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Kuyukov Vitaly

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

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Posted (edited)

 

Okay. How simple nature is arranged. All of these quantum gravity, string theory and loop quantum gravity complicate things. All of them cannot properly obtain the space-time geometry from more distinct constructions. Now I will show that strings / loops are dual to each other, that is, like the duality of electric and magnetic fields.

The idea is based on the fact that Maxwell's equations are applicable not only to electric and magnetic fields, but also to two quantum non-commutative fields, string E and loop A field .

{E, A} = i

Quantum gravity is expressed in the form of the Maxwell equation of a string-loop field.

div E = 0

div A = 0

rot E = - Gh/c4  dA / dt

rot A = Gh/c2  dE / dt

 

Interval field

(l2 A)2 -E2=(l2 AI)2 -EI2

   l2= Gh/c3 =10{-70} m2

As a result, supersymmetry is a consequence of the Maxwell equations of quantum gravity. Symmetry between bosons -graviton, photon (strings) and              fermions - electron, quark (loops).
Lorentz symmetry is just an empty box for super-condensate. Space-time is not a physical object, it is just a relationship in a vacuum super-condensate.
 

More details here

dualism.pdf

Edited by Kuyukov Vitaly

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14 minutes ago, Kuyukov Vitaly said:


Any questions?

It is nice of you to give us a preview, but which peer-reviewed journal is this being published in?

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2 hours ago, Kuyukov Vitaly said:


Any questions?

Any results?

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Posted (edited)
1 hour ago, joigus said:

Any results?

So far modest.
1. The duality of strings (bosons) and loops (fermions)

2. Supersymmetry and Maxwell equations

3. Lorentz symmetry is the most important advantage of the model.

4. A possible solution to the hierarchy problem based on the topology of knots — Wilson loops

5. The laws of conservation of energy and momentum, transmutation of bosons and fermions are satisfied (see the Hamiltonians of particles in the link)

Edited by Kuyukov Vitaly

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57 minutes ago, Kuyukov Vitaly said:

The duality of strings (bosons) and loops (fermions)

It's the other way about. In superstring theory they're all strings. Closed strings are bosons and open strings are fermions.

https://en.wikipedia.org/wiki/String_(physics)#Closed_and_open_strings

59 minutes ago, Kuyukov Vitaly said:

Supersymmetry and Maxwell equations

I'm just curious. Tell me in a few words, if possible, what is SS, please.

 

1 hour ago, Kuyukov Vitaly said:

Lorentz symmetry is the most important advantage of the model.

Good. Lorentz symmetry is an integral part of Maxwell's eqs. AAMOF, Lorentz symmetry was deduced from them. That means probably you didn't make a sign mistake.

1 hour ago, Kuyukov Vitaly said:

A possible solution to the hierarchy problem based on the topology of knots — Wilson loops

Any details, please?

1 hour ago, Kuyukov Vitaly said:

The laws of conservation of energy and momentum, [...] are satisfied (see the Hamiltonians of particles in the link)

Good, so space-time is symmetric. That's a relief. Is the Hamiltonian time-dependent?

1 hour ago, Kuyukov Vitaly said:

[...] transmutation of bosons and fermions are satisfied [...]

No wonder. If your Lagrangian is supersymmetric there should be total symmetry under exchange boson <--> fermion.

But all those symmetry checks are done on the Lagrangian, not the Hamiltonian, which is frame-dependent. Any progress about that?

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Posted (edited)

The use of R^2 isn't particularly practical for your first equation. I would recommend using the full ds^2 line element and applying the full four momentum and four velocity. 

Also the EM field has symmetric and antisymmetric that involve the Lorenz transforms from the E and B fields of the Maxwell equations.

So to state the EM field is symmetric with spacetime isn't accurate. For example 

To to define the right hand rule for EM fields in your equations. Spacetime doesn't require the Right hand rule so you obviously have vector components of the EM field that is not symmetric with the spacetime metric.

 This will also become important for different observers/ detectors at different orientations.

