#### Abstract

An attempt to construct a theory that links the macroscopic and microscopic properties of matter is presented. This is done using a space of more than four dimensions. Equations for microscopic-particle fields are investigated in a fixed six-dimensional metric space. The topology of the space is solely responsible for the quantization of mass and charge. The metric contains terms which transform like the Yang-Mills $B$ field. These terms appear appropriately in all particle equations. Without the $B$ field, the symmetry group of the theory is P×SU(2)/Z(2). The presence of the B field lowers this symmetry. Particle mass spectra are presented for six-dimensional scalar, spinor, and vector fields, and a coupling-constant ratio is predicted. The later part of the paper deals with the cosmological implications of the microscopic model presented in the first part of the paper. It is shown that Einstein's equations for the metric are consistent if a massless cosmological vector field is introduced. A critique of previous higher-dimensional field theories along with a summary of the results of an eight-dimensional theory is given. Since all symmetries dealt with result as approximations to the equations of the model, the no-go theorems are not applicable. Nevertheless, the six- and eight-dimensional models contain the shadows of the $P\times \frac{\mathrm{SU}\left(2\right)\mathrm{}}{Z\left(2\right)\mathrm{}}$ and $P\times \frac{\mathrm{SU}\left(3\right)\mathrm{}}{Z\left(3\right)\mathrm{}}$ symmetries in all particle-field representations.

DOI: http://dx.doi.org/10.1103/PhysRevD.1.488

- Received 9 May 1969
- Published in the issue dated 15 January 1970

© 1970 The American Physical Society