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Home , Magnetic quantum number

Fermions may aggregate

Wen-Xiang Chen∗ Department of Astronomy, School of Physics and Materials Science, GuangZhou University

A new possibility of possible aggregation of fermions is presented in this paper.When the boundary conditions of fermions are determined in advance, many fermions are not the same particle and therefore do not violate the principle of multi-repulsion.Fermions may aggregate when the system is in equilibrium. Keywords: Fermions, superradiance, aggregate

I. INTRODUCTION

The Pauli exclusion principle, also known as the Pauli exclusion principle, is one of the basic laws of microscopic particle motion. It points out: In a system composed of fermions, two or more particles cannot be in exactly the same state. It takes four numbers to completely determine the state of an in an atom, so the Pauli exclusion principle is expressed in an atom as follows: there can be no two or more with the same four quantum numbers, or At most two electrons can be accommodated in an determined by the orbital quantum numbers m, l, n, and the spin directions of the two electrons must be opposite. This has become one of the criteria for the periodicity of electrons arranged outside the nucleus to explain the . The arrangement of the extranuclear electrons follows the Pauli exclusion principle, the lowest energy principle and the Hundt rule. The principle of the lowest energy is that under the premise of not violating the Pauli principle of incompatibility, the extranuclear electrons always occupy the lowest-energy orbital first. Only when the lowest-energy orbital is filled, the electrons enter the higher-energy orbit in turn. It is to make the system energy as low as possible. Hund’s rule is that electrons arranged on equivalent orbitals (each orbitals on the same electron layer and electron sublayer) will share different orbitals as much as possible, and their spin directions are the same. Later, proved that this arrangement of electrons can make the energy the lowest, so the Hundt rule can be included in the principle of least energy as a supplement to the principle of least energy. The Pauli exclusion principle is a principle followed by particles (fermions) with half-integer spins. Referred to as Pauli principle. It can be stated that there cannot be two or more particles in the same single particle state in the whole fermion system. The spin of an electron is 1/2, so it follows Pauli’s principle. It was proposed by Wolfgang Pauli in 1925 to illustrate the periodic law of chemical elements. Pauli originally proposed that no two electrons in an atom can have exactly the same when summing up the atomic structure. The state of electrons in an atom is described by the principal n, the angular quantum number l, the magnetic quantum

∗Electronic address: [email protected] 2 number ml, and the spin magnetic quantum number ms. Therefore, Pauli’s principle can be expressed as that there cannot be two or more in the atom. Electrons have exactly the same four quantum numbers n, l, ml, ms. According to Pauli’s principle, the periodic law of chemical elements can be well explained. The Pauli principle is an important principle followed by all fermions. It plays an important role in all systems containing electrons, in the theory of molecular chemical bonds, and in the theories of solid metals, semiconductors and insulators. Later, I learned that Pauli’s principle is also applicable to other fermions such as protons and neutrons. Pauli principle is the basis for understanding many natural phenomena. The of a quantum system composed of two fermions is completely antisymmetric. And we know that black holes need to meet one condition for classical superradiation instability: The incident perturbation field is the Bose field; Among it is the condition for generating super radiation. In 1972, Press and Teukolsky[14] proposed that It is possible to add a mirror to the outside of a black hole to make a black hole bomb (according to the current explanation, this is a scattering process involving classical mechanics and quantum mechanics[1,3, 10–13, 15]).Regge and Wheeler proved that the spherically symmetric Schwarzschild black hole is stable under disturbance. Due to the significant influence of super radiation, the stability of rotating black holes is more complicated. Superradiation effects can occur in classical and quantum scattering processes. When a boson wave hits a rotating black hole, if certain conditions are met, the black hole may be as stable as a Schwarzschild black hole. When a boson wave hits a rotating black hole, if the frequency range of the wave is under superradiation conditions, the wave reflected by the event horizon will be amplified. Associate Professor Hasegawa Yuji of the Vienna University of Technology and Professor Masaaki Ozawa of Nagoya University and other scholars published empirical results against Heisenberg’s uncertainty principle on January 15, 2012[9]. They used two instruments to measure the rotation angle of the neutron and calculated it. The error of the measurement results obtained was smaller than the Heisenberg uncertainty principle, thus proving the measurement results advocated by the Heisenberg uncertainty principle. The restriction is wrong. However, the uncertainty principle is still correct, because this is the inherent quantum property of particles. In the article[7] follows the method I used to study superradiation and connects the uncertainty principle with the superradiation effect.I found that the measurement limit of the uncertainty principle can be small under the superradiation effect.From that paper we can see that, if boundary conditions are not set in advance, then the probability flow density equations on both sides of the black hole are equal for the incident interference and the coupled wave function in the black hole.However, if the boundary conditions of the incident fermions are preset, the two sides of the probability flow density equation will not be equal, because setting the boundary conditions implies a certain probability.According to the traditional theory, fermions do not produce superradiation.Moreover, if the boundary conditions are set in advance, then the generated possibility is combined with the fermion-coupled wave function, and fermions will produce superradiation phenomenon. We know that superradiation is a process of reducing entropy[2]. When the entropy of the system gradually increases, the entropy decreases when the superradiation process occurs. Slowly, the entropy of the system reaches its maximum value and the system state is balanced. When fermions determine the boundary conditions in advance, then many fermions are not identical particles, so the Pauli exclusion principle is not violated. When the state of the system is balanced, fermions may have the possibility of aggregation. 3

II. FERMIONIC SCATTERING

1 Now[2] let us consider the Dirac equation for a spin- 2 massless fermion Ψ, minimally coupled to the same EM potential Aµ as in Eq..