A key point being many of the Maxwell equations employ the cross product for the angular momentum terms. However the Minkowskii metric employs the inner products of the vectors.

This is an obvious asymmetry between the two fields. Not to mention the curl operators of the EM field. Ie Spinors.

 You will find some of this important for the Pauli exclusion principle as well. 

 

Edited by Mordred

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Posted (edited)
1 hour ago, Mordred said:

The use of R^2 isn't particularly practical for your first equation. I would recommend using the full ds^2 line element and applying the full four momentum and four velocity. 

Also the EM field has symmetric and antisymmetric that involve the Lorenz transforms from the E and B fields of the Maxwell equations.

So to state the EM field is symmetric with spacetime isn't accurate. For example 

To to define the right hand rule for EM fields in your equations. Spacetime doesn't require the Right hand rule so you obviously have vector components of the EM field that is not symmetric with the spacetime metric.

 This will also become important for different observers/ detectors at different orientations.

A key point being many of the Maxwell equations employ the cross product for the angular momentum terms. However the Minkowskii metric employs the inner products of the vectors.

This is an obvious asymmetry between the two fields. Not to mention the curl operators of the EM field. Ie Spinors.

 You will find some of this important for the Pauli exclusion principle as well. 

 

I agree . But note that there are no sources in these equations, the fields simply transform into each other (string) <-> (loop). And disagree with the Maxwell equation contains all the symmetries of special relativity. It is a fact and it makes no sense to argue with this.

Why do I need it. I have studied enough at the university. The general scheme is important to me.
 

 

Edited by Kuyukov Vitaly

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Posted (edited)

Sorry, I hadn't seen your Lagrangians. Thanks for the docs.

Is your,

\[\varPsi\left(A\right)\]

a superpotential?

My questions are very elementary, as you see. I really want to understand what you're trying to do. Irrespective of where you're going.

Still, aren't open strings fermions and loops, or closed strings, bosons?

What are the observables of your theory?

It is a topological theory, right? You're trying to formulate a sourceless field with Wilson loops as the observables. Something like that.

Edited by joigus
mistyped

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15 minutes ago, Kuyukov Vitaly said:

I agree . But note that there are no sources in these equations, the fields simply transform into each other (string) <-> (loop). And disagree with the Maxwell equation contains all the symmetries of special relativity. It is a fact and it makes no sense to argue with this.

I suggest you study the Maxwell equations for the phase angles between the E and B fields then under Lorentz invariance.

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Posted (edited)
13 minutes ago, joigus said:

Sorry, I hadn't seen your Lagrangians. Thanks for the docs.

Is your,

 

Ψ(A)

 

a superpotential?

My questions are very elementary, as you see. I really want to understand what you're trying to do. Irrespective of we're you're going.

Still, aren't open strings fermions and loops, or closed strings, bosons?

What are the observables of your theory?

It is a topological theory, right? You're trying to formulate a sourceless field with Wilson loops as the observables. Something like that.

Well, that will have to be thoroughly explained.

This is the wave function of the quantum state of Wilson loops, the main apparatus of spin networks for fermionic modes (what interested mordred)

W= e^$ci Adx


ci Pauli matrices


An important Wilson loop and quantum particles on a topological basis in the form of a polynomial node

Edited by Kuyukov Vitaly

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11 minutes ago, Kuyukov Vitaly said:

This is the wave function of the quantum state of Wilson loops, the main apparatus of spin networks for fermionic modes (what interested mordred)

ae1e19a0212a987d7ac87acfa3edc07d87a15e3c

Thank you. I know what a Wilson loop is.

25 minutes ago, joigus said:

It is a topological theory, right? You're trying to formulate a sourceless field with Wilson loops as the observables. Something like that.

Gauge theories have a lot of redundant junk that you must dispose of.

Topological theories are very constrained. They have no propagation, because of the high number of constraints. Solutions are pretty much static. Any other evolution can be removed by local gauge transformations/Lorentz transformations.

You must be careful to stick only to gauge invariant properties that are observable.

