On a New Elementary Particle from the Disintegration of the Symplectic &#39t Hooft-Veltman-Wilson Fractal Spacetime

Abstract

Abstract't Hooft-Veltman Wilson dimensional regularization depends crucially upon Borel summability which entails strong links to the modern mathematical theory of transfinite sets and consequently to the fractal-Cantorian spacetime proposal of Ord-Nottale-El Naschie. Starting from the above, we interpret the main step of the mathematical analysis in terms of elementary particles interaction. Thus 't Hooft-Veltman "perturbation" parameter which measures the deviation of the regulated space from the four dimensionality of spacetime is interpreted as an elementary particle with a topological mass charge equal to 0.18033989, i.e. double the magnitude of Hardy's quantum entanglement. In turn, Hardy's quantum entanglement which may be interpreted geometrically as a consequence of the zero set embedded in an empty set could also be interpreted as an exchange of pseudo elementary particles with a topological mass charge equal to Hardy's entanglement

From the Heterotic String Quartet to the Cosmic Dark Matter, Dark Energy and Ordinary Energy Symphony

“…In both cases it is reasonable to assume that we cannot see the remaining 26 4 22 − = dimensions and can regard them as compactified in one way or another similar to how we got used to think of the Kaluza-Klein 5D theory [22]. The next step in our simple scheme is to think of these 22 quasi dimensions as a sort of pre-quantum messenger particles [20][21][22][23][24]. Having accepted this move let us subdivide these 22 messenger particles to 6 plus 16 bosons [20][21][22][23][24][25][26][27].…”

“…The next step in our simple scheme is to think of these 22 quasi dimensions as a sort of pre-quantum messenger particles [20][21][22][23][24]. Having accepted this move let us subdivide these 22 messenger particles to 6 plus 16 bosons [20][21][22][23][24][25][26][27]. The reader has no doubt guessed our disarmingly simple intention to link heterotic strings with the three sectors that make up the entire energy of the cosmos.…”

“…Again an embarrassingly trivial rearrangement of the preceding equation clearly shows that a consistent description of the relevant bosonic filed requires 16 extra coordinates [13][14][15][16][17][18]. It is those 16 extra coordinates corresponding to 16 dimensions or bosonic pre-quantum particles which will play a crucial role in the next section regarding pure dark energy as distinct from dark matter and ordinary energy [20][21][22][23][24]. We note on passing, without going into detail, that the vital 16 extra bosonic spacetime dimensions need compactification and result in a gauge group 16 (1) U which when broken gives us the carrier of pure dark energy [11].…”

“…The essence of this theory is lucidly explained in many papers and text books notably by the creators of the theory, namely a group around Nobel Laureate David Gross [17,18] which is often fondly referred to as the "Princeton quartet" [17,18]. Never the less because we will present this theory in the next section with a minor twist here and there, we felt it pertinent to give here a brief account of the quintessential idea behind heterotic string theory seen from our "pure dark energy and dark matter" explanation view point [20][21][22][23][24][25][26][27].…”

“…Thus whenever we say particles here, we mean pre-quantum particle-like states which will result from symmetry breaking of a corresponding Lie group of certain dimensionality [15][16][17][18][19]. Something similar will be assumed with regard to the word wave with which we mean prequantum wave of the pre-quantum particle [19][20][21][22][23][24][25][26][27][28].…”