Fermion Definition and 112 Threads

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. U

    Quick question on Baryon spin states

    Things I don't understand: What do they mean by "two spin-1/2 doublets and a spin-3/2 quadruplet"? Why do they use the two flavours "+2/3e and -1/3e" ?
  2. C

    How to evaluate a triangular fermion loop

    Say I have a scalar field which decays into to a fermion - anti fermion pair which then interact in a closed loop to produce two photons. How would I evaluate this? Can I just follow the loop backwards from any of the two photon vertices and just write vertex factor, propogator, vertex factor...
  3. C

    Chandrashekhar limit for relativistic fermion gas

    hi fellas, I have been working on Chandrashekhar limit, and I found a mass-radius relationship for the nonrelativistic fermi gases using this formula and i got the graph of this R=((18pi)^(2/3))/10 *H^2/(GmM^(1/3) ) (0.5/n)^(5/3) where H=(6.63*10^-34)/2pi G=6.67*10^-11 m=9.11*10^-31...
  4. pellman

    Commutator for fermion operators?

    If we have two fermion operators with a known anti-commutator AB+BA, what do we do if we find ourselves with AB-BA in an equation? Does this automatically vanish for fermions? if not, is there anything we can say about in general?
  5. A

    Why Do Fermion and Boson Operators Commute?

    For bosons we define states as eg. ln> = l1 0 1 ... > where the numbers denote how many particles belong to the j'th orbital. And similarly for fermions. We then define creation and anihillation operators which raise and lower the number of particles in the j'th orbital: c_j...
  6. S

    Coherent state between a fermion and a photon

    Can we have a coherent state between a fermion and a photon! I mean can there ever be a fermionic polariton?
  7. S

    How does one fermion change the energy of another fermion

    My understanding of how one fermion changes the energy of another is something like: fermion x approaches fermion y and x emits bosons which are absorbed by y. But why does one billiard ball transfer a lot of its energy to another billiard ball on contact? Say billiard ball x approaches...
  8. marcus

    DM candidate anapole Majorana fermion

    http://www.eurekalert.org/pub_releases/2013-06/vu-stm061013.php http://arxiv.org/abs/1211.0503 Anapole Dark Matter Chiu Man Ho, Robert J. Scherrer (Submitted on 2 Nov 2012) We consider dark matter (DM) that interacts with ordinary matter exclusively through an electromagnetic anapole, which...
  9. michael879

    Fermion Mass Structure: Explaining the Reversal of Up/Down Quarks

    I was taking a look at the SM particle table and I noticed that the up/down quarks seem to be "reversed" from the usual structure. Neglecting those two quarks, the "up" family is the most massive, then the "down" family, then the "electron" family, then the "neutrino" family. However for some...
  10. C

    How can Helium 4 be a Boson and Helium 3 be a Fermion?

    Hi there, Just a quick question which I'm sure I'm over complicating in my head.:confused: I've read that Helium 4 is a Boson because it has 0 spin and that Helium 3 is a Fermion because it has 1/2 spin. Is this right? I don't see how whole atoms can be associated with fundamental particle...
  11. L

    Fermion Boson Reaction: Ratio of Fermions to Bosons at T=0

    Homework Statement Fermions and bosons combine through the reaction F + F + ΔE = B (so the creation of a single boson requires 2 fermions and some positive energy). What is the ratio of fermions to bosons at T = 0? Homework Equations 2[nF]/[nB] = K(T), where [nF] is the...
  12. andrewkirk

    What happens when we measure spin of a fermion?

