# 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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### Can multiple electron pairs be present in a single orbital?

An electron pair as a composite system acts as a boson. So why can’t three/four electron “pairs” be present in a single 1 s Hydrogen atomic orbital?
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### Why can't a gas of photons reach a Bose-Einstein condensate?

I have read in many places that as the gas of photons has a chemical potential $\mu=0$ it can't reach a Bose-Einstein condensate (BEC), but I don't understand why. I am reading Greiner's "...
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### Can one combine Jordan-Wigner Transformation and Schwinger-Boson Representation?

Is it technically possible to map a fermionic problem with $M$ Orbitals to a bosonic problem with $2M$ orbitals by combining the Jordan-Wigner transformation with the Schwinger-Boson representation? ...
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### Resourcs on learning about 2-body resources

As a part of my Particle Physics Course, I will need to give a talk on 2-body resonances - What are they? Some examples like 𝐽(Ψ), Z boson and significance of those discoveries. I am looking for ...
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### Why are particles either bosons or fermions in spatial dimensions $d>2$ (in Wigner classification)

This questions might have been asked several times, but I haven't seen a mathematical point of view, so here it is. Based on Wigner classfication: A particle is a representation, because any theory ...
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### Dirac matrix algebra from bosonic creation/anihilation operators?

Using some generic fermionic creation/anihilation operators $a_i$ and $a_i^{\dagger}$ ($i, j = 1, 2, 3, \dots, N$) such that \begin{align} \{ a_i, \, a_j^{\dagger} \} &= \delta_{ij}, \tag{1} \\[...
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### What is the intuitive physical difference between fermions and hard-core bosons?

(This is a soft question.) If we work on a discrete lattice for simplicity, then ordinary bosons are characterized by creation and annihilation operators that satisfy the canonical commutation ...
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### Is a pseudo-Goldstone boson always a pseudoscalar particle?

There are several examples of pseudo-Goldstone bosons which are CP-odd particles, such as the pion, as well as many axion-inspired models. If we invert the logic, Are all pseudo-Goldstone boson of ...
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### A system of two identical non-interacting bosons, one in a stationary state with pos. parity, the other in a state with neg. parity

In a system of two identical non-interacting spinless bosons, one particle is in a stationary state $\psi_{1}(\textbf{r})$ with positive parity and another is in stationary state $\psi_{2}(\textbf{r})$...
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### Symmetry of bosonic propagators and vertices under the exchange of indices

Quoting P. Cvitanovic's lecture notes on field theory: Assumption of additivity of probability amplitudes then implies that the bosonic propagators and vertices must be symmetric under the ...
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### Why does probing Higgs self coupling provides information on *dynamics* of Electroweak Symmetry Breaking?

Why does probing Higgs self coupling provides information on dynamics of Electroweak Symmetry Breaking ? Also, Why does probing Higgs self coupling provides information whether Higgs boson is ...
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### Why is the normal argument for fermions/bosons wrong?

If we have a state $\psi(x_1,x_2)$ of two identical particles and an exchange operator $O$ which swaps the particles. Obviously the physics must be the same and hence $O$ can only introduce an ...
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### Some questions about Dirac's sea? [closed]

Did Paul Dirac develop some way to include bosons in his formulation of the sea of particles? I have read that both electrons and anti-electrons would follow the same Dirac equation. But could there ...
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### Spin dependence of particle decay

I was wondering How does the spin of a decaying particle influence the kinematics of the decay? For example: I know that for a spin-0 particle decay such as $$\pi^0 \rightarrow \gamma\gamma$$ ...
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### Why are the weak force bosons not massless

I thought all bosons were theorized to be massless. The w+and-and z bosons of the weak force are said to carry mass. Dont bosons such as the photon just pass through each other? Is that not a property ...
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### When a Z boson decays into a particle/antiparticle pair, do those particles instantly annihilate each other?

If you look at a Feynman diagram of neutrino-electron scattering, there is the mediation of force by means of a virtual Z boson, and the product of this interaction is just the neutrino and electron ...
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### Where does the extra mass of a $W$ boson come from in particle decay?

I’ve seen everywhere explaining that it can exist because of time/energy uncertainty. I get this. I understand that’s WHY it exists but I’ve still never gotten WHERE the extra mass comes from. Is the ...
If our bosonic annihilation and creation operators are $[a,a^\dagger] = 1$, then for any complex number $\varphi$ we can define the (unnormalized) coherent state $$| \varphi \rangle \equiv e^{\varphi ... 1answer 56 views ### Inverse covariance matrix for a Gaussian state I was reading an article about Gaussian Boson Sampling (https://arxiv.org/pdf/1801.07488.pdf) and following some calculation appear an inverse covariance matrix when he defines the following matrix A. ... 0answers 18 views ### Bosonic Vacuum State under Unitary Transformation I consider a set of independent harmonic oscillators in mass- and frequency weighted coordinates and second quantization representation. The corresponding Hamiltonian reads  \hat{H} = \displaystyle\... 1answer 91 views ### Transformation of the derivative of the scalar field in Ramond's book about QFT In the book by Pierre Ramond about quantum field theory, he explores in chapter 1.4 (p.13) the behavior of fields under Poincaré transformations. He starts by explaining that infinitesimal ... 2answers 167 views ### Why has the free boson a charge c=1 in 2D CFT? In the free scalar field theory in 2D conformal field theory, we consider the correlation functions of the derivatives of the fields, i.e.$$\langle \partial \phi(z) \partial \phi(w) \rangle, \tag{1}$... 0answers 16 views ### How to construct general multiparticle states that respect fermionic or bosonic symmetry? Background: The arena is fixed particle number nonrelativistic quantum mechanics. The state space is $$\mathbf{H}(1)=\mathcal H\otimes\mathcal S,$$ where$\mathcal H$is an "orbital" state space ($L^...
So, our professor introduced the Bose-Einstein statistics by deriving the Grand Canonical Partition function of a boson system associated to a single energy state $\epsilon_r$. So the formula is: \...