[AntonioLao]

The divergence of Feynman one-loop propagator for bosons and fermions could have been replaced by a convergent integral and assuming the existence of fictitious massive particles with ghost couplings. Further simplification could have been accomplished by dimensional regularization. However, none of these fixes can give completely satisfactory explanation why low energy radiations always scatter away from their sources even though high energy ones interact, creating matter and energy profusely in a very short time. The explanatory inability and limitation could lie within the simplified Feynman diagram itself.

Feynman diagram is constructed by a 1-space and 1-time axis analogous to the complex plane. Maybe out of respect for mathematical logic and desire for rules sticking, Feynman chose to keep silent the physical shortcomings of complex numbers outweighed by the usefulness in theoretical physics. Dimensionally speaking, the diagram is basically 2 dimensional (or two-valued), 1-space and 1-time dimension. Similarly, the complex plane is also 2 dimensional, 1-real and 1-imaginary. The imaginary part seems to correspond to the time part of Feynman diagrams and fittingly so since ideas of physical time remain personal states of mind, not something tangible. Subjectively, time is blatantly obvious and hopelessly inevitable. Objectively, it is mysteriously ambiguous and surprisingly reversible. Therefore, imaginary time allows achievement of single-valued physical quantities, e.g. mass, energy, temperature, density, volume, etc. furthermore time is also single valued parameter.

A loop on a Feynman diagram describing its inside and outside in addition to its clockwise and counterclockwise rotation could become extremely complicated. A simpler approach is to choose a system where the center of the loop coincides with the origin of the complex plane. Then the loop becomes simply a complex circle of constant absolute value with arbitrary radius. The problem with this approach is the need for a transformation theory satisfying Lorentz invariance for every particle relative to every other particle. Nonetheless, this complex circle represents 1st power of energy in 2 dimensions. To represent 2nd power or square of energy in higher dimensions, it is necessary to link two complex circles together which would not share a common center but each of the two fundamental radius vectors have two end points serving as centers of each other.

Traditionally, Dirac used spinors to describe squares of energy and spin in higher dimensions. His theory led to positive and negative energy solutions and so sensibly predicted the existence of antimatter. However, it is now well established that antimatter can only exist freely in an environment of extreme temperature (in the present universe, at much lower temperature, matter and antimatter are both slaved asymmetrically to each other as in a hydrogen atom of one proton and electron – mass ratio 1836 to 1), a condition ideally connected to the early universe of Planck’s energy, time, and length. Unfortunately, the existence of spinors is based on a theory of isotropic vectors of zero lengths with infinite degrees of freedom. These are complex circles where their radii vanish or set identically zero with infinitely ineffective directional attributes, nevertheless having 4p rotational symmetries known as the complex phase factors. Reasonably, these freed the theory of complicated shifting of origins. The fact that all hydrogen atoms behave almost (Lamb shifts) the same at the same physical conditions regardless of the spacetime locations suggests that the universal invariance lies within the surrounding quantum vacuum which could be described by singular Hadamard matrices of finite infinitesimal lengths. Coincidently, the surface area of a closed sphere of unit radius is also 4p. Therefore, the rotational symmetry of the complex phase factor is related to this area implying that closed volumes of any arbitrary particle could not be possible if the phase angles are less than or greater than 4p. These volume closure deficiencies appear as holes of Riemann surfaces of positive curvature.