µ γ Ψ;µ = 0 , (1) where γµ are the four Dirac matrices satisfying the anticommutation relation {γµ, γν } = 2gµν . The solution to takes the form Ψ = e−iωtχ(x), where χ is a two-spinor given by   f1(x) χ =   . (2) f2(x)

Using the representation     0 i 0 1 0 i γ =   , γ =   , (3) 0 −i −i 0 the functions f1 and f2 satisfy the system of equations:

df1/dx − i(ω − eA0)f2 = 0, df2/dx − i(ω − eA0)f1 = 0. (4)

One set of solutions can be once more formed by the ‘in’ modes, representing a flux of particles coming from x → −∞ being partially reflected (with reflection amplitude |R|2) and partially transmitted at the barrier

in in iωx −iωx iωx −iωx f1 , f2 = Ie − Re , Ie + Re as x → −∞ (5)

T eikx, T eikx as x → +∞ (6)

On the other hand, the conserved current associated with the Dirac equation is given by jµ = −eΨ†γ0γµΨ and, by equating the latter at x → −∞ and x → +∞, we find some general relations between the reflection and the transmission coefficients, in particular,

|R|2 = |I|2 − |T |2 . (7)

Therefore, |R|2 ≤ |I|2 for any frequency, showing that there is no superradiance for fermions. The same kind of relation can be found for massive fields.

The reflection coefficient and transmission coefficient depend on the specific shape of the potential A0. However one can easily show that the Wronskian

df˜ df˜ W = f˜ 2 − f˜ 1 , (8) 1 dx 2 dx ˜ ˜ between two independent solutions, f1 and f2, of is conserved. From the equation on the other hand, if f is a solution ∗ 2 2 ω−eV 2 then its complex conjugate f is another linearly independent solution. We find|R| = |I| − ω |T | .Thus,for 0 < ω < eV ,it is possible to have superradiant amplification of the reflected current, i.e, |R| > |I|. There are other potentials that can be completely resolved, which can also show superradiation explicitly. 4

The difference between fermions and bosons comes from the intrinsic properties of these two kinds of particles. Fermions have positive definite current densities and bounded transmission amplitudes 0 ≤ |T |2 ≤ |I|2, while for bosons the current density can change its sign as it is partially transmitted and the transmission amplitude can ω−eV 2 2 be negative, −∞ < ω |T | ≤ |I| . From the point of view of quantum field theory, due to the existence of strong electromagnetic fields, one can understand this process as a spontaneous pair generation phenomenon (see for example). The number of spontaneously produced iron ion pairs in a given state is limited by the Poly’s exclusion principle, while bosons do not have this limitation.

We can pre-set the boundary conditions eA0(x) = −yω(which can be µ = −yω)[4][5][6][8], and we see that when y is relatively large(according to the properties of the Fermions, y can be very large), |R|2 ≤ |I|2 may not hold.In the end,we can get ∆x∆p ≥ 1/2 may not hold(in natural unit system).

III. FERMIONS MAY AGGREGATE

If you change the sign of the value of the wave function of any two particles, the wave function is completely antisymmetric.This means that two fermions can never occupy the same quantum state in the same system.Since all quantum particles are indistinguishable, if the quantum states of two Fermions are identical, then the value of the wave function should not change after they are swapped.The only solution to this paradox is that the value of the wave function is zero.For example, in the above example, if the position wave function of two particles is the same, then their spin wave function must be antisymmetric, that is, their spins must be opposite.This principle suggests that two electrons, or two fermions of any other kind, cannot occupy exactly the same quantum state.Also known as Pauli exclusion principle.When the entropy of the system increases gradually, when the process of superradiation occurs, the entropy decreases.Gradually, the entropy of the system reaches its maximum value, and the state of the system reaches equilibrium.When the boundary conditions of fermions are determined in advance, many fermions are not the same particle and therefore do not violate the poly exclusion principle.When the system is in equilibrium, fermions may aggregate.

IV. SUMMARY

This article proposes a new possibility that Fermions Fermions may aggregate.When the boundary conditions of fermions are determined in advance, many fermions are not the same particle and therefore do not violate the principle of multi-repulsion.Fermions may aggregate when the system is in equilibrium.

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