In quantum mechanics, a boson (, ) is a particle that follows Bose–Einstein statistics. Bosons make up one of two classes of elementary particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of Satyendra Nath Bose, an Indian physicist and professor of physics at University of Calcutta and at University of Dhaka in developing, with Albert Einstein, Bose–Einstein statistics, which theorizes the characteristics of elementary particles.Examples of bosons are fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity. Some composite particles are also bosons, such as mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, atomic mass number = 2), helium-4, and lead-208; as well as some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).An important characteristic of bosons is that there is no restriction on the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid. Unlike bosons, two identical fermions cannot occupy the same quantum state. Whereas the elementary particles that make up matter (i.e. leptons and quarks) are fermions, the elementary bosons are force carriers that function as the 'glue' holding matter together. This property holds for all particles with integer spin (s = 0, 1, 2, etc.) as a consequence of the spin–statistics theorem.
When a gas of Bose particles is cooled down to temperatures very close to absolute zero, then the kinetic energy of the particles decreases to a negligible amount, and they condense into the lowest energy level state. This state is called a Bose–Einstein condensate. This property is also the explanation for superfluidity.
I tried to show this equality by explicitly determining what
$$ \overline{(\Delta \eta)^2} $$
is, but I got a totally different answer for some reason, here is my attempt to solve it, what did I miss?
Hi all
I found this expression in a paper that concerns the derivation of some relations about boson operators but it is not very clear to me how the results were obtained. The derivation starts as, let B be an operator as a linear combination of different boson operators:
$$...
Hello, I recently came across the following (apparent, I hope) paradox: suppose we have two H atoms. Now, a hydrogen atom is made up of one proton and one electron (fermions), so it is a boson. Then one could have two hydrogen atoms which are in the exact same state (including position). This...
If a bosonic field is probabalistic, and if it can be emitted (suddenly coming into existence), what determines its probability distribution when it is emitted from a fermion? In other words, one thinks (or at least I think) of a fermion field as already being in existence and already having...
Hi,
It is easy to find discussions about time dilation and muon Half-Life. Is it meaningful to discuss whether bosons capable of pair production can have their decay rate changed if they pass through material?
Homework Statement:: I came across the following in an online article. I am unable to understand how these elementary particles cause a force to exist.
"Each of the four forces results from the exchange of force-carrier particles.".
Above statement is taken from...
Problem: A system contains two identical spinless particles. The one particle states are spanned by an orthonormal system ##|\phi_k>##. Suppose that particle states are ##|\phi_i>## and ##|\phi_j>## (##i \neq j##). (a) Find the probability of finding the particle in the state ##|\xi>## and...
Zero spin of Higgs boson? Is it really zero? Where is the spin (intrinsic angular momentum) of the Higgs boson on so small that we quantify it as having zero spin?I am aware of the reduced plank constant. But I we sure there is nothing in between the reduce Planck’s constant and the zero spin of...
In wikipedia you can find this neat tables with the hypercharge and isospin of a ton of particles and bosons.
What I want to know is: what are the values of Isospin and Hypercharge for the W3 and B bosons?
Now, I know electroweak unification, don't worry about that. I know W3 and B got mixed...
1. Since N is large, ignore the kinetic energy term.
##[-\mu + V(r) + U|\Psi (r)|^2]\Psi (r) = 0##
2. Solve for the density ##|\Psi (r)|^2##
##|\Psi (r)|^2 = \frac{\mu - V(r)}{U}##
3. Integrate density times volume to get number of bosons
##\int|\Psi (r)|^2 d\tau = \int \frac{\mu -...
Although strictly speaking this is motivated by a classical field theory problem, I felt that the quantum physics subforum would be more appropriate because it pertains to topics which to my understanding are almost entirely dealt with in the context of QFT.
The most commonly stated form of...
I'm interested in knowing where can i find the information on decay time of (possibly every?) different type of bosons, hadrons and fermions, which is available to the public (tiletles of books, articles, ...). Any suggestions or ideas?
I'm having a hard time understanding how to treat fermions, bosons, and distinguishable particles differently for this problem.
To the best of my understanding, I know that my overall state for bosons must be symmetric, and because they're spin-0, this means there's only one coupled spin state...
This questions was brought to my attention by Kazu Okayasu.
According to probability theory the probabilities of mutually exclusive events add upp.
As an example we can distribute 2 balls in two boxes with two compartments each.
So there's a box on the left with a lower and an upper compartment...