Is your theory a topological theory? That doesn't require to be thoroughly explained. For the time being, it's enough to say "yes" or "no."

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23 minutes ago, joigus said:

That doesn't require to be thoroughly explained. For the time being, it's enough to say "yes" or "no."

Sorry. I forgot. There's a third category of honest and valid answers, which is "I don't know" or "I'm not sure," or even "I don't know why that's relevant to the discussion."

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Posted (edited)

Consider the ground state of spin networks in the form of Wilson loops

[math] W= e^{Adx} [/math]
We can see this closed holonomy is no longer just a field, but Ashtecker's spin connection

$$ A_{k}^{i}=Г_{k}^{i}+K_{k}^{i} $$

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

Pauli matrices - gamma


Further, the topological action of spin networks is equivalent to the action of Schwartz

$$ S=\int A \frac{dA}{dx} dV $$

Note the fermion energy in proportion to the density of the Lagrangian of the topology of spin networks

$$ E = \frac {G h^2}{c^2} \int e_{ikj} \frac{dA_i}{dx_i}\frac{dA_k}{dx^{i}}dx_j $$

String Energy

$$ E = \frac {c^4}{G} \int e_{ikj} \frac{dE_i}{dx_i}\frac{dE_k}{dx^{i}}dx_j $$

energy the knot

$$ E = \frac {G h^2}{c^2 R^3} = A \frac{dA}{dx}$$

Now we will substitute in the formula the value of the particle energy E = 100 Gev, we get the average size of length R = 10 {-29} m.  Surprisingly, the energy of a particle of the standard model is strictly related to the distance of the theory of great unification according to this formula.

 

 With great difficulty, I print these formulas on the phone!

Edited by Kuyukov Vitaly

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Posted (edited)
1 hour ago, Kuyukov Vitaly said:

Consider the ground state of spin networks in the form of Wilson loops

[...]

Your energy looks dangerously close to being identically zero. Are there any comm. or a-comm. rules for the A's?

Your action (sorry, Schwarzt's) looks dangerously close to being non-diffeomorphism invariant. Care to tell me the p-form character of the A's?

Care to answer any of the questions I'm asking?

Don't sweat it with your LateX phone, please. Simple worded answers will do.

You also have too many contracted indices "i" in your energy expression.

Edited by joigus
addition

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Posted (edited)
29 minutes ago, joigus said:

Your energy looks dangerously close to being identically zero. Are there any comm. or a-comm. rules for the A's?

Your action (sorry, Schwarzt's) looks dangerously close to being non-diffeomorphism invariant. Care to tell me the p-form character of the A's?

Care to answer any of the questions I'm asking?

Don't sweat it with your LateX phone, please. Simple worded answers will do.

You also have too many contracted indices in your energy expression.

The action is invariant

$$ dV^{|}=dV (1-V^2)^{1/2} $$

Respectively

 $$ A^{|}dA^{|}/dx^{|}=AdA/dx (1-V^2)^{1/2} $$

$$ E^{|}=E(1-V^2)^{1/2} $$

You need to study spin networks to start here https://arxiv.org/pdf/1308.4063

22.pdf

Edited by Kuyukov Vitaly

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Posted (edited)

Do you know the difference between Lorentz invariant and reparametrization (diffeomorphism) invariance?

(Rhetorical question.) :-);)

 

One final question. Why do you ask,  

9 hours ago, Kuyukov Vitaly said:

Any questions?

If you're not answering any?

Actually, you have answered one very significant question. Only, you don't know you have.

Edited by joigus
Addition

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8 minutes ago, joigus said:

Do you know the difference between Lorentz invariant and reparametrization (diffeomorphism) invariance?

