What is Fermions: Definition and 176 Discussions

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics and generally has half odd integer spin: spin 1/2, spin 3/2, etc. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.
Some fermions are elementary particles, such as the electrons, and some are composite particles, such as the protons. According to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum number relation.As a consequence of the Pauli exclusion principle, only one fermion can occupy a particular quantum state at a given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. At low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles.
Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter.
The name fermion was coined by English theoretical physicist Paul Dirac from the surname of Italian physicist Enrico Fermi.

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  1. tomdodd4598

    I Physical eigenstates of systems of n particles of spins sᵢ?

    I am relatively well versed when it comes to systems of spin, or doing the maths for them at least, but am unsure whether all of the {L2, Lz, (other required quantum numbers)} basis eigenstates for a general system of n particles of spins si, where si is the spin of the ith particle, can...
  2. H

    A Identical Fermions in identical linear combinations

    According to Pauli principle the two fermions can not occupy one state of a Hamiltonian. Can the two fermions occupy a state which is linear recombination of two states of the Hamiltonian?
  3. gennarakis

    I Quantum Kinetic Energy of Neutrons, Protons and Electrons

    Hi there, I have a problem to solve in Cosmology which says: "Write the formulas for the quantum kinetic energy of neutrons, protons and electrons as well as the formula for the gravitational energy for a neutron star that is comprised of free neutrons, protons and electrons in a ratio of Nn ...
  4. C

    A Time-ordering fermion operators

    If A and B are fermionic operators, and T the time-ordering operator, then the standard definition is T(AB) = AB, if B precedes A = - BA, if A precedes B. Why is there a negative sign? If A and B are space-like separated then it makes sense to assume that A and B anticommute. But...
  5. D

    A The commutations relations for left/right handed fermions

    I have a problem where I have to know the commutation relations for left handed fermions. I know ##\psi_L=\frac{1}{2}(1-\gamma^5)\psi## ##\psi^\dagger_L=\psi^\dagger_L\frac{1}{2}(1-\gamma^5)## and ## \left\{ \psi(x) , \psi^\dagger(y)\right\} = \delta(x-y)## So writing ## \left\{P_L\psi(x) ...
  6. J

    How Do You Determine Rotational Invariance in a Two-Fermion System?

    Homework Statement Homework EquationsThe Attempt at a Solution I suppose to determine if a hamiltonian is rotational invariant, we check if [H(1),L^2], however, I am not sure how to do it if the hamiltonian is operate on a two particle wave function. Is it just to evaluate [S1z Z2 +S2z Z1...
  7. S

    Energy of two fermions in a three-dimensional box

    Homework Statement Two particles of mass m are placed in a rectangular box with sides a>b>c (note 3D-box). The particles interact with each other with a potential V=A\delta(\mathbf{r}_1-\mathbf{r}_2) and are in their ground state (1s). Use first order perturbation theory to find the systems...
  8. MAKK

    How we differentiate between bosons and fermions?

    if we have two particle then how we differentiate between boson and fermion ,any experiment that differentiate them?
  9. N

    How does M theory describe fermions?

    How are fermions, like electrons, described by m theory? Are they closed strings like gravitons, or are they open strings attached to a D2/M2, D4, or M5 branes?
  10. S

    Massless fermions Klein tunneling

    QUOTE: "In 1929, physicist Oskar Klein[1] obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. However...
  11. haael

    Susskind on supersymmetry vs. cosmological constant?

    In one book of Susskind I found the following claim and I wanted to ask for its basis. Susskind says that each kind of boson gives positive contribution to the cosmological constant (the lighter, the better). Each kind of fermion gives negative contribution to the cosmological constant. Thus...
  12. S

    Why chiral fermions don't exist in odd dimensions?

