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Journal of Modern Physics

The Third Kind Of Particles

ShaoXu Ren

Published Jan 1, 2014• 4 citations
Publisher

Abstract

There are two kinds of spin particles in nature, the Boson and the Fermion.Those with integer value spin 0, 1, 2...are called Bosons, with half-integer value spin /2, 3/2, 5/2...are called Fermions.It is well known that everything in the universe is made of Bosons and Fermions.The spin representations of Boson and the Fermion in conventional quantum mechanics are expressed by Hermitian matrices, which are finite dimensional matrices.Are there so-called the Third Kind Of Particles (TKP), for an example, whose spin maybe /3, /4, /5, /6..., which are neither Bosons nor Fermions?This article concerns about the possible math figure of TKP.More detailed material related to derivative process and ideas evolvement of TKP are given.

DOI
10.4236/jmp.2014.59090

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There are two kinds of spin particles in nature, the Boson and the Fermion.Those with integer value spin 0, 1, 2...are called Bosons, with half-integer value spin /2, 3/2, 5/2...are called Fermions.It is well known that everything in the universe is made of Bosons and Fermions.The spin representations of Boson and the Fermion in conventional quantum mechanics are expressed by Hermitian matrices, which are finite dimensional matrices.Are there so-called the Third Kind Of Particles (TKP), for an example, whose spin maybe /3, /4, /5, /6..., which are neither Bosons nor Fermions?This article concerns about the possible math figure of TKP.More detailed material related to derivative process and ideas evolvement of TKP are given.
Particles that must have symmetric states are called bosons; pions, photons, and He 4+ nuclei are such particles. Particles whose states must be ant symmetric under interchange of the two particles are called fermions; electrons, protons, and neutrons are examples of fermions. Particles with integer spin are always bosons while particles with half-integer spin are always fermions. It is not at all obvious from the point of view of non-relativistic quantum mechanics why this relation, called the connection between spin and statistics, is true, and one must look within the framework of relativistic quantum field theory to understand it fully theoretically. Effects of identity can also show up in the scattering of seemingly non-identical particles. The elastic scattering of a He 4+ ion from a He 4+ atom, both are in their ground states. These are certainly distinguishable particles, since they have different charges. Particle identity also plays an important role in determining the properties of molecules made of identical atoms.
Abstract We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics, and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection.
In quantum mechanics, elementary particles of the same type are considered identical. For example, an electron in an atom could be replaced by another electron and the atom would behave in exactly the same way. Nature has taken particular advantage of this, allowing only two types of elementary particles: bosons and fermions. They differ fundamentally in how a collection of identical particles interact. Identical fermions cannot occupy the same quantum state (only one per state!). Identical bosons can occupy the same quantum state. The statistics of identical particles (how they act in groups) has profound affects. For example, the rich and complex structure of the periodic table arises from the principle that only one electron can occupy each quantum state. The spin and the statistics of particles are closely connected: (fermions) bosons have (half-)integer spin. (Spin is an internal angular momentum measured in units of Planck’s constant.)
We define statistics of quantum mechanical particles, obtaining the Bose–Einstein and Fermi–Dirac varieties of indistinguishable particles. After finding the rotation and Lorentz matrices in different Lorentz representations, we describe the spin-statistics theorem, relating fermions with half-integer spin and bosons with integer spin. We explain two simple proofs and say some words on two others. We end by discussing symmetries in more generality, and we discuss the fact that internal symmetries must commute with spacetime ones, due to the Coleman–Mandula theorem.