Some More Stuff About Course 6 -- As To The Toroidal Nature Of Strings

The metrics of that substringular phenomena, that are based on the past and future occurences that happen --  act, among such tiny particles and gauge-actions, that effect the metrics of the rest of that substringular arena -- that exist along the kinematically Fourier differentiation of phenomena, that interact from both within and from outside of the Ultimon.  The main exception to the condition of those metrics, that do not have as much of a probability of effecting the surrounding metrics in a necessarily spontaneous way -- is when eigenstates of space that proceed from within a series of space matrices, are often re-distributed to a sequence that functions as part of a different universe.  (Parallel universes that are different, do not necessarily have a directly corresponding spontaneous interaction with other universes -- during a covariant-related determination of group instanton.)  All of the parallel universes and time-potentials -- as well as all of the sets of parallel universes that exist -- are of the fabric of the Ultimon.  For an allegorical example that anyone would know -- the earth appears flat, yet the earth is not flat.  The direct fabric of the Ultimon -- appears completely topological and smooth, yet during certain metrics and submetrics that exist over the stretch of space and time, this is not always so.  This means -- that after each duration of the Bases of Light, the flow of the phenomena of the Continuum, -- tends to adjust in a multiplicit manner per each individually taken discrete increment of energy, by one or more discrepancy interiorly on either side of its construction.  This tendency of discrepancy -- is due to the fact, that there is no such thing as a completely one or a completely two dimensional phenomenon.  The conditions that define certain phenomena as one or two dimensional, are the Ward Conditions that define the spacial parameters -- that are used to scope the conformal dimensionality, that is used to determine the inter-relationships of dimensionality itself.  So, based on certain physical definitions that are used to extrapolate what determines something to be either one, two,...or up to 32 dimensional -- has to do with discrete physical Ward Conditions.  Remember, everything has length, thickness, and width.  Accordingly, a tori-sector-range has phenomena on either side of such a superstringular structure, that curve relative to the prime given externalized phenomena, -- by the radius of a discrete number of second-order point particles.  A second-order point particle, is the smallest type of phenomena that may be diveed-out in free space.  Third-Order point particles only exist, where second-order point particles are at. 
I will continue with the suspense later.  Sincerely, Sam. 

Some Interesting Stuff About The Beti Number

The Beti number is the Hodge-Index, as to either the net decrease or the net increase in the number of spatial dimensions, that a superstring is to respectively either compactify into or decompactify into -- over the course of the so-eluded-to translation of the said superstring -- as it is to be undergoing one of a multiplicit array of iterations of instanton.  A superstring is to tend to always bear a tense of a relatively momentary compacification of dimensionality, right before its correlative iteration of BRST -- while such a superstring is to tend to always bear a tense of a relatively momentary decompactification of dimensionality, during its correlative iteration of the Regge Action.  The Beti number is always a positive integer for the scalar amplitude of the decrease in the discrete dimensionality of a superstring, in terms of the discrete number of spatial dimensional parameters that it is to have decreased by when it is compactified.  The Beti number is always a negative integer for the scalar amplitude of the increase in the discrete dimensionality of a superstring, in terms of the discrete number of spatial dimensional parameters that it is to have increased by when it is decompactified.  This tends to be the case, when a superstring is altering in the number of spatial dimensions that is it here to exhibit -- as a Hamiltonian operator of Noether Flow.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Noether Flow And Lagrangian-Related Path

Let us initially consider a general Stoke's-based Lagrangian-related path, that may be extrapolated in many different potential ways -- since such a said path may vary in its relative multi-dimensional depth, over time.  Let us next consider the given arbitrary respective orbifold eigenset, that is to be able to go through such a general genus of a path -- over a here considered evenly-gauged Hamiltonian eigenmetric, which may vary in its specific duration, -- when this is in consideration of the actual specific as contrasted with just the general path, that is here to be extrapolated.  Let us next consider, that the said orbifold eigenset here -- is to be undergoing a Noether-related flow, over the course of its translation through the extrapolated Lagrangian-related path -- that is here to be brought through, via an even set of a sequential series of instantons, in the process of an even-function-based Fourier series.  The higher that the tense of the Majorana-Weyl-Invariant-Mode is, that is of the said orbifold eigenset -- the more conformal invariant that the directly corresponding translation will be, of the correlative Lagrangian that is related to the transfer of the said orbifold eigenset from one spot to the next over time, that is here to be traversed over a general path that may vary in the specifics of its depth-related parameters, as is according to the specific manner of the correlative extrapolated Stoke's-related depth. The more conformal invariant that the directly corresponding translation will be, of the correlative Lagrangian that is related to the transfer of the said orbifold from one spot to the next over time, -- the more time that it will tend to take for the said orbifold eigenset to then to be able to be translated over the general said Stoke's-based Lagrangian-related path --  since the said orbifold eigenset will then tend to have less of a thrust of motion over the course of going through the said general extrapolated path, as a set of discrete quanta of energy that function to form one specific operation, to where the so-eluded-to holonomic substrate of energy as being the said orbifold eigenset, will then tend to have less energy of net transversal motion, as this will then tend to cause the general transversal Lagrangian to be impeded along its general path, when this is taken along the so-eluded-to specific path of a potentially varying depth.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Added Stuff As To Gravitons And Gravitinos

