Fermions
Fermions
Consider a multiway graph representing the time evolution of some quantum states.
Case 1: the edges merge (bosons)
Case 1: the edges merge (bosons)
I.e. the path weights add, and you get a single quantum state out of these multiple inputs
Case 2: the edges don’t merge (fermions)
Case 2: the edges don’t merge (fermions)
If it is a pure tree, you have to go back to the beginning of the universe to get a merger: i.e. the states will be maximally separated in branchial space : i.e. they will have opposite phases
And these states can never get together: i.e. the “electrons” can never wind up in the same state.
And these states can never get together: i.e. the “electrons” can never wind up in the same state.
Essentially: the branchtime worldlines of different fermions do not converge, but they do for bosons.....
Essentially: the branchtime worldlines of different fermions do not converge, but they do for bosons.....
Total antisymmetry with n fermions: everything has to be at an opposite corner of branchial space
Total antisymmetry with n fermions: everything has to be at an opposite corner of branchial space
In[]:=
KaryTree[31]
Out[]=
Minimal case: n independent paths.
Why exactly is it antisymmetrizing? I.e. are taking the various path weights, and combining
In[]:=
Array[p,5]
Out[]=
{p[1],p[2],p[3],p[4],p[5]}
In[]:=
Array[p,2]
Out[]=
{p[1],p[2]}
In[]:=
ResourceFunction["MultiwaySystem"][{"A""AB"},"AA",5,"BranchialGraph"]
Out[]=
In[]:=
ResourceFunction["MultiwaySystem"][{"B""BA"},"BB",5,"BranchialGraph"]
Out[]=
In[]:=
ResourceFunction["MultiwaySystem"][{"B""BA","A""AB"},{"AA","BB"},3,"BranchialGraph"]
Out[]=
In[]:=
{mwGraph1=ResourceFunction["MultiwaySystem"]["A""AB","AA",8,"StatesGraphStructure"],mwGraph2=ResourceFunction["MultiwaySystem"]["A""BA","AA",8,"StatesGraphStructure"]}
Out[]=
,
In[]:=
{branchialGraph1=ResourceFunction["MultiwaySystem"]["A""AB","AA",8,"BranchialGraphStructure"],branchialGraph2=ResourceFunction["MultiwaySystem"]["A""BA","AA",8,"BranchialGraphStructure"]}
Out[]=
{
,
}
In[]:=
rulialGraph=ResourceFunction["MultiwaySystem"][{"A""AB","A""BA"},"AA",8,"StatesGraphStructure"]
Out[]=
In[]:=
HighlightGraph[rulialGraph,{mwGraph1,mwGraph2}]
Out[]=
In[]:=
rulialBranchialGraph=ResourceFunction["MultiwaySystem"][{"A""AB","A""BA"},"AA",8,"BranchialGraphStructure"]
Out[]=
Potential claim: the fermion wave function is very “puffy” and fills out a volume that is essentially LeviCivita * basis vectors
Whereas the boson wave function is “branchially” just a point...
Whereas the boson wave function is “branchially” just a point...
The next step: spin-statistics / spinors
The next step: spin-statistics / spinors
When projected to make a “spatial slice”, the boson case will be “two way” and the fermion case not....
Next up: spin / spin quantization
Next up: spin / spin quantization
Basic concept of fermions
Basic concept of fermions
[[Fermions exist because branchial space does not contract to a point. In other words, fermions “maintain quantum mechanics”. Analogous to the maintenance of space. ]]