Consider the field creation operator ψ†(x) = ∫d3p ap†exp(-ip.x)
My understanding is that this operator does not add particles from a particular momentum state. Rather it coherently (in-phase) adds a particle created from |0> expanded as a superposition of momentum eigenstates states...
Hi guys,
I'm studying my first-year physics in college, and I'm having to write a report of some proton-proton collisions that were registered in the LHC of CERN years ago. The main goal is to identify different bosons (W and Z) that are decaying into other elemental particles. I've been asked...
For 2 bosons each of which can occupy any of the energy levels 0 and E the microstates will be 3
0 E
a a
aa -
- aa
the partition function is therefore $$z=1+e^{-\beta E}+e^{-2\beta E}...(1)$$
Another approach to do..
The single particle partition function is
$$z=1+e^{-\beta E} $$...
I get it that nothing can travel faster than the speed of light in a vacuum, and that only massless particles can move that fast. Must move that fast. A photon, the massless boson that carries the electromagnetic force, moves as c, which is given by the inverse root of the electric permability...
For the probability of finding R out of N (indistinguishable) bosons in one half of a volume with a total of 2g states (g in each half) I get the following expression:
PR = WR / WT
where WT is the number of ways of distributing N particles in the total volume:
WT = (N+2g-1)! / (N! (2g-1)!)...
I am searching for anything on quantum fluctuations and virtual bosons for someone who is a serious but amateur physicist ie. I have completed undergrad physics/math and some graduate level math at university. I am having a hard time finding anything that isn't beyond pop science. Not really...
Heavier bosons like ##W## or ##H## require high energy accelerator to be detected. Yet these bosons fulfill their function in the ambient energy of the universe. Why is it that their detection takes high energy environment but their function is possible in lower ambient energy?
Hello everybody!
I have a question regarding the forbidden decay ##\rho^0 \rightarrow \pi^0\pi^0##, but it is a general doubt.
My book states that one of the reasons why the decay is forbidden is Bose-Einstein statistics, the final state of two equal pions must be in an antisymmetric state...
Because massive gauge bosons have a finite half life, are they excluded from the (infinitely, asymptotically remote?) in and out states of QFT? Or, to put it another way, are they restricted to the internal legs of Feynman diagrams, i.e. to being virtual only? We can see W and Z tracks in...
Hello everybody!
I have a problem with this exercise when I have to find the possible angular momentum.
Since ##\rho^0 \rho^0## are two identical bosons, their wave function must be symmetric under exchange.
$$(exchange)\psi_{\rho\rho} = (exchange) \psi_{space} \psi_{isospin} \psi_{spin} =...
Hi, I'm starting to study how to use Hubbard operators and I cannot understand one property:
Consider the hopping terms for a lattice Hamiltonian with bosons:
$$\sum_{i,j\neq i} t_{i,j} b^\dagger_i b_j$$
when writing this term in the basis of Hubbard operators $$X^{a,b}_i =| a,i \rangle \langle...
I'm wondering about the fundamental difference between fermions and bosons. Isn't it true that bosons are always their own antiparticle but fermions are not? But then I wonder about the Weak bosons, W+, W-, Z0. All these are bosons, right? But isn't the W+ the antiparticle of the W-. Or is it...
Homework Statement
After proving the relations ##[\hat{b}^{\dagger}_i,\hat{b}^{\dagger}_j]=0## and ##[\hat{b}_i,\hat{b}_j]=0##, I want to prove that ##[\hat{b}_j,\hat{b}^{\dagger}_k]=\delta_{jk}##, however I'm not sure where to begin.
2. The attempt at a solution
I tried to apply the...
Homework Statement
Following from \hat{b}^\dagger_j\hat{b}_j(\hat{b}_j
\mid \Psi \rangle
)=(|B_-^j|^2-1)\hat{b}_j
\mid \Psi \rangle
, I want to prove that if I keep applying ##\hat{b}_j##, ## n_j##times, I'll get: (|B_-^j|^2-n_j)\hat{b}_j\hat{b}_j\hat{b}_j ...
\mid \Psi \rangle
.
Homework...
I've never been able to get my head around the idea that forces are particles. In the case of fermions, a particle seems to be a natural concept. Even though it's really a wave, or an excitation in a quantum field, I can envision it as being something in a particular place. For bosons that...