    I am trying to understand the measurement of spin, in order to understand Bell's paper on the Einstein-Podolsky-Rosen paradox. When we measure the spin of a fermion in the direction of unit vector a, will the result be: 1. a value of either +0.5 or -0.5, and upon measurement, the fermion...
  13. P

    Dimensional analysis of the fermion mass renormalization

    In the textbook, usually the fermion mass renormalization is introduced as follows: the mass shift \delta m must vanish when m_0=0. The mass shift must therefore be proportional to m_0. By dimensional analysis, it can only depend logarithmically on \Lambda (the ultraviolet cutoff): \delta m \sim...
  14. P

    Average Fermion Current: Understanding the Relation to Background Fermions

    Hi! I have a little problem. Consider a 4-fermion interaction (neglecting constant factors) of the form \overline{\psi_{a \mathrm{L}}} \gamma^{\lambda} \psi_{b \mathrm{L}} \overline{\psi_{c \mathrm{L}}} \gamma_{\lambda} \psi_{d \mathrm{L}} . I want to average this interaction over a...
  15. W

    What is the Meaning of Vectorlike Fermion in Particle Physics?

    In many papers about hep theory, I can find the concept, vectorlike fermion. But, I cannot get the exact meaning of vectorlike fermion. I would like you guys to explain vectorlike fermion. Thank you.
  16. T

    Could a Fermion be Entangled with a Boson ?

    Could a Fermion be Entangled with a Boson ?
  17. L

    Fermion Anticommutation Relations (nightmare)

    Hi. I've been thinking about this proof for over a day now and have reached the point where I can't come up with any new approaches! I'm trying to prove equation (5.15) in these notes: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf Just above eqn (5.15) we are told that the proof...
  18. B

    Is the universe a fermion or a boson?

    From introductory QM class, my understanding is that one can consider any number of "fundamental" particles as a composite system and pretend it is a particle. When 2 fermions are considered as a single composite system/particle, it becomes a boson. When 1 fermion and 1 boson are considered...
  19. fluidistic

    Concept of boson and fermion applied to atoms and more

    Sometime I read that the helium atoms can be considered as boson, but I don't understand why. I know that its nucleous has a spin of 2 (integer) and that its 2 electrons gives the atom a total spin of 3, an integer. But then why isn't hydrogen considered also as a boson? I think it's considered...
  20. S

    Contribution of one fermion to entropy of one-particle state

    Homework Statement Hello, I'm studying for my final exam on statistical physics, and I found an exercise of which I think it is really easy but I'm unsure of how to do it! So now I wonder if I actually don't understand what I'm doing at all! The question is as follows: Calculate for...
  21. E

    Fermion Current Commutators in 2 dimensions

    Homework Statement Given the current: J^{\epsilon}_{0} (t,x) = \overline{\psi_{L}}(t,x + \epsilon) \gamma^{0} \psi_{L}(t,x - \epsilon) = \psi_{L}^{\dagger} (x + \epsilon) \psi_{L}(x - \epsilon) with \psi_{L} = \frac{1}{2} (1 - \gamma^{5}) \psi_{D}. Use the canonical equal time...
  22. Z

    Fermion Rotations: Exploring the Mystery of 720 Degree Symmetry

    It is interesting that our elementary fermions have 1/2 spin, meaning it takes a full 720 degree rotation to bring them back to their original state and these fermions constitute ordinary matter, eg. quarks, and electrons. Classical nature, however, does not have a 720 degree symmetry, but...
  23. Vorde

    Discovering Majorana Fermions - A Groundbreaking Physics Find

    http://science.slashdot.org/story/12/04/13/1547242/scientists-find-long-sought-majorana-particle Is this legitimate? I tried reading the original paper but my physics skills weren't quite enough to keep up with it.
  24. Y

    Is whole Carbon 13 atom (not just the nucleus) a fermion or boson?

