We review the formulation of graphene’s massless Dirac equation, under the chiral electromagnetism approach, hopefully demystifying the material’s unusual chiral, relativistic, effective theory. In Dirac’s theory, ...We review the formulation of graphene’s massless Dirac equation, under the chiral electromagnetism approach, hopefully demystifying the material’s unusual chiral, relativistic, effective theory. In Dirac’s theory, many authors replace the speed of light by the Fermi velocity, in this paper we deduce that in graphene the Fermi velocity is obtained from the connection between the electromagnetic chirality and the fine structure constant when the electric wave E is quasi parallel to the magnetic wave H. With this approach we can consider the properties of electric circuits involving graphene or Weyl semimetals. The existence of the induced chiral magnetic current in a graphene subjected to magnetic field causes an interesting and unusual behavior of such circuits. We discuss an explicit example of a circuit involving the current generation in a “chiral battery”. The special properties of this circuit may be utilized for creating “chiral electronic” devices.展开更多
The usual choice of an orthogonal set of four plane-wave solutions of the free-particle Dirac equation does not lend itself readily to direct and complete physical interpretation in the case of Dirac neutrino particle...The usual choice of an orthogonal set of four plane-wave solutions of the free-particle Dirac equation does not lend itself readily to direct and complete physical interpretation in the case of Dirac neutrino particle. A different choice of solutions can be made which yields a direct physical interpretation at all energies. Besides the separation of positive and negative energy states there is a further separation of states for which the spin is respectively parallel or antiparallel to the direction of the momentum vector. This can be obtained from the Maxwell’s equation without charges and current in the configuration. Scenery of our study is at high temperature T where coexist electron-positron pair and neutrino-antineutrino pair, (i.e., T≥1 MeV). Taking into consideration the possibility of negative mass, we can describe the observed behavior of antimatter in response to electromagnetic fields by assuming that the anti Dirac neutrino has a negative mass, so a new causal symmetry can be obtained.展开更多
Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom ...Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom induces a connection which is completely calculated. This allows us to discover the global and chiral properties of the space-time connection, with spin 2.展开更多
We revisit the two-component Majorana equation and derive it in a new form by linearizing the relativistic dispersion relation of a massive particle, in a way similar to that used to derive the Dirac equation. We are ...We revisit the two-component Majorana equation and derive it in a new form by linearizing the relativistic dispersion relation of a massive particle, in a way similar to that used to derive the Dirac equation. We are using thereby the Pauli spin matrices, corresponding to an irreducible representation of the Lorentz group, and a lucid and transparent algebraic approach exploiting the newly introduced spin-flip operator. Thus we can readily build up the Majorana version of the Dirac equation in its chiral representation. The Lorentz-invariant complex conjugation operation involves the spin-flip operator, and its connection to chiral symmetry is discussed. The eigenfunctions of the Majorana equation are calculated in a concise way.展开更多
The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neu...The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The ?gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.展开更多
文摘We review the formulation of graphene’s massless Dirac equation, under the chiral electromagnetism approach, hopefully demystifying the material’s unusual chiral, relativistic, effective theory. In Dirac’s theory, many authors replace the speed of light by the Fermi velocity, in this paper we deduce that in graphene the Fermi velocity is obtained from the connection between the electromagnetic chirality and the fine structure constant when the electric wave E is quasi parallel to the magnetic wave H. With this approach we can consider the properties of electric circuits involving graphene or Weyl semimetals. The existence of the induced chiral magnetic current in a graphene subjected to magnetic field causes an interesting and unusual behavior of such circuits. We discuss an explicit example of a circuit involving the current generation in a “chiral battery”. The special properties of this circuit may be utilized for creating “chiral electronic” devices.
文摘The usual choice of an orthogonal set of four plane-wave solutions of the free-particle Dirac equation does not lend itself readily to direct and complete physical interpretation in the case of Dirac neutrino particle. A different choice of solutions can be made which yields a direct physical interpretation at all energies. Besides the separation of positive and negative energy states there is a further separation of states for which the spin is respectively parallel or antiparallel to the direction of the momentum vector. This can be obtained from the Maxwell’s equation without charges and current in the configuration. Scenery of our study is at high temperature T where coexist electron-positron pair and neutrino-antineutrino pair, (i.e., T≥1 MeV). Taking into consideration the possibility of negative mass, we can describe the observed behavior of antimatter in response to electromagnetic fields by assuming that the anti Dirac neutrino has a negative mass, so a new causal symmetry can be obtained.
文摘Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom induces a connection which is completely calculated. This allows us to discover the global and chiral properties of the space-time connection, with spin 2.
文摘We revisit the two-component Majorana equation and derive it in a new form by linearizing the relativistic dispersion relation of a massive particle, in a way similar to that used to derive the Dirac equation. We are using thereby the Pauli spin matrices, corresponding to an irreducible representation of the Lorentz group, and a lucid and transparent algebraic approach exploiting the newly introduced spin-flip operator. Thus we can readily build up the Majorana version of the Dirac equation in its chiral representation. The Lorentz-invariant complex conjugation operation involves the spin-flip operator, and its connection to chiral symmetry is discussed. The eigenfunctions of the Majorana equation are calculated in a concise way.
文摘The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The ?gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.
