Mordred

Yes and to program such things requires structure and mathematical formalism. Are you trying to write your own code or be reliant upon others code? here is the pdf's (probability density functions in Mathworks as one example click on each hyperlink https://www.mathworks.com/help/stats/pdf.html Notice the Rayleigh distribution and Poisson distribution is already included? that took me less than 30 seconds to locate

I think they follow set rules as per a flow chart in the background development, Hence a set formalistic structure. I have written lots of programming codes, though my programming is more geared towards Robotic and plant automation applications. The same basis still applies, the less calculations you need to adapt formalisms the better for computational times. You want the reductions via the group structure not added caclulations in translations. For example division by 2 is simply a bit shift left operand saves on clock cycles. Think about a matrix and tensors what function could the indices serve if every entry serves as an operand? ie this for example http://www.ece.ubc.ca/~msucu/documents/matlab/examples of programming in matlab.pdf

LOL try a simulation of 1000+ particles for simply doing galaxy rotations on a computer, I did that once in N_body and locked up my comp for 3 months for a few rotations.

Then you only require 1 formalism every operation that can be transferred to a computer can be done using the standard gauge groups under G when properly done including string theory. They follow one specific formalism under G for the quantization rules. That is the whole purpose behind lie groups in the first place How much flexibility do you want in your program? N-body codes can do a lot

If your purpose is to develop GUT theory others can use piecemeal methods is garbage as you will be the only person who will ever know how you developed your equation. You won't even have sufficient understanding to be able to teach it to anyone else. What good is it ever going to do if no one else can follow your work ? via switching formalism, piecemealing different equations etc? Lets do an example. 1) Provide a holomorphic projection map of your different field manifolds from your Euclid space to the Fock space via the Ghost operator. Provide the diffeomorphisms that result from these connected/disconnected manifolds. 2) What are the principle constraint equations pertaining to the Ghost operators as they pertain to the Euler and Noether's theroem. 3) define each principle fibre bundle of each manifold and define the principle operators of each as well as the boundary conditions for each fibre bundle.

why not? define your entangled state is it going to be single particle or many particle? I have a real hard time seeing how you can piece meal different treatments into different sections then expect to get intelligent answers in your equations.

Always jumping to the middle and end but never following from the beginning and you expect it to work?

Or another method is to gather the necessary research already done by others in every group your applying. Then tossing that into Wolfram

No your missing my point. OK lets try this angle. Lets say I want to use the Loop quantum gravity quantization rules to build a complete GUT treatment to arrive at the equivalent of SO(10). LQG uses Wicks rotation for quantization. Each group is then modelled using these same wick rotations which alters each group. This is also very possible and forms the basis of loop quantum cosmology. You apply a different quantization methodology then by the precise same rules you must apply those quantization rules to each group. This is where I have you at an advantage in that I have followed big G treatments from beginning to end on all SO(10) including the SU(N). So I learned just how extensive quantization rules apply throughout groups. Once you modify the basis groups you must follow those treatments to the higher dimension groups as well

Is it completely integrated throughout all portions of your equation ? any quantized element must follow the BRST quantization including the GR portions

That is precisely my point once you modify U(1) you must follow the modifications throughout all SU(n) groups as the lie algebra of those groups are all G homeomorphisms not little g. However there is treatments available and work already done for each group once you dig deep enough into the avail literature.

here start here with the BRST quantization https://en.wikipedia.org/wiki/BRST_quantization note any group G is replaced by little group [math]\mathcal{g}[/math] mentioned on that page.

Yes the ghost operator can definetely be used for Yang mills but it also modifies Schrodinger and Klein equations in how to handle the spinors. Google specifically SO(10) and BRST. Look through the arxiv papers that have BRST treatments One paper I encountered suggested using a double ghost operator on Schrodinger for quaternions.

Vmedvil if your planning on introducing the BRST action treatments to Yang Mill and Dirac actions which does have validity. Your going to have to literally start from scratch to properly build your model. I've been reading up on the BRST treatments out there and can see the viability but I can also see numerous potential conflicts if you don't step back. It is a literally a separate quantization methodology and as such should be taken from its rudimentary groups forward. It is quite possible to fully develop a model using this methodology but must be done properly to get it to work. Its never a valid policy to mix treatments. I'm seriously hoping you already realize that critical detail as it redefines how bosonic and fermionic action is handled.

Your getting there no worries. No the e for energy density is not the critical density. The critical density is the density that expansion will halt its expansion but for a flat universe will take an infinite amount of time. Your numbers are within the right order of magnitude which is good. The confusion your having with e in the equation is related to thinking of it as the critical density. It isn't its the total energy for a spatially flat universe it should be approximately the critical density which you have above. [math]\epsilon_t=\epsilon_\lambda+\epsilon_{matter}+\epsilon_{radiation}[/math] in the notation being used in this paper So for the individual equations of state you need to look at the mixed states of the fluid equation and use the condition [math]P<\frac{-\epsilon}{3}[/math] to derive w=-1 see bottom of that link. The previous steps is matter then radiation equations of state. Here this procedure has a more thorough procedure to follow http://www.m-hikari.com/astp/astp2013/astp9-12-2013/siongASTP9-12-2013.pdf hopefully you will see the connection to the fluid equation without giving the direct answer. As the first link note4 is giving 3 separate examples of deriving the individual equations of state from the fluid equation (specifically the deceleration equation which is the hint for the minus sign. See note if [math]\epsilon[/math] an P are both positive the universe decelerates.

k good enough always have to check that you don't run into that conflict there is procedures to downgrade or upgrade propagators and operators

Not saying it doesn't but its safer to use the propogator/ operator terminology particularly when you deal with Strings as one example. It was just a word of caution to be careful when using different treatments. Lets put it this way VP is associated with the propagator but the propagator is not VP

The reason for the caution is its not always correct to associate VP as a propogator. We have to watch that when using field treatments as opposed to QM. It depends on how the two are defined in the treatments applied

Careful there you might want to look at what the definition of Operator and Propogator entails https://en.wikipedia.org/wiki/Operator_(mathematics) https://en.wikipedia.org/wiki/Propagator#Non-relativistic_propagators for Feyman path integrals the propagators are your S-matrix internal lines with the operators being the real particle states

Then that's the one I would use for the Ghosts and entanglement http://www.scholarpedia.org/article/Faddeev-Popov_ghosts https://pure.tue.nl/ws/files/3500680/727432508244297.pdf OK BRST quantification that changes things lol the last two links helps now I'm following you better. In particular thee Lorentz gauge on the last paper. Interesting idea be interesting to see

the paper is a multi particle treatment not a single particle treatment in entangled states which in turn will generate internal turbulent flows and and be self interfering. Hence they are using hydrodynamics to describe the internal multi particle state its an approximation of the internal state forces. https://en.wikipedia.org/wiki/Reynolds_number either way its not the paper you want for the Langevian treatment What Langeevian are you specifically looking for (entangled states)?

D'oh ok forgot all about that number roflmao that makes far more sense lmao

this the right paper title? Spin-polarized supercurrents for spintronics: a review of current progress ooops no wrong paper typed in wrong found it let me look through it https://arxiv.org/ftp/arxiv/papers/1509/1509.02442.pdf As per our PM convo its specific to this papers application as electron radius

Good question that one isn't common to normal QFT treatments can you pin that arxiv so I can study it before I answer

yeppers lol I'll let you work on it my advice study materials specific to those three groups it will have all the Langevians and symmetries you will need for the SM model