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. E

    Pauli exclusion principle and fermions, bosons and quarks

    Homework Statement Which of these particles don't follow Pauli exclusion principle and thus have a symmetric wave function? a) Bosons b) Fermions c) Quarks d) All particles follow Pauli exclusion principle Homework Equations None. The Attempt at a Solution I think that...
  2. J

    Second Quantization for Fermions

    Please let me know if I get this right. Second Quantization for Fermions used the definition of its annihilation and creation operators instead of wavefunctions. We use second quantization to express this many body problem in a hamiltonian. Am I right? Can someone please explain this to me in...
  3. I

    Can an even number of Fermions be a Bosonic system?

    Hi everyone, I've just done a problem where we are dealing with two protons with the same spin directions and the system is treated as a fermionic system. I always had the notion that two (or an even number of) fermions, for opposite spin perhaps, act as bosons. Is this true? If so, when...
  4. marcus

    Interesting Claus Kiefer article: fermions decohere geometry

    The interest of this article was first pointed out by Tom Stoer in biblio thread comment. The idea is to take seriously the quantum nature of geometry and its interaction with fermions at the quantum level. The idea is even that geometry might be as we experience it BECAUSE her little triads...
  5. B

    Exclusion principles for fermions and bosons

    Hello, I was curious about how the exclusion principle applied to fermions and bosons differently. My current understanding is that the exclusion principle states that no two fermions may be in the same state of motion and that bosons do not obey the exclusion principle. My problem with this is...
  6. bcrowell

    Gauge invariance requires gauge bosons, why not for neutral fermions?

    My understanding is that for electrons, there is a standard argument that the electromagnetic interaction between them is required, not optional. Since they're identical particles, we should be able to take the wavefunction of two electrons and mix up their identities by any amount we like, and...
  7. N

    Fermions vs Bosons: Low Temp Effects

    why is that at relatively low temperature bosons can occupy the same state while the fermions cannot? and how does we macroscopically see the effects of bosons (with explanations)? a theoretical answer is preferable
  8. D

    Identical fermions in a box - degenerate states

    The ground state for two identical fermions in a box (in 1D) is given by: \psi (x_{1},x_{2})_{12} = \frac{\sqrt{2}}{a}[sin(\pi x_{1}/a)sin(2\pi x_{2}/a) - sin(2\pi x_{1}/a)sin(\pi x_{2}/a)] The book I'm reading though says that this state is non degenerate, and that the next excited state...
  9. fluidistic

    Fermions, density of states

    Homework Statement Consider a gas of non interacting electrons in two dimensions with electronic density n by unit of area and mass m. The gas forms a square of sides L. 1)Assume periodic boundary conditions, find the density of states by unit of area. 2)Find the Fermi energy in function of...
  10. A

    Do fermions produce virtual bosons when they interact?

    Dear Physics Forum, I understand that forces between fermions are mediated by virtual bosons. My "sense" of it is that a fermion produces virtual bosons (quarks would produce photons, gluons, and W/Z bosons; electrons photons and W/Z; neutrinos W/Z) within the confines of the uncertainty...
  11. matt_crouch

    Fermions that can access 10 distinct energy states; Statistical Physics

    Homework Statement Consider a system made of 4 quantum fermions that can access 10 distinct states respectively with energies: En=n/10 eV with n=1,2,3,4,5,6,7,8,9,10 1) Write the expression for the entropy when the particles can access all states with equal probability 2) Compute...
  12. K

    Bosons and Fermions in a rigorous QFT

    I'm wondering, is there still a sharp distinction between Bosons and Fermions in a rigorous QFT, if exsits? My question is motivated by the following, consider one of the equations of motion of QED: \partial_\nu F^{\nu \mu} = e \bar{\psi} \gamma^\mu \psi In our familiar perturbative QED (Here...
  13. N

    The dipole interaction and fermions

    Hi When looking at the interaction between an EM-wave/field E with an isolated atom, we know that they interact via the time-dependent dipole interaction V = dE. This can be derived by looking at an electron bound to an atom, and it is used in systems, where the atom can be rightfully...
  14. R

    Is there a representation diagram for fermions like the 8 fold way for mesons?

    I was wondering if there was something similar to the 8 fold way representation used on mesons for the fermions?
  15. M

    Light fermions and ~125 GeV Higgs from asymptotic safety

    From http://arxiv.org/abs/1112.2415, "Planck scale Boundary Conditions and the Higgs Mass", I learn of http://arxiv.org/abs/0912.0208, "Asymptotic safety of gravity and the Higgs boson mass", which predicts a Higgs mass of 127 GeV as a consequence of the vanishing of the Higgs self-interaction...
  16. N

    What is the origin of mass(both fermions and bosons)?