Assuming a system of bosons at high density and low temperature so that they obey Bose-Einstein statistics. If one had a high resolution, ultrafast tomographic imaging system that would allow to track every particle in this system and therefore make the particles distinguishable, what would...
The BE-distribution for the case of only one state per energy level (gi = 1) is
ni = 1 / (exp(ui - μ)β - 1)
This is a reasonable and well defined distribution as far as I can see.
On the other hand the number of possibilities to realize a given distribution of bosons among k energy levels with...
Is there an expression similar to the Sackur-Tetrode equation that describes the statistical entropy of fermions or bosons, maybe for the electron gas in a metal or the photon gas in a cavity?
For the free boson, the field operators satisfies the commutation relation,
$${\varphi}_{x'}{\varphi}_{x} - {\varphi}_{x}{\varphi}_{x'} = 0$$ at equal times.
While the fermions satisfies,
$${\psi}_{x'}{\psi}_{x} + {\psi}_{x}{\psi}_{x'} = 0$$ at equal times.
I interpret ##{\varphi}_{x}## and...
Hi Everyone! Hope everyone is really enjoying pushing the Physics frontiers!
Really need some help here. In the Electroweak sector of the Standard Model, it is apparently the case that the success of renormalisation to remove the Ultraviolet Divergence relies on the fact that at high energies...
These ideas come from the book Quantum Physics by Eisberg and Resnick (specifically ch11), can anyone explain what the inhibition factor and enhancement factors are in a little more detail?
I do not understand what the book is trying to explain, and I can't seem to find these anywhere online...
Homework Statement
So, my textbook proposes a to check what will change in mass and mass eigenvectors of Z and photon in terms of ##W_{3}## and ##B_{\mu}## fields in Higgs mechanism for EW if we choose a vacuum hypercharge to be -1 and compare results to SM (where we know that photon is...
Now from my basic understanding of particle physics, matter is supposed to be fermions, while particles involved in force interactions are bosons (photons, gluons, W/Z, and Higgs). Now, apparently there are also some composite particles of matter that are considered to be bosons too. For...
In the Standard Model fermions interact via exchanges of massless (virtual) spin-1 particles. Fermions are turned into a boson. How is that different from the SUSY transformation that turns fermions into bosons?
Homework Statement
In a particle physics lab, an electron e− and a positron e+ collide, annihilate, and produce a W+ boson and a W− boson. Just before the collision, the electron and positron have a total energy of E = 100 GeV each, with velocities pointing along the +x-axis and -x-axis...
I am confused about the production of bosons in annihilation processes.
If we have a positron and an electron coming together and annihilating, we can always find a frame in which the net momentum is zero, which would suggest that a single photon can never be produced in such an interaction...
Consider the following facts:
1. For a particle with momentum ##k##, the two transverse polarization vectors ##\epsilon({\bf k}, \lambda_{1})## and ##\epsilon({\bf k}, \lambda_{1})## are purely spatial and orthogonal to ##\bf k##, that is,
##\epsilon^{0}({\bf k}, \lambda_{1}) = 0,##...
Are tachyons force Particles/messenger particles ? Is so do they act messenger between two entangled particles and allow faster than light information exchange? Thank for the answer.
A straightforward argument for showing that indistinguishable particles in 3D can either be bosons or fermions goes as follows.
Consider the wavefunction of identical particles 1 and 2 at positions \psi (\vec{r}_1, \vec{r}_2). If we swap these particles around then this just becomes \psi...
The coupling of the Higgs boson to the electroweak gauge bosons in the Standard model is given by
$$\mathcal{L}_{\text{H-g}} = - \left( \frac{H}{v} + \frac{H^{2}}{2v^{2}} \right) \left(2M_{W}^{2}W_{\mu}^{+}W^{-\mu} + M_{Z}^{2}Z_{\mu}Z^{\mu} \right).$$
However, in Cliff Burgess' textbook 'The...
Hello,
I'm trying to understand how the superfluidity is connected with the Lagrangian of the system: in some textbooks (e.g. Antony Zee qft in nutshell) it is stated, that in case, when the excitations in the fluid have energy spectrum linear with momentum , there is a critical velocity, which...
Introduction and warm up
Suppose H_0 is some Hamilton's operator that has eigenvectors |\psi_n\rangle for n\in\mathbb{N} with some eigenvalues E_n so that
H_0|\psi_n\rangle = E_n|\psi_n\rangle,\quad \forall n\in\mathbb{N}.
Suppose we define a new Hamilton's operator by setting H=H_0\otimes...