    In four dimensions, left and right chiral fermion can be written as \psi_L= \begin{pmatrix} \psi_+\\ 0 \end{pmatrix},\qquad \psi_R= \begin{pmatrix} 0\\ \psi_- \end{pmatrix}, respectively, where \psi_+ and \psi_- are some two components spinors(Weyl spinors?). In this representation, the...
  13. moriheru

    String Theory & Fermions: Exploring Differences & Why They Matter

    This is a stupid question (good that I ask). String theory treats bosons and fermions in different ways e.g fermion potential are differ from boson potentials,actions differ and so on... My question is simply : why? Yes I know fermions and bosons are different groups of particles (integer and...
  14. D

    Why are all particles bosons or fermions?

    Why is it not possible for a particle to be neither symmetric nor antisymetric on exchange? If a particle can have 1/2 integer spin why can't it have 1/3 , 1/4 etc. I know it's a weird question to ask but I've been wondering about it for a while.
  15. Z

    Geometric measure of entanglement for fermions or bosons?

    For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...
  16. T

    Anticommutation of Fermions and the Lorentz irreps

    Hi everyone! I have two questions that arose during the path integral quantization of theories involving fermions. First of all, when we prove the equivalence between the path integral formalism and the canonical quantization we make use of the eigenvalue defining equation...
  17. Spinnor

    Graphically rep. 1+1D Weyl fermions, does this work?

    Does the following construction allow one to represent both the spinor and spacetime parts of the wavefunctions of the four massless Weyl fermions of a given magnitude of momentum p? In 3 dimensional space let there be some x,y,z coordinate system. Let the x and y-axis represent the complex...
  18. LarryS

    Generalized Dirac Equation for All Fermions?

    The original Dirac Equation was for the electron, a particle of spin 1/2. Is there a "Generalized Dirac Equation" that has been experimentally proven to work for all fermions, not just those of spin 1/2? Thanks in advance.
  19. Coffee_

    Idential particles, postion wavefunction for fermions.

    1. In griffiths the following is written down in the chapter of identical particles: ##\Psi(\vec{r_{1}},\vec{r_{2}})=\pm \Psi(\vec{r_{2}},\vec{r_{2}})## Where it's + for bosons and - for fermions. However in class we have seen that for two electrons in the spin singlet situation the POSITION...
  20. Safinaz

    Fermions Mass Terms in SM: Questions & Answers

    Hi all, I have some points not so clear for me about the fermions mass terms in SM; first, why ## \bar{\psi}\psi = \bar{\psi}_L \psi_R + \bar{\psi}_R \psi_L ##, that since ## \bar{\psi} = \bar{\psi}_R + \bar{\psi}_L ## and ## \psi = \psi_R + \psi_L ## Where are such terms: ## \bar{\psi}_R...
  21. binbagsss

    Decays possible? Parity conservation, bosons, fermions

    1. Homework Statement The question is to determine which decays are possible for: i) ##P^0 ->\prod^+ \prod^-## ii)##P^0 ->\prod^0 \prod^0## Homework Equations where ##J^p = 0^-, 1^- ## respectively for ##\prod^+, \prod^- , \prod^0## and ##P^0## respectively. The Attempt at a Solution For...
  22. Xenosum

    How to order Feynman Rules for Fermions

    Homework Statement This is more of a general question-- as the title suggests I'm not too sure how to place the terms given by the Feynman rules for fermions (since they involve operators and spinors, the order does of course matter). I've been reading Peskin & Schroeder and the rules are...
  23. CrimsonFlash

    Exchange symmetry when adding angular momentum and in LS coupling?