    Please teach me this: What is the origin of mass of both fermions and bosons?Is it correct that the origin is the spontanious broken symmetry of Higgs Field?(I know that Higgs mechanism is the origin of mass of vector boson W and Z in weak interaction). Thank you very much for your kind helping.
  17. B

    A system consists of two indistinguishable spin-1 fermions, both confined

    Homework Statement A system consists of two indistinguishable spin-1 fermions, both confined inside the same box of length L centred on the origin. The particles do not interact with each other. a) What is the total energy of the ground state of this system? (Use the standard formulas for...
  18. H

    Can Atoms Be Made of Different Fermions?

    hi, i have been reading this book about antimatter, "Antimatter" by Frank Close, and have a question. CAN ATOMS BE COMPRISED OF DIFFERENT FERMIONS OTHER THAN PROTONS, NEUTRONS, AND ELECTRONS? could they be comprised of those fermions if they have the same charges as protons, neutrons, and...
  19. M

    What does the R-Symmetry do to scalars and fermions in N=4 U(N) SYM?

    Hi, I have forgotten all about my supersymmetry knowledge and all about my group theory knowledge. I am trying to understand what the R-symmetry in N=4 U(N) SYM does. Sadly I have never actually learned anything about supersymmetry which is larger than N=1. I know the R-symmetry is SU(4) and...
  20. L

    Integer Spin and Half Spin: What's the Difference? (Bosons vs. Fermions)

    bosons have integer spin, fermions have half spin, what does that mean? why bosons (integer spin) is able to avoid pauli's exclusion principle?
  21. R

    Exploring the Interaction of Fermions and Bosons

    Just wondering... If the interactions between fermions are the emittance of a boson (from what I understand from the grand design book by stephen hawking) then when you punch someone, is it just high levels of bosons being emmited and clashing or are the actual boson particles colliding?
  22. P

    When will we know whether neutrinos are Majorana fermions?

    As I understand, the answer will have to come from neutrino-less double beta decay experiments. When will these experiments reach the required sensitivity and gather enough data, to provide us with a definite answer about the nature of neutrinos?
  23. M

    How do fermions acquire mass as opposed to gauge bosons?

    Hello, if someone could enlighten me I'd be most grateful. Also, if anybody could point me in the direction of some really good free resources that would be great too. Thanks.
  24. S

    Time-reversal operator for fermions (Sakurai)

    In Modern Quantum Mechanics (2nd ed.) by J.J. Sakurai, in section 4.4 on 'The Time-Reversal Discrete Symmetry' he derives the time-reversal operator, \Theta, for the spin-$\frac{1}{2}$ case as (pg.: 277, eq. (4.4.65)): \Theta = \eta e^{\frac{-i \pi S_{y}}{\hbar}}K = -i \eta \left(...
  25. L

    Quantum entanglement between fermions

    Hi all Can you help me? Can the quantum entanglement exist between fermions which never interacted each other? For example – if this states of fermions are described by Slater determinant Does exist some papers from scientific journals about this theme? Thank you in advance...
  26. marcus

    Spinfoam Fermions, Lqg now has matter

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  27. S

    Pauli exclusion principle between 2 identical fermions

    hi, can we say that the Pauli exclusion principle between 2 identical fermions implies logically entanglement because of the antisymmetric wavefunction, that can not be factorized as a tensor product: http://en.wikipedia.org/wiki/Slater_determinant "However, it is not satisfactory for...
  28. K

    Total ground state energy of N fermions in a 3D box

    Hello everybody, I just have no idea how to start this problem so i was hoping you guys would point me in the right direction and then i'll be able to go on by myself the problem asks to show that the total ground state energy of N fermions in a three dimensional box is given by E total =...
  29. I

    Fermions with no mass, and helicity coupling.

    Hi, I was reading a lecture of qft and I found that two equations: \begin{flalign*} i \gamma^\mu \partial_\mu\psi_R - m\psi_L=0 \\ i \gamma^\mu \partial_\mu\psi_L - m\psi_R=0 \end{flalign*} after splitting in two Dirac's equation with Weyl's projectors. I found that really interesting that the...
  30. N

    Exploring the Contradiction of Non-Interacting Fermions in Superconductors

    Hi In superconductors, the fermions are interacting. In order to diagonalize our Hamiltonian (which contains the product of four fermion operators), we use Wick's theorem to approximate the product of four fermion operators by the product of two fermion operators. Now, a Hamiltonian...
  31. M

    Identical Fermions in an infinite square well

    If you have 2 identical, noninteracting Fermions in an infinite 1 dimensional square well of width a, I was thinking the state would be: \frac{1}{\sqrt{2}}\psi_1(x_1)\psi_1(x_2)(\uparrow\downarrow - \downarrow\uparrow ) where \psi_1 is the ground state of the single particle well problem...
  32. V

    Identical particles, spin, fermions, etc.

    Homework Statement I got two particles, spin-(1/2), in a box of finite length and I must compute the energy and wavefunctions for the three lowest states. The particles are in a singlet spin state. Homework Equations E = \epsilon_{1} + \epsilon_{2} +... The Attempt at a...
  33. B

    2 non-interacting fermions in 1D SHO

    Homework Statement Two identical non-interacting spin 1/2 particles are in the one-dimensional simple harmonic oscillator potential V(x) = kx2/2. The particles are in the lowest-energy triplet state. a. Write down the normalized space part of the wave function. b. Calculate the energy of...
  34. P

    Can string theory include fermions without supersymmetry?