    This ought to be simple, I think. But I haven't found a consistent way to think about things yet. Is it as simple as adding up all the spins of the elementary particles in the particle and checking whether the total has inter or half-integer spin? Homework Statement State whether the...
  25. Z

    Evidence for fermion statistics among neutrinos

    Is there any evidence for quantum fermi-dirac distributions among neutrinos, besides the obvious fact about their spin? I was wondering how Pauli exclusion principle would work with a neutrino 'gas', and what kind of quantum numbers they could have. It has been expected that if we ever did...
  26. V

    Superposition betweeen Boson and Fermion

    Is it possible to put a Boson and Fermion in superposition? If not possible, why not?
  27. D

    A fermion oscillator interacted with a boson oscillator

    It is known to all that the Hamiltonin H=p^2/m+x^2 can describe the boson and fermion particle, but how can embody the fermion properties when a fermion oscillator interacted with a boson oscillator? what is their interaction form?
  28. B

    Consider a fermion gas of N electrons in volume V

    Consider a fermion gas of N electrons in volume V. Using the density of momentum states , show that the Fermi energy can be written as (h^2)/(2m (subscript e)) ((3N)/(8pi V))^(3/2) Homework Equations g(p)=(V/h^3) (4pi) p^2 The Attempt at a Solution N=integral from 0 to k(subsript...
  29. R

    Proton Wavefunction: Antisymmetry & Fermions Explained

    I still don't understand antisymmetry and fermions. Is the proton wavefunction equal to this: |\psi_p>=\frac{1}{\sqrt{6}}\left(2|u\uparrow u\uparrow d \downarrow \rangle - |u\uparrow u\downarrow d \uparrow \rangle - |u\downarrow u\uparrow d \uparrow \rangle \right) or this...
  30. Feeble Wonk

    Every known boson and fermion has a corresponding anti-particle

    Please take a moment to help enlighten a poor ignorant layperson. My understanding is that every known boson and fermion has a corresponding anti-particle, with the only exception being the photon. If true, can anyone explain WHY that that is?
  31. E

    Calculating Weak Interaction Processes: Four Fermion Invariants in Fermi-Theory

    In calculations of weak interaction processes in the Fermi-theory, there are some amplitudes of the form: \bar{a}(\gamma_{\alpha} + \lambda \gamma_{\alpha}\gamma_{5}) b \bar{c}(\gamma^{\alpha} + \gamma^{\alpha}\gamma_5)d where a,b,c,d are Dirac-spinors. Now, if this is a Lorentz-scalar. In that...
  32. C

    Is an Electron a Boson or a Fermion?

    I'm studying particle physics now and am confused with all these terminologies.
  33. W

    Why in nature there is no spinless fermion?

    why? i can see the link between spin value and the statistics in quantum mechanics
  34. C

    Proving Fermion Occupation with Commutation Relations

    Homework Statement prove , using appropriate commutation relations that the number operator yields the values 0 and 1 for fermions , and any non - negative values for bosons. Homework Equations the commutation relations for bosons and fermions. The Attempt at a Solutionthe boson...
  35. D

    Fermion creation and annihilation operators

    Hi. If c and c^\dagger are fermion annihilation and creation operators, respectively, we know that cc^\dagger+c^\dagger c=1 and cc=0 and c^\dagger c^\dagger=0. I can use this to show the following [c^\dagger c,c]=c^\dagger cc-c c^\dagger c=-cc^\dagger c=-c(1-cc^\dagger)=-c But on the...
  36. J

    Local lorentz tranformations of fermion action

    The action for a fermion in curved spacetime is S = -\int d^4 x \sqrt{- \det(\eta^{ab} e_{a\mu}e_{b\nu})} \left[ i\overline{\psi} e^\mu_a \gamma^a D_\mu \psi + i m \overline{\psi}\psi \right] where g_{\mu\nu} = \eta^{ab} e_{a\mu} e_{b\nu} and the derivative operator acting on fermions is...
  37. haael

    Fermion annihilation operators from position and momentum

    Is it possible to express fermion annihilation operator as a function of position and momentum? I've seen on Wikipedia the formula for boson annihilation operator: \begin{matrix} a &=& \sqrt{m\omega \over 2\hbar} \left(x + {i \over m \omega} p \right) \\ a^{\dagger} &=& \sqrt{m \omega...
  38. B

    Fermion Gas Problems: Avg Speed & Density Comparison

    Homework Statement Consider the collapse of the Sun into a white dwarf. For the Sun, M = 2 \times 10^{30} kg, R = 7 \times 10^{8}m, V = 1.4 \times 10^{27}m^{3} . (c) What is the average speed of the electrons in the fermion gas? (d) What is the density of the electron gas? Compare it...
  39. P

    What Is the Most Likely Speed for a Fermion Versus Temperature?