Gravitons exist in orbifold eigensets, that may be described of as g-fields.  G-Fields exist in a minimum of five spatial dimensions plus time -- via any directly corresponding Fourier Transformation.  Gravitinos exist in orbifold eigensets, that may be described of as gr-fields.  GR-fields exist in a minimum of five spatial dimensions plus time --via any directly corresponding Fourier Transformation.  Both g-fields and gr-fields -- when these are individually taken -- exist as a set of one or more closed-loop strings of eminent gravitational import -- that operate in so as to perform one specific given arbitrary function.  Aside from the tendency of the occasional swivel-shaped conditions, that are here to exist in the two-dimensional behavior of such so-eluded-to closed loop phenomenology, the added three or more spatial dimensions that I  have just eluded to, may be attributed to the Ward-Cauchy-related Fourier-based activity of both g-fields and gr-fields, when these are individually taken, to where such added spatial parameters are here to come into play, when such said fields are going through each successive iteration of the Regge Action, of which is to happen at the end part of each successive iteration of instanton.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Poisson Integral And The Green Function

Let us consider here, a one-dimensional superstring -- of which is, over a sequential series of instantons, is to make a mappable-tracing of a flat-space cohomology, -- of which we are to here to only consider the two most directly corresponding spatially-related dimensional parameters, in this given arbitrary respective case.  Let's next say, arbitrarily, that one-thousand iterations of instanton are to  have just happened -- that are here to be involving the earlier mentioned one-dimensional superstring of discrete energy permittivity.  Let us next consider the Ward-based conditions of the so-eluded-to mapped-out two-dimensional cohomology, that is here to be most directly pertinent to the Hamiltonian operand that is to here to be most directly associated with the region that is to have been just covered by the Lagrangian-based path of the said one-dimensional superstring.  Given a relatively decent synapsis, as to the behavior of the said superstring -- as it had worked to have just formed what is to now to be a non-time-oriented world-sheet, that is to be considered here at a contextual framework, that is most explicitly in only two spatial dimensional parameters, -- as such a partially integrative cohomological texture is to now be considered in a Laplacian-based manner, in only two of its several spatial-based dimensional parameters.  Such a two-dimensional mapping-out of a cohomology, may be described of here as taking a respective Ward-Cauchy-based means of a Poisson Integral.  Furthermore, if one were to reverse the said Poisson Integral -- back into its initially translated superstring of discrete energy permittivity, that was to have just formed the region that had been mapped-out as a Poisson Integral -- such a process of taking the derivative of such a Poisson Integral, in so as to relate, in a Laplacian-based manner, the origin of such a Hamiltonian-based world-sheet in the substringular, -- may be done by utilizing what is known of as the Green Function.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Course 5 on Compactification And Yakawa Couplings, Session One, Part One

When a lot of interconnected solids are folded together, the shape of the overall structure changes. When this folding is done in one dimension, that dimension is cut in size. If the interconnected solid is folded in the middle, then the overall structure is cut in size by one-half in that dimension. If the prior dimension was the length of the structure, then the length would be cut in half while the width would stay the same. If the length and width of that solid were folded alone, then the thickness would be multiplied by four. If all three parameters of the solid were folded in the the middle, then each of the parameters in what we normally view of as our three-dimensional delineation in terms of the solid will be cut in half, yet a fourth dimension would have to be multiplied by six. Question. If you fold something up, won't the thickness increase? You would think so. Do you know what a trash compactor is? It smushes things into a smaller overall size. How many things are infinitely dense? Not many. Since every interconnected solid is made up of atoms, and atoms of a planet tend to form molecules, a solid object tends to contain many molecules. Are atoms smushed together in molecules? Certainly not! Molecules have a lot of empty space. Atoms are mostly empty space for that matter. Do many different types of molecules exist for certain types of solids? Yes! Are there spaces between these different types of molecules? Yes. The further you move away from the atom, the easier it is to smush things down. For instance, how easy is it to rake leaves? It is pretty easy for most people to do such a procedure in general. Yet how easy is it for a person to split or smush an atom? Now this will take some nuclear engineering. I will continue with the suspense of this session later. I hope that my readers are following along and learning about what I am writing as I go. Don't worry. I will not teach anything dangerous on this blog. This blog is just a means of teaching fundamental string theory. Have a phenomenal day!
Sincerely,
Sam.