    I'm taking an introductory string theory course which focuses on bosonic string theory. The lecturer says to include fermions supersymmetry must be included (aka. superstrings). If we face the event that the LHC fails to find any supersymmetry at TeV scale and the physics community lose faith in...
  35. M

    Fermions must be described by antisymmetric and bosons by symmetric

    :confused: friends, we know that fermions must be described by antisymmetric and bosons by symmetric wavefunctions. but i was wondering why a particle of certain class behaves like that for ever? ie. say, an electron will never behave like a boson ?? my book says that there is a spin...
  36. P

    Desintegration of particle into 2 fermions

    Why the spin part of wavefuncition of two particle of half-integer spin (fermions) which was created after desintegraton of spinless particle is always antisymmetric (let's assume that orbital angular momentum was 0 before and after desintegration). This implies that spatial part of wavefunction...
  37. E

    Which fermions are chiral besides neutrinos?

    Wen local bosonic emergent string net model states he can give rise to electrons and photons, quarks and gluons but not chiral fermions. I know neutrinos are chiral. Any other fermions? If he can provide an explanation for masses and mixing angles for all SM particles except neutrinos...
  38. W

    Ground-state energy of fermions

    Homework Statement What is the ground-state energy of 24 identical noninteracting fermions in a one-dimensional box of length L? (Because the quantum number associated with spin can have two values, each spatial state can be occupied by two fermions.) (Use h for Planck's constant, m for the...
  39. Z

    Fermions in bound states and their wavefunctions

    Hello all, This may be my very first post on Physics Forums. I am a 1st year physics grad student and need some help on something that's been bugging me. Suppose we have two spin half particles in a bound state. The total spin will either be 0 or 1. The spin 0 state, for example, would be...
  40. A

    Couplings of fermions and bosons to the Higgs

    Homework Statement I have to show that the couplings to the Higgs ( W+ W- h , ZZh, hhh, and e+e-h) are proportional to the mass squared (for bosons) or mass (for fermions) of the particles. But according to this problem I don't have to explicitly construct the interaction terms in the...
  41. D

    Why can fermions occupy only one state and

    Why can bosons occupy more? Surely the reason must be more than the maths? Whats the physical reason?
  42. tom.stoer

    Torsion in GR and QG from fermions?

    I know that GR is essentially a Riemann theory w/o Torsion; the Levi-Cevita-Connection is symmetric and therefore the torsion vanishes. What happens when fermions are included? Does the spin-connection still guarantue that the covariant derivative comes with a torsion-free connection...
  43. F

    Are black holes bosons or fermions?

    The question says it all. Black holes have mass, and they have angular momentum. - Is the angular momentum an integer or half an integer? Or neither/both? - What happens when two black holes are exchanged? François
  44. N

    Fermions & Parity: Exploring 3-Particle System

    Hi all. This isn't a homework question, but something I thought about. When looking at a system of 2 fermions, we have that: \Psi(r_1,r_2)=-\Psi(r_2,r_1). Now if we look at a 3 fermion system, then what is the demand for the waveequation? Does it have to be anti-symmetric when switching two...
  45. J

    Bound states of massless fermions

    If I look at the energy of the hydrogen atom, the energy is proportional to the mass of the electron (or more precisely, the reduced mass). Does this mean that without a Higgs mechanism, there are no bound states of the hydrogen atom? (Or is it just an artifact of a non-relativistic theory that...
  46. F

    Energy States- Bossons & Fermions

    Homework Statement Consider the 3-D infinite potential well (length=L). The energy levels for this system are given by E=(h bar)^2\pi^2/(2ML^2)*(n(sub x)^2+(n(sub y)^2+(n(sub z)^2) There are 10 particles in this potential well. What is the lowest energy of this ten-particle state when the...
  47. N

    Statistical Physics: Partition function and fermions

    Homework Statement Hi all. The partition function for fermions is (according to Wikipedia: http://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)#Relation_to_thermodynamic_variables_2) given by: Z = \prod\limits_i {\left( {1 + \exp \left[ { - \beta \left( {\varepsilon _i -...
  48. B

    Identical bosons vs. fermions in square potential well

    The following Wolfram web page shows the probability density functions for two identical bosons in a square potential well. It also shows the probability density for two identical fermions. http://demonstrations.wolfram.com/WaveFunctionsOfIdenticalParticles/ So it appears that each is...
  49. J

    A question regarding the number of fermions with a certain velocity component

    Homework Statement Prove that the number of electrons whose velocity's x-component is between [x,x+dx] is given by dN = \frac{4\pi V m^2 k_B T}{h^3} ln [exp(\frac{E_F -mv_x^2/2}{k_B T})+1]dv_x Homework Equations The Fermi-Dirac Distribution function: \frac{dn}{dE}=\frac{4\pi V...
  50. M

    Ground state of Hamiltonian describing fermions

    Homework Statement I have been given the Hamiltonian H = \sum_{k} (\epsilon_k - \mu) c^{\dag} c_k where c_k and c^{\dag}_k are fermion annihilation and creation operators respectively. I need to calculate the ground state, the energy of the ground state E_0 and the derivative...
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