 

Of course I know. To me at work, then I will answer

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Posted (edited)
2 hours ago, Kuyukov Vitaly said:

Consider the ground state of spin networks in the form of Wilson loops

W=eAdx
We can see this closed holonomy is no longer just a field, but Ashtecker's spin connection

 

Aik=Гik+Kik

 

 

Ak=γiAik

 

Pauli matrices - gamma


Further, the topological action of spin networks is equivalent to the action of Schwartz

 

S=AdAdxdV

 

Note the fermion energy in proportion to the density of the Lagrangian of the topology of spin networks

 

E=Gh2c2eikjdAidxidAkdxidxj

 

String Energy

 

E=c4GeikjdEidxidEkdxidxj

 

energy the knot

 

E=Gh2c2R3=AdAdx

 

Now we will substitute in the formula the value of the particle energy E = 100 Gev, we get the average size of length R = 10 {-29} m.  Surprisingly, the energy of a particle of the standard model is strictly related to the distance of the theory of great unification according to this formula.

 

 With great difficulty, I print these formulas on the phone!

 

2 hours ago, Kuyukov Vitaly said:

Consider the ground state of spin networks in the form of Wilson loops

W=eAdx
We can see this closed holonomy is no longer just a field, but Ashtecker's spin connection

 

Aik=Гik+Kik

 

 

Ak=γiAik

 

Pauli matrices - gamma


Further, the topological action of spin networks is equivalent to the action of Schwartz

 

S=AdAdxdV

 

Note the fermion energy in proportion to the density of the Lagrangian of the topology of spin networks

 

E=Gh2c2eikjdAidxidAkdxidxj

 

String Energy

 

E=c4GeikjdEidxidEkdxidxj

 

energy the knot

 

E=Gh2c2R3=AdAdx

 

Now we will substitute in the formula the value of the particle energy E = 100 Gev, we get the average size of length R = 10 {-29} m.  Surprisingly, the energy of a particle of the standard model is strictly related to the distance of the theory of great unification according to this formula.

 

 With great difficulty, I print these formulas on the phone! 

Running latex from a phone is something I have grown used to.

I'm assuming your following standard notation on the transformation matrix [math]A_i^k[/math] which is a mixed group of covariant/contravariance (for other readers, OP knows Einstein summation)

 Are you applying gamma matrix as per [math]\gamma^5[/math]

By the way welcome aboard I'm happy to get a good thread for discussion of this caliber. (Happens rarely). +1 

Notation clarification (not one I recognize of the superscript.) Is this a parallel vs perpendicular ) commonly indicated on the subscript. If not please clarify.

 

[math]A^|[/math]

 

Edited by Mordred

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9 minutes ago, Mordred said:

(for other readers, OP knows Einstein summation)

Ok. Thank you. It must be an index convention I don't know about. I just wanted to know if the theory was topological. But to no avail.

Actually, my question,

1 hour ago, joigus said:

Are there any comm. or a-comm. rules for the A's?

was pretty stupid. Now I realize, as he implicitly gave the algebra. I'll take a back sit and try to learn something from it.

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Posted (edited)
4 hours ago, joigus said:

Ok. Thank you. It must be an index convention I don't know about. I just wanted to know if the theory was topological. But to no avail.

Actually, my question,

was pretty stupid. Now I realize, as he implicitly gave the algebra. I'll take a back sit and try to learn something from it.

Einstein  summation has its topological  applications. The summation specifically involves the covariant and contravarient terms of each group. 

The superscript is being the covariant terms. The  subscript contravarient while a mixed group will have both. The full Kronecker delta is an Ideal example to study.

 Granted the Levi Cevita adds additional degrees of freedom.

PS I tend to think more gauge group than topological, while Studiot for example thinks the latter. ( I haven't seen enough of your posts but I am thinking your more the latter as well)

@the OP I have  zero problems with applying Wilson loops  to the SM model In an entirely. It is a viable alternative. So I support the OP on thus methodology though myself I am more up to date on canonical treatments as per GFT. Doesn't invalidate other treatments.

 I fully support you in showing the Langrangians as per observable vs propriogator action particularly in terms of show to apply the Ops model to the QED and QCD applications. (The Higgs can be addressed later ).

Edited by Mordred

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13 minutes ago, Mordred said:

The superscript is being the covariant terms. The  subscript contravarient while a mixed group will have both.

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.

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