    Homework Statement (a) If you had a particle of mass 9.1*10^-31 kg, plot its most likely speed versus temperature, in a range from 0 to 6000 K, assuming it behaved as a classical particle. (b) repeat part (a) if the particle behaved as a fermion. Homework Equations The Attempt at...
  40. D

    How Is the Depth of the Potential Well Calculated for Free Electrons in Gold?

    Homework Statement For free electrons in a metal, the depth of a potential well can be determined by observing that the work function is the energy required to remove an electron at the top of the occupied states from the metal; an electron in this state has the Fermi energy. Assuming...
  41. B

    Physical interpretation of Lorentz invariant fermion field product?

    Hey all! Just a very short question: May I interpret the Lorenz invariant quantity \bar\psi\psi as being the probability density of a fermion field? Thanks! Blue2script
  42. 0

    Understanding of the Fermion, Boson difference

    Ok my understanding of the Fermion, Boson difference is this: Identical Particles carry a representation of the permutation group. Since we have not found any para statistics, this representation must be one dimensional. And there are only two one dimensional irreducible representations of...
  43. B

    Velocity dependent fermion number?

    Hi all! Just a short question I am wondering about. Take a bound state with some valence and sea level. The momentum distribution of the valence quarks and antiquarks has a very direct interpretation. But what about the fermion density? Say the fermion number of the valence quarks is 4 and for...
  44. Z

    Why do we need more fermion generations in particle physics?

    Old quantum adage: Anything not forbidden, will occur. So why not more fermion generations - on the cheap, in regards to energy? Look for higher mass charged leptons. Tau has mass of ~1.7 GEV. A number of accelerators could search for such charged leptons.
  45. A

    Evaluating Feynman diagram in QFT without external fermion lines

    ...like in Photon-Photon-scattering. I know this doesn't make sense physically but the value for the diagram should still be computeable. If I want to put the expression for the matrix element together, I get a matrix, but it should be a scalar, right? Since the spinor bi-product is missing...
  46. S

    Axial Anomaly and Fermion Mass

    It is often said that fermions are protected from large mass corrections by chiral symmetry. My question is does the axial anomaly generate corrections to fermion masses, and if so, doesn't this ruin the protection afforded by chiral symmetry to some extent? Thanks, Ben
  47. J

    Psi^4 Theory: A Fermion with Quartic Self-Interaction

    I've been analysing the following toy theory which I've called psi^4 theory for want of a better name. \mathcal{L} = :i\bar{\psi}\gamma^\mu\partial_\mu \psi - m\bar{\psi}\psi + \lambda (\bar{\psi}\psi)^2:. Ie a fermion with quartic self-interaction. This interaction can describe contact...
  48. J

    Interactions of Fermion & Scalar Fields: Exploring the Difference

    Suppose I couple a fermion field to a scalar field using \mathrm{i} g \bar{\psi}\psi \varphi and \mathrm{i} g \bar{\psi}\gamma_5\psi\varphi. I'm trying to understand what would be the physical difference between these interactions. I know that (1/2)(1\pm \gamma_5) approximately projects out...
  49. A

    Understanding the Nature of Cooper Pairs: Fermions or Bosons?

    i have a little doubt about the nature of the cooper pair that carries the super current if it is bosons or fermions? and why?
  50. tiny-tim

    Higgs fermion … the march is over … ?

    Good morning everyone! :smile: What do people think of the Higgs fermion candidate reportedly being studied at the Albanian reactor at Loöf Lirpana? … :confused: http://en.wikipedia.org/wiki/Higgs_boson#LoofLirpana
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