Emmm... Don't start twisting my words sir. I have been doing work on it. My own personal investigation into it. That is work nonetheless.
What precisely is this 'personal investigation'? If you can't do the mathematics than you are only able to 'investigate' it by reading other people's wordy explanations of their investigations. Even if you could then reach a viable qualitative conclusion you have no way of examining whether or not your conclusions are true as you're unable to examine the equation's mathematical properties.
There's nothing wrong with reading about it or finding out how its used by physicists or the formulation in terms of mathematics but if you think you're investigating it in the way someone writing research papers on it would then you're deceiving yourself. This isn't me trying to twist words or be rude, its just a bit of advice that I'm sure a great many people who do research into the Dirac equation will agree with.
Alphanumeric, do not start to talk to me like the others here. If you do, I will do to you what I did to guest. Ignore mode, it's an excellent action in some cases.
This is hardly the way to behave if you're intellectually honest. I've been through the whole process of learning about the Dirac equation and I know many people who have done it too, so I know from first and second hand experiences that you're not going to do anything worthwhile if you aren't willing to put in the effort for the basics. There's a reason advanced university courses often have 'required courses', without the basic fundamentals understood then someone cannot do the more advanced material which builds on them.
If you think that this is such an insulting thing for me to say that it warrants putting me on ignore than you really need to consider what it is you want to do, do you want to learn something or just appear to learn something? Its no skin off my nose if you want to do the latter though.
That's all very nice, but is the idea consistent?
Renormalisation? Yes. And its not 'all very nice', as my point was that you were mistaken about the development and meaning of the things you mentioned. Do you now accept that you were mistaken or do you wish me to explain further? I just don't want you to brush off my correction and ignore it, as its only hurting your own learning if you do that.
Entanglement as I am sure you know, involves connected particles quantum mechanically, and, it also involves particle pairs - one system is connected to another system, if the two where created from the same source. If antiparticles truely do not come in pairs, and if there is always another two virtual particles in the vacuum, then all four particles can be quantum mechanically-connected, or atleast, I would have presumed so.
Why are you talking about 4 particles? The entanglement would be between the two particles created in
pair production. Other pairs need not be involved, though it is possible occasionally they might interact and form entangled systems for a while.
This illustrates my point, in order to examine entanglement in quantum field theories you're going to need to know some quantum field theory, non-relativistic quantum mechanics and entanglement. Entanglement in non-relativistic quantum mechanics has particular properties which can be formulated nicely in terms of the bra-ket notation so if someone were to attempt to describe in any non-arm waving away entanglement in spinor fields of quantum field theory they'd need to demonstrate similar structures to the non-relativistic case are formed when pair production occurs.
In the case of your claim you'd need to demonstrate that not only does pair production produce entangled pairs but it produces entangled pairs of entangled pairs! Even in the simplest examples you can get different types of entanglement, depending on which particles entangle with which. The GHZ state $$\frac{1}{\sqrt{2}}\Big( |000\rangle + |111\rangle \Big)$$ and the W state $$\frac{1}{\sqrt{3}}\Big( |100\rangle + |010\rangle + |001\rangle \Big)$$ are both 'maximally entangled' triplets of qubits but they are not equivalent. This only gets worse as you increase from qubits to qudits and triplets to arbitrary numbers. Hence 'investigation' into entanglement in quantum field theory pair production would need to be very precise and methodical. If you lack the knowledge to be able to do the details then there's very little investigation you can do.
My advice, speaking from personal experience, is you start with non-relativistic quantum mechanics, understand formal entanglement properties in it and
then move onto quantum field theory (and that's assuming you also learn all the required things for those!). Of course the only person's time you'll be wasting if you don't is your own but if you aren't just wanting to appear well read but to actually
be well read then you'll heed my advice.
This was based on Susskinds work cosncerning that quarks do not come individually, but always by pairs or more.
Pair production and colour confinement are two different things, other than if you put enough energy into a system to pull colour charges apart you 'snap' the gluonic flux tube and you get more quarks via pair production. Pair production facilitates colour confinement but it doesn't cause it. And quarks don't come in matter-antimatter pairings always, that's only for mesons. Baryons have 3 quarks, so you can't have pairings in that. The reason for the pairings and triplets of quarks is their colour, not what you're implying.
Again, if you read up on the basics before making conclusions you will make less flawed conclusions.
My question is very simple. Is the idea consistent or flawed? One problem might be, is if there is no infinity in the equations, would this result in a constraint where electrons can show up, in their real forms? If there is atleast a small amount of spacetime where the virtual particles do not fill, will this place a crucial limit for instance, on where real particles can show up?
I think you need to first get your head around the a 'virtual' particle is.
You've skipped ahead and now making mistake after mistake. Yes, it takes people doing this stuff full time 3~5 years to get to quantum field theory but there's a reason for that, just as there's a reason universities teach quantum field theory
after quantum mechanics, special relativity, electrodynamics, linear algebra and vector calculus, QFT is very complex and requires an understanding of a great many areas of maths and physics. Without that understanding you aren't going to get far, even if you manage to convince yourself otherwise.