5_BLOG Information on Unified Field Theory  

 

Invitation to "Unified Field Theory"

Dear ones.

This is a invitation to the blog of papers on unified field theory.
If you are interested in "Unified Field Theory" of physics, please click the link below to take a look.

Also, if you know some friends who might be interested in this matter, please share this information.

If you enter from twitter, please share / retweet.

This is a theory in which space-time quantization is introduced and Canonical transformation group is used as gauge group, and neither super symmetry (SUSY) nor super string theory is necessary.

(I think Super String theory is very doubtful.  I wish I were the kid who shouted "But he has put nothing on at all", in Hans Christian Andersen's Fairy Tales "The Emperor's New Clothes".)

The entire consists of 3parts (part-I, II, III) and the entire "Cover + Preface" and "afterword" are added to them. They are linked to each other and can be entered from anywhere.

Unified field theory based on canonical gauge principle： 

▷Link (MS_word ／pdf) 

● Cover+preface: Theory of Field Unification based on Canonical gauge principle
●Ⅰ: Principle of field unification and existence logic of elementary particles
●Ⅱ: Foundation of state-constructive Field Theory 
●Ⅲ: Quantum Gravitational Field Theory  
● Unified Field Theory: Conceptual Trajectory & Summary of Theory+Afterword 

  Link to Japanese version (御招待窓口) 

Though this work contains many basic and fundamental discussions, however, it also has succeeded in deriving some conclusions, so I will explain it a little below.

Ⅰ：Principle of field unification and existence logic of elementary particles 

・Denial of manifold model for space-time

According to the principle of quantum mechanics, space-time  appears by observation associated.
A set of Canonical Conjugate linear operators , position / momentum (x.p) should be introduced instead of ordinary coordinates.
The transformation between observers is given by space-time preserving canonical transformation.  Only from this assumption, the following will be derived naturally.

 

・Explication of the origin of symmetry

Bosons are classified into 2 types : FF type and BB type, according to their connection type, and the related symmetries are su(3)⊕gc, and u(2)＝u(1)⊕su(2), respectively.
Where, gc is Lie ring of spinor transformation generated by (1, iγ5).
This Lie ring corresponds to the spinor connection field (below).

 

・ Unification of Boson / Fermion：

Boson and Fermion are both derived as Canonical gauge connection.

 

・Reality of preon model:

The preon model as a substructure of quark / Lepton, especially the rishon model, becomes realistic.

 

・Existence of spinor connection field:

The existence of spinor connection field , so called the 5th force, is shown that is previously unknown.  It can be considered that this boson (spinor connection field) condense in universe, and has some relationship with dark energy, and also with Higgs meson.
Also this becomes a origin of mass of one type of preon.(above)
 

・Explication of Relationship between chirality and mass:

Related to the existence of the spinor connection field above, the consideration on transformations in spinor space provides a relationship between chirality and mass in preon level.
This leads to a new recognition of Dirac equation in the next section. 

・Derivation of unified field equations

Naturally, the unified field equation is derived that contains Dirac equation. (described  below)
With respect to gravity, we get an equation that is different from A. Einstein's theory. 

The validation of this equation in classical level will be discussed in Part III.

・New recognition on Dirac equation: 

In Canonical gauge unified field theory, Lagrangian is a quadratic form of the 1st-order space-time derivative with respect to the field variable, so the understandings of Dirac equation becomes a problem. 

Factorization on ring R[iγ5] becomes a key concept, but we get results that suggest a relationship between the two solutions and two preon flavors.

・etc

Ⅱ：Foundation of state-constructive Field Theory 

・Interpretation of divergence difficulty:

Even if the correct field equation is obtained by unified field theory, the theory cannot be developed unless it can be solved. The divergence difficulty is a stumbling block in field theory, and it is important to understand the cause of difficulty.

 

・Denial of adiabatic hypothesis

It is considered that the divergence comes from introduction of  interaction representation based on adiabatic hypothesis and from calculation method using the propagator by the diagram technique.
So, adiabatic hypothesis should be denied.
The adiabatic hypothesis insisting that interaction becomes negligible asymptotically in scattering problem, becomes a logical contradiction if self-interaction exists.
The self-interaction itself is divergent, but it depends on the composition model of particle and for composite particle, the divergence may be only appearance.
From the point of view of energy divergence, the isolated existence should be denied for non-composite and elementary Fermion.
Compositeness is necessary (but not always sufficient) for ensuring the symmetry for existence.
This is consistent with the absence of isolated single quark (preon complexes) .

 

・Interpretation for renormalization

The renormalization prescription is interpreted as a method for absorbing the contradiction of the adiabatic hypothesis and the self-interaction due to model defects.

 

 ・State-constructive field theory - Avoiding divergence difficulty

State-constructive field theory is proposed. 

This is a quantum field theory that avoids divergence difficulty and provides calculation method instead of diagram technique.
This is elementary and quite faithful to the principles of quantum mechanics.

 

*Constructive definition of state space,

Followings are reconfirmed:
Construction of the state space,  projectivity of the field operator, and  operator interpretation of state (embedding of state space into  differential algebra)

*Theory on solution of field equations

As the theory of solving field equations, state separation method and finite mode excitation approximation method are introduced, which are related with  finite element method in engineering and separation of variables in partial differential equations.

