Grand Unified Theory



(pdf, in Russian)

24.04.2003 1. A reason of quantum phenomena
Quantum phenomena can be explained by algebraic structure of a space of fundamental physical quantity – action.
27.05.2003 2. Clifford algebra as candidate for action algebra
The sought action algebra is provided with vector multiplying rules the same exist in algebra of Dirac matrices.
5.06.2003 3. Is it possible to deduce Dirac matrices?
Dirac matrices are derived from multiplication rules for Clifford algebra.
4.07.2003 4. Contravariant action algebra and quantum postulates
This lecture completes to explain quantum phenomena by algebraic structure of action vectors.
31.07.2003 5. Wave functions of leptons
Vectors of Clifford algebra allow to describe three lepton generations.
4.03.2004 6. Antileptons and contravariant conjugate Clifford algebra
Hermitian conjugate operation and conjugate action algebra are discussed.
4.03.2004 7. Antileptons and covariant conjugate action algebra
Antileptions are described by using of covariant conjugated Clifford space.
20.05.2004 8. Space-time of leptons
Leptons have its own space-time being the Clifford algebra the formative space of which is the special relativity space-time. A conjugated space-time generalized to the Clifford algebra allows to describe spatio-temporal structure of antilepton. The space-time of leptons is quantized and appropriate quantum postulates are the structure equations of the space-time algebra.
6.08.2004 9. Equations of quantum mechanics for leptons
We produce a generalization of the Dirac equation. It considers among two leptons of single generation. More, a similar equation for virtual lepton is derived. A case when action differs too much from Plank's constant is studied singly. A generalized equation of quantum mechanics is formulated with respect to the wave function of lepton space-time.
24.10.2004 10. Special relativity in the space-time of lepton
We study linear space-time transformations that save interval length in the space-time of lepton.
23.01.2005 11. Towards the quark algebra
The denial of multiplication anticommutativity results to an algebra of hypothetical fundamental particles called us leptino.
26.02.2005 12. Algebra of nonrelativistic quarks
Algebras of quarks differ by sign of multipliers permutation in multiplication of generating basis vectors for geometrical space. Its own variant of algebra corresponds with each quark.
24.04.2005 13. Algebra of relativistic quarks
Variants of permutable relations with time basis vector correspond to colour varieties of quarks. In the standard representation, equations for quarks of one generation are split in two independent sets. The first set of equations applies to upper quark and the second set applies to lower quark.
9.05.2005 14. Classification of fundamental particles and tensor symmetries
Our classification of fundamental particles is based on Young diagrams that sort with symmetries of tensors. Fundamental elementary particles of certain kind correspond to each of stems of the Young tree. At that some hypothetical particles must be put into use. These particles are two-colored leptons, three-colored quarkino and two-colored leptino.
09.08.2011 Appendix to Lecture 14. Color interaction of electrons
The short-range attraction between electrons is considered. The existance of such attraction follows from the wave function symmetry of fundamental particles.
31.07.2005 15. Hypothetical fundamental particles
Black leptons, colored (blue, yellow, red) quarkino and black leptino were introduced in the previous Lecture. Here we obtain relativistic quantum equations for these hypothetical particles. It follows from the standard presentation that black leptons and blue quarkino are two-component particles of upper and lower levels. In contrast, black leptino, yellow and red quarkino are four-component particles.
31.07.2005 Appendix to Lecture 15
Structural matrices of algebras of hypothetical fundamental particles.
20.10.2005 16. Tensor algebra as algebra of fundamental particles
We complete examination of fundamental particles using the tensor algebra. The algerba describes all fundamental particles with common viewpoint and may be assumed as basis of unified theory of interactions.
5.02.2006 17. Intermediate particles
An action for intermediate particles is linear transformation of action vector for fundamental particle. These linear transformations constitute algebra. Its equation of structure is quantum equation for free intermediate particles. We derive equations set describing interaction between these particles.
27.03.2006 18. Kinematic algebra
We study algerba of linear transformations operating on algebra of space-time for fundamental particles. Both algebras form kinematic algebra that is responsible for space-time motion of fundamental particle as of a single whole. Union of kinematic and conjugate kinematic algebras generalizes classical group of invartiant transformations (the Poincare group).
21.05.2006 19. Gauge field
A gauge field is defined by way of linear transformations of action space. In special case, we discuss wave equations for leptons in electroweak field. Unlike Salam-Weinberg standard model, the system of wave equations includes equation for right neutrino interacting only with weak Z-field.
9.09.2006 20. Dualism: intermediate particles contra gauge field
We coordinate two methods for description of charge interaction: by means of intermediate particles and gauge field.
23.10.2006 21. Intermediate particles of the second genus
New hypothetical particles are introduced. Their interaction with fundamental particles generates ordinary intermediate particles. These particles do not exist in free state. We call them intermediate particles of the second genus.
18.02.2007 22. Spacetime as affine space
We discuss forming of a spacetime conception in physics. Translation group, vector, scalar product of vectors are chosen as base mathematical notions. They must be extended to curved space-time. This implies Riemann geometry – basis of Einstein gravity theory – must be revised.
14.11.2008 23. Spacetime as curved space
We discuss a curved spacetime and its representation in a reference spacetime. Common concepts such as translation group, vector, scalar product of vectors are represented on the curved spacetime. Thereby developed curved space can take the place of Riemann geometry as base of gravity theory.
17.09.2011 24. Unified theory of interactions. Theses (in English)
Here we will bring together the results of the previous lectures and put them together as a short introduction to the Unified Theory of Interactions.
(See also Russian original of this lecture).
12.12.2011 25. Curved differentiation
Here we discuss a generalized differential calculus called by us curved. In our opinion, the curved differential calculus should help to build a new picture of the world.
16.06.2012 26. Kinematic algebra in a gauge field. Secondary kinematic algebra
Kinematic algebra relations (from Lecture 18) is generalized in case of a gauge field. Then we supplement kinematic algebra by vectors which are responsible for accelerated motions. Such algebra is called by us secondary kinematic algebra.
16.07.2012 27. Five-dimensional theory of gravity and electromagnetism
In this lecture we explain meaning of five coordinate and develop results of Kaluza's five-dimensional theory of gravity and electromagnetism.
17.09.2012 28. Permutation relations
Permutation relations of differentiation operators are discussed. They follow from an algebraic structure of the kinematic space and are necessary for a derivation of dynamics equations.
5.12.2012 29. Transformations of dynamic variables. Dynamic equations
Here we consider dynamic equations for a gauge field. Equations are deduced from a generalized method of canonical transformations.
28.05.2014 30. Strong gravitation and weak electromagnetism new
Here we present arguments for the existence of additional manifestations of gravitation and electromagnetism and derive the equations describing these manifestations. At that, we postulate analogy between gravitation and electromagnetism.