is a one-dimensional space built of 12 poles with 6 distinct charges. Thus, poles
X
Boolean
occur in pairs. Since one-dimensionality must be maintained for the theory to work, pairs of poles form “loops,” going from 0 to some charge of 1 to 0 again. This means that
can be thought of as knotted. Charges are allowed to change what pole they
X
Boolean
are attached to by going from a 1 to a 0 to a new 1.
2.0. The Structure of a Lie-Hilbert Space with a Basis of X
Boolean
2.1. A Lie Hilbert Space in which a Pseudo-Boolean Space Acts as a Base Vector
Until now, the Pseudo-Boolean space has been discussed almost exclusively. The Pseudo-Boolean space is a way of describing a single-particle space, or Fock space.
However, this theory posits that Fock spaces act as points when observed instantaneously and become vectors when integrated in respect to time. It’s predicted
that these vector spaces act as a basis for a macroscopic Lie Hilbert space, .
V V
.. V
= a
1
+ a
2
+ . + a
n
Which can also be denoted
{V } = a · ∑
n α
α
And since is the basis vector of , which in this theory has been set as the
V
α
Pseudo-Boolean Fock space, we can substitute. Given that
, }
X
F ock
∈ {X
Boolean
{X }
= a · ∑
n α
F ock
α
Using as the Hamiltonian operator and given that
is Lie
Ⓗ
Ⓗ Ⓗ X
}, ] = [
: {
F ock
a
This space has highly unusual topological properties of variable density and separability. Separability varies based on neighborhood overlap, but since the neighborhood of points
is actually the neighborhood of basis vectors in which varies relative to time, separability is variable. Density is also variable, and both properties will be discussed
below.
2.2. Hamiltonian Operators in the Lie Space
In the Lie Hilbert Space, the Hamiltonian operator will not be treated as a Lie operator, but as a special case of addition and Lie multiplication. This is not difficult, given that the
Hamiltonian is represented as
fyb985
Ⓗ = Ⓣ + Ⓥ
Where Ⓣ is the kinetic energy operator and Ⓥ is the potential energy operator. The potential energy operator for a system of n-numbered non-interacting particles is
traditionally notated as
Ⓥ r , t
= ∑
n i=1
V
i
But it can be notated more conveniently for a Lie space as
[ {X } , n ]
Ⓥ = Π
Boole
So that the series Lie Bracket represents the same n non-interacting particles. The Hamiltonian is used to represent the necessary energy to perform a topological
deformation of a pseudo-Boolean space within the Lie Hilbert into a topologically equivalent pseudo-Boolean space.
Since deformations can be performed in two directions, this theory provides a solution to the creation of subatomic particles without symmetry breaking.
2.3. The Time Dimension as Being of Variable Density