*Legacy structure of approximation method

The approximate calculation method contains conventional solution method in classical mechanics or quantum mechanics in the initial stage of approximation. Considering that divergence difficulties emerged first in field theory, it would be a supplemental proof of avoidance of divergence difficulties.

 

*Method for stationary state problem

For stationary state problems, state-constructive approximation method proposes successive approximation with a finite degree of freedom.
This method has been applied to a simple non-relativistic hydrogen atom model and confirm the methodological feasibility of the successive approximation method.
As a by-product, it naturally revealed to the insensitivity of electromagnetic interaction to the self-field.

*Method to scattering problem

For the scattering problem, the contribution eliminated self-interaction for state transition is provided.

*Additional notes on quantum gravity

Regarding quantum gravity, there is no reason to worry about  divergence difficulty  in the form of replacing conventional Einstein theory with canonical gauge gravity, denying the adiabatic hypothesis and eliminating the diagram technique.
(There is a possibility that quantization conditions can be imposed from the viewpoint of state normalization.)

The method of approximate solution of the above-mentioned field equation needs to be developed into a systematic and sophisticated one in the future.

・etc

Ⅲ: Quantum Gravitational Field Theory   

・Verification of quantum gravity at the classical level:

At present, the verification of quantum gravity theory in Canonical gauge unified field is restricted into classical theory level, and there is no choice but to compare it with A. Einstein's theory, especially regarding the matters already verified.

Though the origin and composition of Lagrangian in 2 theories are essentially different, but assuming spherical symmetry, and selecting an appropriate interaction constant, the two can be matched.

In this sense, canonical gauge quantum gravity theory has been verified at the current level.

・Solving the Big Bag singularity problem:

Freidmann equation of expanding universe can be derived from the canonical equation in canonical gauge  unified field gravity theory.

Hamiltonian of scale factor shows that there are no singularities in Big Bang. This is because the canonical representation makes clear the application of uncertainty principle in quantum mechanics.

With introducing Canonical formalism, we can also get the wave function of scale factor, but it will be our future task to extract the true physical meaning beyond the usual meaning as a probability amplitude.

・Derivation of modified Freidmann equation and expansion in early universe:

Deriving the equation of motion for early universe using variational principle yields "modified Freidmann equation". 

It turns out that the expansion rate of universe is dominated by  (quantum theoretical) state expected value of Lagrangian. 

It seems that the void structure of  universe can be explained by the relationship between materialization and Lagrangian expected value during phase transition.

 

・Interpretation of particle antiparticle asymmetry:

Concerning early universe, pair creation/annihilation state of preons, we imagine and interpret that apparent imbalance between matter and antimatter is actually balanced in preon level. 

The sum of all charges in universe looks like zero for example. Also, explanation by symmetry breaking would be difficult from the standpoint of elements reductionism.  Antiparticles are hidden like d = (TVV)* for example.

 

(c, s), (t, b) are interpreted as excitation state of (u, d). Leptons are also considered as e+＝(TTT) ,ν＝(VVV) and their excited state. 

Therefore, the proton decay will occur since  p＝(uud).

 

・Solution to the problem of accelerated expansion of the universe:

Currently, it is known from observation that the expansion of  universe will accelerate, and I think that the "spinor connection field" found in part I is a candidate for this cause or as the true nature of dark matter. 

Quantitative discussion is difficult but it is surely dark because there is no electromagnetic interaction. That field has self interaction term and it can be considered to be in Bose-Einstein condensation throughout the universe.

 

・Black Hole from Quantum mechanical view:

One of the conclusions obtained in part II is that the field in classical theory is the state expected value of the field operator, so-called mean field.
For gravitational fields, the solution in classical field theory does not include quantum variance effects, because the self-interaction term induces non-linearity. In this respect, I am skeptical about reality of  Schwarzschild solution of gravity.
In quantum theory, the spatial continuity of field variables cannot be denied so easily, and I imagine that Schwarzschild barrier cannot exist due to the quantum variance effect.
However, there is currently no prospect of how much results will be achieved by pursuing this problem deeply, and it seems that a brave risk-taking is necessary to implement it.

・etc

For details, please see the text of the blog and add a critical review.

 

【Copyright】

I would like to respect the development of scholarship, the development of intellectual freedom and imagination, and above all, the intellectual adventures of human beings, and I would like you to actively introduce and disseminate the work, which is my thought.

However, I claim copyright.

Please observe the following principles when quoting articles.

(1) Inevitable citation.

(2) Visual clarification of quoted part / range.

(3) Mainly your own work, and use citations complementarily.

(4) Clarification of citation source: Site name / article name (content name) / URL (link).

Also, when you use it, I would be grateful if you could contact me with a word in text format.

gusr.310@gmail.com              .

【keywords】

mainly rel.part I	mainly rel.part Ⅱ	mainly rel.part Ⅲ
Quantum space-time Field Unification theory Unified field Canonical gauge field theory   spinor connection  o(1,1)  preon,  rishon model su(3)⊗u(2) Canonical transformation Chirality Dirac equation Lagrangian	State space Field operator Renormalization Divergence difficulty State-constructive Field Theory Finite mode excitation approx.	Canonical gauge theory of gravity Quantum gravitational theory Big Bang  Solution of singularity  dark energy   dark  matter                     Black Hole Quantum variance effect Accelerated expanding Universe

 

 

PS:

  I used Google's Blogger for my blog.For the description of the actual contents, 

  please read the files with the link shown above.

thank you and best regards.
T.sato   Kawasaki, Japan