# Super condensate, strings (bosons) and loops (fermions)

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21 minutes ago, joigus said:

I just thought symmetric contracted with antisymmetric gives naught. After you intervened, I thought "maybe it's something like double-index spinor gravity." But I think now it must go deeper. He's not very talkative. I'll wait and see. I still want to know if the theory is topological. Topological theories are kind of my obsession. I'm scavenging for information in field theories.

Well an obvious asymmetry is any treatment involving inner products as opposed to cross products. Differential geometry applies to any field treatment.

Hence Kronecker delta and Levi Cevitta applications are essential along with the holomorphic (holonomy etc) connections. An obvious necessity in higher dimensional applications along with the limits of any applicable equation. (Highly common application phase polarities and other applicable wavefunction).

This leads back to my first post on the observer orientation aspects.

Which I need to clarify with the topology application as being defined as a fully coordinate independent treatment. (QFT for example has a coordinate dependence (strongly allied in the weak field appromation as per SR) though second order to QM first order treatments).

Cross product fields require an velocity operator to comply to the right hand rule. Under group applications this is often the [math]\ mathbb{Z][/ math] this is also applicable to parity operators.

Edited by Mordred

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1 hour ago, Mordred said:

I haven't seen enough of your posts but I am thinking your more the latter as well

Yes. I'm topological at heart. I'm totally enamoured of SU(2)*xSU(2) Ashtekar-Plebanski formulation of gravity with constraints. Gauge groups I tend to see as coverings of ST groups. Probably wrong as groups go deep. But you must simplify at some point. Totally concur with you that scalar field is something to be understood as the final touch after the rest of the variables have been understood. To me it's no coincidence that scalars seem to be key to both cosmology and mass spectrum. Easy to say, but... And probably not for me, but I want to have a first row seat when someone comes up with the answer.

I'm not making much sense. It's too late here.

Edited by joigus

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You are to me, Myself I concentrate more on the canonical treatments under QFT.

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The main solution to the problem of hierarchy in our opinion in the supersymmetric vacuum of early cosmology.

I’m writing from the phone will be brief.

Wilson loops are also topological knots

$$W= e^ {\int \gamma_{i} A^{i}_{K} dx^{K}}$$

$$A_{k}=\gamma_{i} A^{i}_{k}$$

The energy of the loop (fermions) depends on the internal strains of the spin connection

$$E= \frac{Gh^2}{c^2} \int e_{ikj} \frac {dA_{i}}{dx_{k}} dA_{j}$$

In topological field theory, the curvature of spin connection is introduced

$$K= \frac {dA}{dx}+AA$$
Now consider the energy of the loop.

In a free state, the loop tends to stretch out in space, its energy tends to a lower value.

However, due to the quantum fluctuations of the vacuum, the Wilson loop should deform with an increase in its linear dimensions, this means that the topological curvature increases, and THE LOOP ENERGY WILL NOT TEND TO THE LOWEST VALUE.

Due to quantum fluctuations, the curvature of the topological loop already clearly depends on the linear dimensions in the form of some function.

$$K= \frac {dA}{dx}+AA =f(x,y,z)$$

This means the loop energy is between two extremes, between zero and planck values.

Consider the influence of a scalar field on the deformation of a topological loop.
We introduce the scalar field of the Lagrangians of this model

$$E= \frac{Gh^2}{c^2} \int e_{ikj} ( \frac {dA_{i}}{dx_{j}} \frac{dA_{k}}{dx_{j}} +\frac { d \phi}{dx_{j}} \frac{d \phi}{dx_{k}} ) dx_{j}$$

In general, gives a differential equation

$$dE dl = \frac{Gh^2}{c^2} (dAdA + d\phi d\phi)$$

$$C =\frac{c^2}{Gh^2} \int dE dl$$

$$C = A^2+\phi^2$$

$$C \psi = -\frac {d^2\psi}{dx^2} + \phi^2 \psi$$

The solution to this equation depends on finding the scalar field function and imposing additional conditions. Notice this is not the Higgs field. Although it can be similarly added to this model.

Edited by Kuyukov Vitaly

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After all, string theory was originally a boson theory. Fermions were obtained only due to the expansion of supersymmetry.

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Well I'm not familiar enough with the Wilson loop methodology itself. Although I have studied it a bit I prefer the perturbation methodologies of QFT

So other than seeking obvious mistakes I wouldn't be a great help.

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