scholarly journals Magnetic monopoles, electric neutrality and the static Maxwell-Dirac equations

1999 ◽  
Vol 32 (31) ◽  
pp. 5807-5822 ◽  
Author(s):  
Chris Radford ◽  
Hilary Booth
2020 ◽  
Author(s):  
Deep Bhattacharjee

Gravity has been leaking in higher dimensions in the bulk. Gravity being a closed string is not attached or does not have any endpoints unlike photons to any Dirichlet (p)-Branes and therefore can travel inter-dimensional without any hindrance. In LHC, CERN, Gravitons are difficult to detect as they last for such a short span of time and in most of the cases invisible as because they can escape to higher spatial dimensions to the maximum of 10, as per 'M'-Theory. Gravity being one of the 4-Fundamental forces is weaker than all 3 (strong and weak nuclear force, electromagnetism) and therefore a famous problem has been made in particle physics called the 'hierarchy problem'. Through comprehensive analysis and research I have come to the conclusion that if dimension is 5 (or 4 if we neglect the temporal dimensions) then an old approach is there for the compactification of the dimensions as per Kaluza-Klein theory and the most important implications of this theory is that an unification of electromagnetism with gravitation occurs in the fifth dimensions, therefore we can conclude that both the charge (electric as well as magnetic and gravity) are dependent of each other in case of Dimensions greater than 4 (5 if time is added). Now, basic principles of electromagnetic theory states that the field-flux density through a closed surface like a T 2 Torus when integrated over the surface area leads to a zero flux. That means there is no flux outside this closed surface integral. However, if the surface is open then the field flux density is not zero and this preserves the concept of magnetic monopoles. However, in a paper in 1931,[1] Dirac approaches monopole theory of magnetism through a different perspectives that, if all the electrical charges of the universe is quantized[2] then there is a suitable (not yet proved though) existence of monopoles; however this are not well understood as of today's scenario. In condensed matter physics, plasma physics and magneto hydrodynamics, there are flux tubes and as the both ends of the flux tubes are independent of each other then the net flux through the cylinder is zero as the amount of field lines entering the tube on one side is equal to the amount of field lines exit from the other end. And in the sides of the cylinder or the flux tube there is no escape of field lines, hence, net flux is conserved. There also exists a type of 'Quasiparticles' that can act as a monopole.[3][4][5] Now, from the perspectives of the Guess law of electromagnetism, if there exists a magnetic monopole then the net charge or flux density over a surface is not zero rather the divergence of the flux density B is 4 [6]and an alternative approach of the 'monopole' can be achieved by increasing the spatial dimensions by a factor of 1 or more. The Gravity has no such poles and therefore can be considered as a unipolar flux density existing throughout the universe and is applicable to the inverse square law of decreasing magnitude via distance as 1/r 2. However, a magnet is always of bipolar with a north and South Pole. If a magnet can be broken then also the broken parts develop the other poles and become bipolar. However, there are tiny domains inside a magnet and if a magnet can be heated to approx. 700℃ then all the poles disappeared and if its cooled quickly, rather very quickly then the tiny domains inside the magnet would not get enough time to rearrange themselves and multipolar magnet is developed therefore to preserve the bipolar properties, the magnet should be cooled slowly allowing the time given to the tiny domains top rearrange themselves. Therefore, even multipole can be achieved quite easily but not the monopoles. So, the equation for a closed surface integral of a flux density without monopole is ∯(S) B dS = 0 or ∇ • B = 0 and that closed surface can be considered as 2 types namely (we will discuss about torus) as because in string theory compactification of higher spatial dimensions occurs in torus.


Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.


2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Michael Dunia ◽  
Timothy J. Evans ◽  
Douglas Singleton
Keyword(s):  

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Joydeep Chakrabortty ◽  
George Lazarides ◽  
Rinku Maji ◽  
Qaisar Shafi

Abstract We consider magnetic monopoles and strings that appear in non-supersymmetric SO(10) and E6 grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter Gμ spans the range 10−6− 10−30, where G is Newton’s constant and μ is the string tension. We show how intermediate scale monopoles with mass ∼ 1013− 1014 GeV and flux ≲ 2.8 × 10−16 cm−2s−1sr−1, and cosmic strings with Gμ ∼ 10−11− 10−10 survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio r lies between 0.06 and 0.003 depending on the details of the inflationary scenario.


Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.


2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.


2009 ◽  
Vol 17 (3) ◽  
pp. 235-256 ◽  
Author(s):  
Jian Ding ◽  
Junxiang Xu ◽  
Fubao Zhang
Keyword(s):  

2014 ◽  
Vol 60 (1) ◽  
pp. 49-58
Author(s):  
Toru Ozeki ◽  
Katsuzo Takigawa ◽  
Kohki Tanida
Keyword(s):  

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.


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