Fermions Definition and 178 Threads

What happens if I shoot a fermion at another identical fermion at rest? For example, do the fermions stick together, or do they bounce? Let's ignore gravity, electro-magnetism, weak force and strong force. Edit: We are considering the Pauli exclusion principle.

Homework Statement The global topology of a ##2+1##-dimensional universe is of the form ##T^{2}\times R_{+}##, where ##T^{2}## is a two-dimensional torus and ##R_{+}## is the non-compact temporal direction. What is the Fermi energy for a system of spin-##\frac{1}{2}## particles in this...

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...

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?

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 ...

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...

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) ...

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...

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...

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

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?

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...

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...

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...

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...

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.

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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

Does modern physics allow for the existence of massless fermions?

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...

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?

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...

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>...

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...

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...

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...

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

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...

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...

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...

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...

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...

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?

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...

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...

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...

Are the wimps claimed to be bosons or fermions?

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

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

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...