Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.


1990 ◽  
Vol 02 (03) ◽  
pp. 355-398 ◽  
Author(s):  
G.P. Pron’ko

The relativistic string theory is considered from the Hamiltonian point of view. It is proposed to formulate the dynamics of string in d-dimensional space-time with the help of the auxiliary spectral problem. This approach gives the possibility to construct a completely new set of variables of string relevant for Lorentz-invariant gauge fixing. The notion of smooth string is introduced for which the successive relativistic invariant quantization could be done explicitly for the d=4 case.


2019 ◽  
Author(s):  
Wim Vegt

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics


Author(s):  
Yasunari Nishikawa

Abstract We study a two-loop finiteness of an effective potential for a Higgs boson that is the fifth component of a gauge field in an U(1) gauge theory coupled to quantum gravity on the five-dimensional space-time M4 × S1. There are two types of diagrams including quantum gravitational corrections. We find that only one type of diagram contributes to the effective potential for the Higgs boson in fact and its magnitude is finite.


1991 ◽  
Vol 06 (14) ◽  
pp. 2497-2517 ◽  
Author(s):  
M.S. PLYUSHCHAY

The quantization of the massless Brink-Schwarz superparticle in four-dimensional space-time in terms of independent variables and by the Gupta-Bleuler method is developed. The connection between these two approaches to quantization of the model is retraced and covariantization of the latter one is realized. The properties of the system under spatial inversion are explored and the quantum theory which is invariant with respect to it is constructed.


1988 ◽  
Vol 03 (17) ◽  
pp. 1699-1702
Author(s):  
H.R. KARADAYI

By studying the first 6 levels, it is shown that SO(10) begins to survive to be the little group of space-time at higher levels of the L-sector in SO(32) string theory. This shows us that there is an interrelation between SO(32) gauge symmetry and 11-dimensional space-time.


2019 ◽  
Author(s):  
Wim Vegt

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics


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