Questions tagged [bosons]

Bosons are integer-spin particles that obey Bose-Einstein statistics. Two bosons can occupy the same quantum state.

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23
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2answers
3k views

Why do bosons tend to occupy the same state?

It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable"...
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Are fermions and bosons fundamentally different?

Looking at various particles regarding being fermions or bosons, it seems to me that fermions are something fundamentally different from bosons. What I mean by "fundamentally different" is "as ...
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Why are all force particles bosons?

All of the force-particles in the standard model are bosons, now my question is pretty short, namely: Why are all force particles bosons? This can't be a coincidence.
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Huge confusion with Fermions and Bosons and how they relate to total spin of atom

I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, ...
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How do particles become entangled?

A person asked me this and I'm just a lowly physical chemist. I used a classical analogy (how good or bad is this and how to fix?) Basically, light has a net angular momentum of zero, insofar as ...
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Can He-4 atoms create black holes?

Suppose that in the intergalactic space far from any significant gravitational attractors there is a relatively small concentration of He-4 atoms. Due to gravitational attraction fermions in this case ...
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Meaning of the chemical potential for a boson gas

My lecturer told me that the mu is the Chemical potential is zero or negative, in the following example, mathematically it acts as a Normalisation constant. But is there any Physical insight about why ...
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1answer
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How can a massless boson (Gluon) mediate the short range Strong Force?

I thought massless particles were mediators for long range forces such as electromagnetism and gravitation. How can the massless gluon mediate the short range strong force?
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For ideal classical gasses, in terms of the energy levels why do we ignore whether the particles are fermions or bosons?

I am confused as to why when dealing with ideal classical gasses, the dependency of the particles being either fermions or bosons is ignored. How does this relate to the energy levels within the ...
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1answer
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Who added $\frac{3}{2} \partial^2 c$ to the virasoro BRST current (and why)?

I've been looking at the literature on quantizing the bosonic string, and I noticed that there was a change made in the definition of the BRST current around 1992. However, I haven't found any ...
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343 views

Combining two finite number fock spaces into one

Say I have two separate systems of identical Bosons, one with N Bosons the other with M. System one is described by a state $|\psi_1\rangle$ the other with $|\psi_2 \rangle$ which are expressed in a ...
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Is there a reason why the spin of particles is integer or half integer instead of, say, even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...
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Are there Goldstone bosons in 1D or 2D?

The Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with short-range interactions in dimensions d ≤ 2. And Goldstone bosons ...
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Elementary Particle of Magnetic Field

If gravity - a field force - has an elementary particle, the graviton, why don't other field forces like magnetic fields have their elementary particles? I mean, why isn't there a magneton? Or, what ...
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Is electric charge truly conserved for bosonic matter?

Even before quantization, charged bosonic fields exhibit a certain "self-interaction". The body of this post demonstrates this fact, and the last paragraph asks the question. Notation/ Lagrangians ...
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Is there record of a bosonic Stern-Gerlach measurement?

I cannot seem to find any peer-reviewed (or other) reference to an integer-spin Stern-Gerlach experiment. It shouldn't be too hard to do: just find you friendly neighbourhood Deuterium ion and shoot ...
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Identical particles seem to reduce probability

$\newcommand{\ket}[1]{| #1\rangle}$This question basically has two very related parts. This came up in the context of trying to verify something my professor said a while ago: that if the wave ...
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Fermions in the same state

I need some clarification of what is meant when someone says "fermions cannot occupy the same quantum state". Consider two bosons: $$\psi(\vec{r_1}, s_1, \vec{r_2}, s_2) = \frac{1}{\sqrt{2}} \left( \...
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1answer
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Chemical potential in quantum field theories

The chemical potential enters the grand canonical ensemble, in statistical physics, as the Lagrange multiplier ensuring the conservation of particle number. In QFT and relativistic theories in ...
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Can we regard a spin-1 particle as combination of two spin-1/2 particles?

As we know, the square of time-reverse operator is -1 acting on fermion and +1 on boson. I can prove it by regarding the time-reverse operator as 2π rotation around $y$-axis multiply the complex ...
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Why don't we call the fermions in the standard model force carriers?

Maybe this is a chicken-and-egg problem, but couldn't we call all the bosons fundamental and treat the fermions as force carriers between them? EDIT: After all we never see the asymptotic states of ...
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1answer
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Operator norm of creation and annihilation operators

Are the creation and the annihilation operators $a(f)$ and $a^{\dagger}(f)$ for the bosonic Fock space bounded? What is their norm? So far I did not have found any note about this in the linked ...
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Why do Photons want to be together?

So I've heard that when a photon flies by a atom excited enough to release a photon there's a good chance it will. Because Photons want to be together and have the same direction etc? Is this true? ...
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1answer
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Fock space with mixed anti-commutation/commutation relations?

Let's say we have two modes, with the following labeling of occupation number states: $ \lvert \Psi \rangle = \begin{pmatrix} 0,0 \\ 0,1 \\ 1,0 \\ 1,1 \end{pmatrix} $ An example of (what I assume to ...
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Is ground energy of interacting fermions always higher that that of bosons?

Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or ...
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Are composite bosons always bosonic (e.g. the pion-cloud surrounding the nuclei)?

The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the ...
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Helium Nucleus as boson

I am rather perplexed with this fact that though Helium Nucleus is a boson, the particles insides it: protons and neutrons are essentially fermions. How the nucleus which is made by fermions can be a ...
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Fermion vs. Bosons and particle vs. wave: is there a link?