    When you add two angular momentum states together, you get states which have exchange symmetry i.e. the highest total angular momentum states (L = l1 + l2) will be symmetric under the interchange of the two particles, (L = l1 + l2 - 1) would be anti-symmetric...and the symmetry under exchange...
  24. S

    Spin inversion under dipole-dipole interaction of fermions

    Homework Statement Consider two spin 1/2 particles interacting through a dipole-dipole potential \hat{V} = A\frac{(\hat{\sigma_1} \cdot \hat{\sigma_2})r^2 - (\sigma_1 \cdot \vec{r})(\sigma_2 \cdot \vec{r})}{r^5} If both spins are fixed at a distance d between each other, and at t = 0 one of...
  25. V

    Eigenfunction of a system of three fermions

    I have to find the eigenfunction of the ground state \Psi_0 of a three independent s=1/2 particle system. The eigenfunctions \phi_{n,s}(x) = \varphi_n(x) \ \chi_s and eigenvalues E_n of the single particle Hamiltonian are known. Becuse of the Pauli exclusion principle, there must be...
  26. N

    Fermions & Bosons: Can They Be Converted to Energy?

    Since everything is energy, can fermions and bosons be (theoretically) converted to energy too?
  27. LarryS

    Massless Fermions: Physics & Existence

    Does modern physics allow for the existence of massless fermions?
  28. R

    Spin assumption for fermions in potential well.

    Hi, Assume I’m solving a 2-particle (fermions) problem in a potential well. If I set the wavefunction as anti-symmetric, then by default I’m assuming that the two particles has the same spin and hence exchange interaction has to be accommodated for. But what if the 2 fermions have different...
  29. S

    Is the Higgs Field Truly Responsible for the Mass of Fermions?

    It is said that the Higgs field is responsible for the mass of all particles. But the Higgs mechanism provides mass to the gauge bosons, and as far as I know the mass of the fermions is put "by hand" into the Lagrangian. Why, then, is the Higgs field responsible for the mass of the fermions?
  30. F

    Bosons and Fermions - interactions

    Homework Statement A particle of mass m is confined to the region |x| < a in one dimension by an infinite square-well potential. Solve for the energies and corresponding normalized energy eigenfunctions of the ground and first excited states. (b) Two particles are confined in the same...
  31. M

    Wave function of two different fermions

    Hi! According to quantum field theory, must the wave function of two different fermions be antisymmetric? If I have a state of two equal fermions: b^\dagger(p_1)b^\dagger(p_2)|0> I can construct the general state of two fermions: \int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)b^\dagger(p_2)|0>...
  32. B

    Finding Highest Energy for Fermions and Bosons in a Box

    Homework Statement a. Electrons and neutrons are fermions. Put 12 of them (6 each) in a box, and determine the n value for the ones with the highest energy. b. Do the same for 12 bosons (6 are pi zero bosons and 6 are alpha particles). Homework Equations En = (h2n2)/(8mL2) The...
  33. lpetrich

    Massive Majorana fermions - nontrivial gauge multiplets?

    From supersymmetry, gauge particles have superpartners, gauginos. Supersymmetry breaking will make all the gauginos massive, since none have been observed. But that has certain problems. A gauge field is a multiplet in its gauge group where each member corresponds to a generator of that...
  34. H

    Diagonalization of a Hamiltonian for two fermions

    Homework Statement Hi, I want to diagonalize the Hamiltonian: Homework Equations H=\phi a^{\dagger}b + \phi^{*} b^{\dagger}a a and b are fermionic annihilation operators and \phi is some complex number. The Attempt at a Solution Should I use bogoliubov tranformations? I...
  35. E

    One family of fermions SU(2)LXU(1)

    Hello, all If now I only have one family of fermions (a neutrino, a charged lepton, an up-type quark and a down quark), what is going to change of the Lagragian and also the Feynman rules of SU(2)LXU(1) electroweak theory? Euphemia
  36. H

    Density of states for fermions and bosons

    To take into account the density of states for an ideal gas, we first calculate it ignoring the spin. Then to take into account the spin for a system of electrons we put the number 2 for two spin directions. Why don't we do such this for a boson gas? For example if we have a gas of spin 1...
  37. L

    Why do fermions have 1/2-integer spins?

