ≈ 2 which corresponds to the observed fractal distribution of galaxies and the logarithmic behavior of the Newton's potential for a point source. It is also shown that in MOFT fermions obey the so-called parastatistics and at large scales can violate the Pauli principle. The Modified Field Theory (MOFT) was suggested in Ref. [1] to account for spacetime foam effects and as it was recently demonstrated in Ref. [2] MOFT provides a reasonable alternative to the dark matter paradigm. It was shown that in some range of scales r min < r < r max the Newton's and Coulomb's energies of interaction between point particles in MOFT show essentially logarithmic (instead of 1/r) behavior. From the dynamical standpoint this looks as if every point source is surrounded with a halo of dark matter and dark charge. In addition to logarithmic potentials MOFT seems to require that the Universe has a fractal structure in the same range of scales with dimension D ≈ 2 [3], which is supported by the observed fractal distribution of galaxies (e.g., see Refs. [4]-[7]). It is natural to expect that these two facts (logarithmic potentials and the fractal distribution) have a common pure geometrical origin. In the present paper we show that it is really the case. It turns out that in the range of scales r min < r < r max there takes place some kind of a dimensional reduction of space, i.e., in this range an effective number of dimensions of the Universe is D ≈ 2. This, however, requires that fermionic and bosonic fields in MOFT have to be considered on an equal footing. Indeed, the basic idea of MOFT (e.g., see Ref. [1]) is the fact that nontrivial topology of space displays itself in the multivalued nature of all observable fields, i.e., the number of fields represents an additional dynamical variable. Moreover, the number of fields was shown to depend on the position in the momentum space [1, 2]. The topological origin of this additional variable means that the number of fields N (k) should represent a specific function of wave numbers k which is common for all types of fields and serves as a geometric characteristic of …