I'm puzzled since several years on this basic aspect of quantum mechanics. Quantum theory is supposed to describe particle-wave symmetry of our world. It also describes our universe in term of bosons ...
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Bose Enhancement Factor

How may one explain the fact that the probability of a boson transferring to a state with an occupation number n is 'enhanced' by a factor of (1+n), compared to the classical case? (In the classical ...
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4answers
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Chemical potential of a Bose gas

In my course, there is this fact : In a Bose gas, the chemical potential $\mu$ must always be lower than the smaller level of energy $\epsilon_0$. I find this strange, because if we put a Bose ...
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Why zero chemical potential does not allow the Bose-Einstein Condensation of Phonons?

Here I report the reasoning from which my question comes. According to: O.V. Misochko, Muneaki Hase, K. Ishioka, and M. Kitajima. Transient bose–einstein condensation of phonons. Physics Letters A, ...
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What is special about the indistinguishability of Boson and Fermions?

In the treatment of Bosonic or Fermionic systems that I'm familiar with, you start with a state containing at least two particles: $$ \left| a_{i}, a_{j} \right\rangle $$ And define a permutation ...
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“Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon).”?

Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st ...
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Is Supersymmetry really swapping fermions with bosons?

I've been studying supersymmetry for the last few months, and while I can do some mathematics with the Wess-Zumino model (show the Lagrangian is invariant under a susy transformation, find the Noether ...
5
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1answer
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What happens during a weak interaction?

For e.g. during $\beta^-$ decay a $W^- $ boson is emitted changing an up quark to a down quark. This seems very weird to me as it looks like that up quark is not interacting with some other particle ...
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1answer
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Atoms: boson or fermion? [duplicate]

The spin of fundamental particles determines if they are bosons or fermions. The atoms also have bosonic or fermionic behavior, for example $\require{mhchem}\ce{^4He}$ has bosonic and $\ce{^3He}$ has ...
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1answer
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Why does exchanging coordinates produce a phase of $\pm 1$ in an identical particle wavefunction?

Consider a system of two identical particles described by a wavefunction $\psi(x_1, x_2)$. There are two kinds of exchange operators one can define: Physical exchange $P$, i.e. swap the positions of ...
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Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
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1answer
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Super conductivity and energy gap in fermionic/bosonic subspaces

I am trying to understand the phenomena of super-conductivity from a broader level. What I understand for now is that for super-conductivity to be possible in a system, a necessary requirement is that ...
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1answer
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Enormous masses of $X$- and $Y$-bosons in GUTs

I was reading an article on Wikipedia about the hypothetical particles called $X$ and $Y$ Bosons. Looking at their "calculated" masses, I felt quite weirded. Their mass should be $$ m = 10^{15}\,\...
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1answer
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Probability enhancement for bosons: Probability goes over 1?

It is said that if there is already n bosons in a particular quantum state, the probability of another boson joining them is (n+1) times larger than it would have been otherwise. But if we apply this ...
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About the rigour of replacing spins by hardcore Bosons

In literature one sometimes find that spins are replaced by hardcore bosons. Formally one replaces spin operators $\sigma^- \leftrightarrow a$, $\sigma^+ \leftrightarrow a^\dagger$, $\sigma_z \...
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1answer
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Bosonization and Commutation Relation

I'm playing a bit with bosonization $ψ→:e^{-φ}:$ and $ψ^*→:e^{φ}:$ in the sense that $$ \Bigg\langle 0_\mathrm{F} \Bigg|∏_{i=1}^nψ(z_i)ψ^*(w_i)\Bigg|0_\mathrm{F}\Bigg\rangle = \Bigg\langle 0_\mathrm{...
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Spin-statistics theorem proof details

Recently I have read one book where there was some incomprehensible proof of the Pauli's spin-statistics theorem. I want to ask about a few details of the proof. First, the author derives ...
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Is deuterium a boson or a fermion?

I want to know if deuterium is a fermion or boson. Please give me a descriptive answer. I tried the formula that is the combination of protons and electrons which gives odd number but the answer is ...
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2answers
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Slater's determinant for Bosons/Symmetric Particles?

For Slater's determinant it is obvious how this describes two or multiple fermions/anti-symmetric particles. By definition the determinant introduces a negative sign in front of the second product. $$...
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5answers
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Are there more bosons or fermions in the universe?

The question is in the title: are there more bosons or fermions in the universe? Or is there the same number of bosons and fermions? I think there is the same number but I don't know why exactly.
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Why do weak interactions exclude gluons?

Weak interactions seem the most universal after gravitation. A very few particles avoid them, only the photon and gluon, plus right leptons. The photon, however, is a part of the electroweak ...
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1answer
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Can quarks of different generations enter a $Z$ boson vertex?

Reading through my particle physics book (Thomson's "Modern Particle Physics"), it appears that when calculating the possible decays of the $Z$ boson, we do not consider decays such as $Z\rightarrow u ...
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1answer
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Vectors of polarizations from vector boson field solution

Let's have the solution for vector boson Lagrangian in form of 4-vector field: $$ A_{\mu } (x) = \int \sum_{n = 1}^{3} e^{n}_{\mu}(\mathbf p) \left( a_{n}(\mathbf {p})e^{-ipx} + b_{n}^{+} (\mathbf p )...