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Physics World

Ultracold fermion race is on

Randall G. Hulet

Published Aug 1, 1999• 2 citations
Publisher

Abstract

At the quantum level, particles behave very differently depending on whether their spin angular momentum is an integer or a half integer. Half-integer spin particles are known as fermions, and include all the constituents of atoms: electrons, protons and neutrons. Bosons, on the other hand, are particles with integer spin, such as photons.

DOI
10.1088/2058-7058/12/8/25

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A free-electron Fermi gas is a gas of electrons with spin https://www.w3.org/1998/Math/MathML" display="inline"> S = 1 / 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003606857/19698a40-dbd9-4f9a-9cb7-890a1d39adce/content/math8_1.tif "/> . A fermion is a particle with half-integer spin S such as the electron. A boson is a particle with integer spin https://www.w3.org/1998/Math/MathML" display="inline"> S ≥ 0 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003606857/19698a40-dbd9-4f9a-9cb7-890a1d39adce/content/math8_2.tif "/> . By a gas is meant that there are no interactions between the particles making up the gas. Thus a Fermi gas can exhibit no phase transitions by itself. On the other hand, a free boson gas can exhibit an interesting quantum phase transition into a superfluid state, qualitatively similar to that of the superconducting state of a metal, called Bose-Einstein condensation . In contrast, an electron Fermi liquid would be a system containing electrons that do interact with each other. We will see in the last two chapters of this book that when such interactions occur, magnetic or superconducting transitions associated with the electrons can happen.

CRC Press eBooks•Mar 13, 2025•1 citation
At the quantum level, particles behave very differently depending on whether their spin angular momentum is an integer or a half integer. Half-integer spin particles are known as fermions, and include all the constituents of atoms: electrons, protons and neutrons. Bosons, on the other hand, are particles with integer spin, such as photons.
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.
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.)
Why is it that particles with half-integer spin are Fermi particles whereas particles with integer spin are Bose particles? An explanation has been worked out by Pauli from complicated arguments from quantum field theory and relativity. He has shown that the two must necessarily go together … but we have not been able to reproduce his arguments on an elementary level. This probably means we do not have a complete understanding of the fundamental principle involved… R. P. Feynman, R.B. Leighton and M. Sands, Feynman Lectures on Physics , Volume 3, Chapter 4, Section 1, Addison-Wesley, Reading, MA (1963) Introduction Particles with half-integer angular momentum obey the Pauli exclusion principle (PEP) – a restriction that a non-degenerate single-particle quantum state can have occupation number of only 0 or 1. This restriction was announced by W. Pauli in 1924 for which, in 1945, he received the Nobel Prize in Physics. Soon after Pauli, the exclusion principle was generalized by P. Dirac and E. Fermi who – independently – integrated it into quantum mechanics. As a consequence half-integer spin particles are called Fermi–Dirac particles or fermions . PEP applies to electrons, protons, neutrons, neutrinos, quarks – and their antiparticles – as well as composite fermions such as He 3 atoms. Thermodynamic properties of metals and semiconductors are largely determined by electron (fermion) behavior.
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.
A free-electron Fermi gas is a gas of electrons with spin https://www.w3.org/1998/Math/MathML" display="inline"> S = 1 / 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003606857/19698a40-dbd9-4f9a-9cb7-890a1d39adce/content/math8_1.tif "/> . A fermion is a particle with half-integer spin S such as the electron. A boson is a particle with integer spin https://www.w3.org/1998/Math/MathML" display="inline"> S ≥ 0 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003606857/19698a40-dbd9-4f9a-9cb7-890a1d39adce/content/math8_2.tif "/> . By a gas is meant that there are no interactions between the particles making up the gas. Thus a Fermi gas can exhibit no phase transitions by itself. On the other hand, a free boson gas can exhibit an interesting quantum phase transition into a superfluid state, qualitatively similar to that of the superconducting state of a metal, called Bose-Einstein condensation . In contrast, an electron Fermi liquid would be a system containing electrons that do interact with each other. We will see in the last two chapters of this book that when such interactions occur, magnetic or superconducting transitions associated with the electrons can happen.