# Tagged Questions

Bosons are integer-spin particles that obey Bose-Einstein statistics.

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### Showing phase change for fermions

When discussing identical particles books often use that the states are eigenstates of the permutation operator: $P_{ij}|\psi\rangle = \lambda |\psi\rangle$ for bosons this is easy to see if I use ...
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### Capturing superfluid condensation with exact diagonalization

Doing exact diagonalization on bosonic systems is tricky, because the possibility of multiple occupancy means that even the single-site Hilbert space is infinite-dimensional. It's my understanding ...
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### Can fermions composing a boson ignore Pauli's principle?

After a discussion with a fellow student, we came above this problem asked as question in the title. A similar question was answered here. But it doesn't answer the question for us. In a BEC, many, ...
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### Working out range and lifetime of W boson [duplicate]

I am starting to study A-Level physics and I would like to have some help with this question, as I got no clue how to answer it: State the approximate range of W boson and estimate it's lifetime, ...
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### Clarification of the concept of Boson Mediator and 'Mediation' in Physics? [closed]

I would like to have a clear concept of Higgs 'mediator' and that 'mediation' speak in physics, what you 'swap' a particle with ...
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### What does the “protophobic fifth force” imply?

There is a recent paper on arxiv http://arxiv.org/pdf/1604.07411v1.pdf and prl http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.042501 It seems that the authors found the fifth force. ...
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### What does it mean that a Cooper pair behaves as a boson but respects the obligations of fermions?

I refer to the fact that it has integer spin, but antisymmetric wavefunction. How is this possible?
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### What is more fundamental $E=\hbar \omega$ or $E=c\hbar k$?

Let us say I have a massless particle (not necessarily a photon) then in a medium where $\omega \ne c k$ (e.g. a dispersive medium) what is the energy of the particle? As my title indicates are think ...
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### Stern-Gerlach experiment with Bosons

I'm new to this forum and I'm studying semiconductor physics at the moment. I just wanted to ask a thing about the concept of spin: when it was studied for the first time, in the Stern-Gerlach ...
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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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### What is the difference between the generation of mass for Fermions compared with Bosons in the standard model?

I've seen a few questions asking how the Higgs mechanism generates mass for particles of the standard model. However, I haven't seen any which specify the differences between Bosons and Fermions in ...
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### How to determine the direction of arrow on Feynman diagram for $W$ boson line?

I am somewhat confused. Looking through these slides (especially the 11th), which show Feynman diagrams involving $W$-bosons, I can't figure out which way to draw the arrow near the $W$ boson? How do ...
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### Inverting density in favour of fugacity

In these notes on pages 80 and 81 the following step was used The density in terms of fugacity is $$\frac{N}{V} = \frac{z}{\lambda^3}\left ( 1+ \frac{z}{2 \sqrt{2}} + \ldots \right )$$ and this ...
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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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### 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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### Quick clarification needed on degeneracy

I need some hints about degeneracy. So, I consider an energy level degenerate if there are two distinct wave functions at that energy. Then, let's say I have two spin1/2 fermions in a 1D box. Is ...
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### Exchange principle in terms of states and coordinates?

I have seen the exchange principle written in two ways, one in terms of coordinates and the other in terms of states: If $\psi_{AB}(1,2)$ represents particle $A$ in state $1$ and particle $B$ in ...
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### Physical interpretation of the chemical potential in Bose and Fermionic gas

I understand that both Fermions and bosons have the chemical potential $\nu <0$ when it is T>0, but still behave classically, the fermions would increase its chemical potential at T=0, whereas the ...
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### Do we expect to find a dark energy boson?

Is dark energy expected to be a force carrying particle that interacts with all forms of matter?
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### Charge conjugation of particle and anti particle system

I've seen in the literature that quark and anti-quark (or in general, fermion and anti-fermion) bound states, such as the neutral pion or positronium, have C eigenvalue of (-1)^(L+S), where L is their ...
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### Massless bosons but not massless fermions?

I noticed some article on massless Weyl fermions and it got me thinking. I'm wondering if there is any explanation for why bosons (specifically gauge bosons) can be massless (photon and gluon) but we ...
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### Why do we need to suppose the chemical potential is zero in this situation?

I've been working on some statistical mechanics problems and one of them asks to compute the pressure with chemical potential zero of a boson gas whose particles do not interact and whose energies are ...
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### systems of particles that are not symmetric or anti-symmetric; Helium 4

Suppose I have an electron and a proton, and that the electron is in the spin-up state, and that the proton is in the spin-down state. The particles are distinguishable, so I should just be able to ...
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### How to mathematically describe a spin-0 particle [closed]

I don't know all the technical things like Eigenstates. I want to know, mathematically written out for beginners, how to make a quantum field theory of a scalar boson. To spare confusion- I understand ...
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### Can someone explain the quote “there would be no chemistry if electrons acted as bosons”?

I am reading a book and in a quote it says that if electrons acted as bosons, then all the electrons would occupy the lowest energy state, and there would be no chemistry. What does the author mean ...
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### Intuitive explanation for the existence of an energy gap in superconductors

In 2012 there was a nice answer explaining basic superconductivity. It ends with the sentence: The trouble is you're now going to ask for an intuitive description of why the electron correlations ...
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### How do I show that a given Hamiltonian does not affect the overall number of particles in a given state?

I'm struggling with the following problem: Consider a system of an arbitrary number of indistinguishable bosonic particles. The system has two sites and $a_i^{\dagger}$ and $a_i$ are the ...
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### Why is the isothermal compressibility of the ideal boson gas larger than of the classical ideal gas?

Recently I came across (or well, derived in a lecture) the isothermal compressibility for an ideal boson gas. This was done in the context of statistical physics, using the quantum version of the ...
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### Can a Fermi gas and a Bose gas be both at the same pressure and temperature?

The title says it all: can a Fermi gas and a Bose gas be both at the same pressure and temperature? It comes from a quiz about statistical mechanics