    Hello, Could anyone explain why fermions have half-integer spins and obey the fermi-dirac statics, whereas bosons have whole integer spins and don't? I have read lots of explanations at a fairly basic level for this, which say that this happens because fermions have antisymmetric...
  38. K

    About degrees of freedom of fermions

    There are something I don't get about the degrees of freedom(dof). For massive dirac spinor, there are four complex components or 8 dofs. But for electron/position, there are only 4 dofs in total ( electron up &down, position up&down). Does it mean the equation of motion eliminate the other...
  39. ShayanJ

    Fermions and Coherent States: What's the Connection?

    I know coherent states are minimal uncertainty states and can provide a link from quantum to classical physics.But when I hear fermions can't have coherent states,or at least are limited in this sense,I can't see any relationship! What's the point? And...another thing...is there sth called...
  40. M

    Would anything going the speed of light kill you and would fermions?

    I had to cut the title short but would anything going the speed of light kill you even though it is impossible? I know that light is going the speed won't kill you but would it count? Because since fermions are transferring forces like photons transfer the electromagnetic force between two...
  41. Sivasakthi

    Are fermions truly antisymmetric in their wave function?

    I have a doubt regarding the antisymmetry in the wave function of fermions.The antisymmetry is in the complete wave function or it is in the spin?
  42. lfqm

    QED Interaction Lagrangian with two different fermions

    Let say I want to study electron-proton scattering (without considering proton's quarks, i.e. no QCD), which is the Lagrangian? I've seen two different answers to this question :confused: First one: L=\bar{ψ}e(i∂-me)ψe+\bar{ψ}p(i∂-mp)ψp-\frac{1}{4}Fμ\nuFμ\nu-e\bar{ψ}eγμψeAμ+e\bar{ψ}pγμψpAμ...
  43. T

    Changing the chirality of fermions in interactions with Higgs

    Am i correct when i say that the fermions get a mass and interaction term with the Higgs from the SU(2)_{L}\times U(1)_{Y} invariant Yukawa interaction -g_{y}\bar\psi_{L}\phi\psi_{R} - g_{y}\bar\psi_{R}\bar\phi\psi_{L} where \psi is the fermion field and \phi the Higgs field. My...
  44. andrewkirk

    How can bosons made of fermions occupy the same quantum state?

    I've been reading about Bose-Einstein condensates, in which multiple bosons can occupy the same quantum state. I thought I understood how that could work until I learned that some atoms, such as Helium-4, are bosons. It seemed to me that if two He-4 atoms H1 and H2 occupy the same quantum...
  45. S

    Understanding the Nature of WIMPS: Bosons or Fermions?

    Are the wimps claimed to be bosons or fermions?
  46. G

    Bosons are the glue that hold fermions together

    If Wiki is right when it says bosons are the glue that hold fermions together then how does the photon hold atoms together?
  47. shounakbhatta

    Why Do Fermions Have +1/2 and -1/2 Spin?

    Hello, Fermions have a +1/2 and -1/2 spin. Is there any reason for that or is it just an intrinsic property?
  48. M

    Production of bound states of slow fermions- Peskin 5.3

    Hi all, I've been reading section 5.3 of Peskin and Schroeder, in which the authors discuss the production of a bound state of a muon-antimuon pair close to threshold in electron-positron collisions. Here \xi,\xi' are the Weyl spinors used to construct the Dirac spinors for the muon and...
  49. Z

    Fermions and Bosons in a distribution

    Homework Statement Consider a system of N distinguishable particles which are distributed across levels with energies 0, 1, 2, 3, 4, 5... The total energy of the system is U. Determine all the possible combinations of the particles in this system and hence determine the total number of...
  50. J

    Second Quantization for Fermions: Creation Operator

    So, I'm studying Second Quantization for fermions and came across this equation. I was just wondering why there is a summation needed? And why do we do it with (i≠p).? Please can someone explain this to me? Reply and help is much appreciated.
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