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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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Do Helium-4 atoms behave like photons?

I know that the Helium-4 atom is a boson. Does this mean that, like photons, many Helium-4 atoms can be placed at the same point in space? How its possible? It includes fermions (Protons, Neutrons, ...
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What exactly does it mean for two bosons to be in the same state?

If I understand QM correctly, it's a fact that two bosons can have the same wave function in principle. What I'm wondering is if the particles governed by the wave functions can also be in the same ...
Francisco Skrobola's user avatar
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Why do heavy bosons have less range?

Why is it that there's a precise relationship between the mass of a mediator particle and its range? Because mass shouldn't directly affect decay time, right?
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Superpose two spatially separated single-photons into the same spatically mode

Consider two single photons, and let the states of them be $|H,A; V,B\rangle$. Here, $|H, A; V,B\rangle$ means that a horizontally-polarized single photon state is highly localized in spatial mode $A$ ...
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Vacuum expectation of polynomial of bosonic creation and annihilation operators [duplicate]

Let $\hat{a}^\dagger,\hat{a}$ be creation and annihilation operators with commutator $$ [\hat{a},\hat{a}^\dagger] = 1. $$ Let $|0\rangle$ be vacuum state that $$ \hat{a} |0\rangle=0. $$ Let $\beta$ be ...
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Number Operator "Ordering" for Higher Order Bosonic Operators

I'm considering the algebra of a single harmonic oscillator where $[\hat{a},\hat{a}^\dagger]=\hat{\mathbb{I}}$. Typically, one is interested in normal, antinormal or symmetric ordering. I am ...
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Boundary-condition-changing Operators for Free Boson BCFT with Dirichlet Boundary Conditions (or more general BCFTs)?

Is there any literature about boundary-condition-changing (b.c.c.) operators for the Free Boson with Dirichlet Boundary Conditions? The b.c.c. operators I'm interested in would replace boundary ...
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Permanent operation's result

N-body fermionic systems are constructed by Slater determinant, and it is equal to Vandermonde polynomial. Are there any special polynomial for the permanent which is used to construct N-body ...
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What's the relationship between wavefunction (anti-)symmetrization and entanglement? [duplicate]

Wavefunction symmetrization for bosons, or antisymmetrization for fermions, renders the wavefunction no longer a simple tensor product, i.e. it is no longer separable. This is the same thing that ...
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How does the CDF II $W$ boson mass measurement position itself relative to previous measurements?

The paper High-precision measurement of the W boson mass with the CDF II detector compares their results to the results of previous measurements in Fig. 5. While they show this visual comparison, ...
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Was the singularity a boson? [closed]

I was wondering if there is any truth in the perspective that the singularity point at the beginning of our universe would be considered a boson. I have heard it said that the universe at that one ...
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$Z$ bosons coupling to other $Z$ bosons

I'm learning about Higgs boson production at the moment. One way that it's produced is by 'vector boson associated production' or VH, which has this Feynman diagram: What I'm wondering is: how can $Z$...
user374355's user avatar
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Expressing the spin-1/2 operators in terms of the quantum rotor variables

In this paper, a spin-1/2 Hamiltonian is introduced on a cubic lattice [Eq. (12)]: $$ H_c = -J \sum_{\Box} (S_1^+ S_2^-S_3^+S_4^- + \text{H.c.}), $$ where the sum runs over all plaquettes of the cubic ...
Hao's user avatar
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Qubits vs Fermions, Bosons and Anyons [closed]

I found out recently that qubits are different from fermions, bosons and anyons. And, which is why we use Jordan-Wigner Transformation to map them to their fermioinc counterpart. I think I am trying ...
CuriousMind's user avatar
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Why can't other bosons fluctuate up the potential curve and gain mass?

If a Higgs boson is able to gain mass by fluctuating up the Mexican hat potential, what stops other bosons from doing the same thing and gaining mass without the need of the Higgs mechanism?
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Two species of bosons [closed]

Consider the Bose-Hubbard model for a single species of boson in a square lattice, \begin{equation} H_{a}=-t\sum_{<ij>} a^{\dagger}_{i}a_{j}+U \sum_{i}a^{\dagger}_{i}a^{\dagger}_{i}a_{i}a_{i}-\...
Santanu Singh's user avatar
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Is a fermionic boson possible?

We know that bosons need an overall symmetric wavefunction. So is it possible for a boson to have an anti-symmetric spatial wavefunction and an anti-symmetric spin wavefunction? Such that upon ...
Despaxir's user avatar
3 votes
2 answers
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A confusion: Why are composite bosons possible?

I am not a physicist, but trying to understand the standard model to some extent. My understanding is that the essential property of Bosons and Fermions is that two distinct Bosons can occupy the same ...
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Jordan-Wigner transformation in transverse field Ising model

Jordan-Wigner transformation provides an exact solution for transverse field Ising model in both the ferromagnetic phase and the paramagnetic phase. Yet this seems to imply that in both phases, the ...
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Multiple excitations of composite bosons?

Fundamental bosons, which are the mediators of the Standard Model interactions, are permitted to have multiple excitations with the same quantum number. Fermions, on the other hand, obey the Pauli ...
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The interpretation of the Bose occupation factor

I was reading into the Oxford solid state basics, by Steven H.Simon and I stumbled upon a confusing interpretation of the Bose Occupation factor: $$n_B (x) = \frac{1}{e^x-1}$$ with: $$x = \beta \hbar \...
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Superfluid helium bosonic and fermionic degrees of freedom?

I have looked at Helium Nucleus as boson How can multiple fermions combine to form a boson? Why are He-4 nuclei considered bosons, and He-3 nuclei considered fermions? but I still feel like saying &...
dragomang87's user avatar
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Exchange Particles for IMF

Quantum field theory describes forces as being mediated by a field (e.g. gluon field for strong force, electromagnetic field for electromagnetic force). These are often modeled as a mediating boson ...
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Normalization of one particle state wave function in fock space - commutator

In deriving the 1/$\sqrt{N!}$ normalization factor the first step is looking at the one particle state (see image below). I am confused about how we got from the first line to the second? Maybe I am ...
choochoochooo's user avatar
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Quasi-distribution for the composite (fermions + bosons) system

Let us have a system which consists of $N$ electrons with the spin (i. e. fermionic subspace has a dimension of $4^N$) and $K$ bosonic modes (let us consider $K=1$ for simplicity). Let us say, we ...
MightyPower's user avatar
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Operator that gives a permutational symmetry factor

Suppose that we have a system with $N$ bosonic modes, meaning that there is a vacuum state $|0\rangle$ and a set of $N$ pairs of creation-annihilation operators $a_i$ and $a^{\dagger}_i$. When ...
V. Asnin's user avatar
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Lindhard Function for Boson

We know the density-density response for a non-interacting system with electrons is given by \begin{equation} \chi(q,\omega)=\sum_{k} \dfrac{f_{k}-f_{k+q}}{\omega+\epsilon_{k}-\epsilon_{k+q}+i\eta} \...
Santanu Singh's user avatar
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How are chiral bosons defined?

What is the definition of chiral bosons? Until now I only knew the derivation of the chiral fermions (used in the Dirac field equation).
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Bogoliubov transformation for a two mode bosonic Hamiltonian

Suppose we have a Hamiltonian given by \begin{align} H &= \omega a^{\dagger}a + \omega b^{\dagger}b + g a^{\dagger}b^{\dagger} + g^{*} ab \end{align} where the operators obey the usual commutation ...
Physics437's user avatar
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Quantum statistical distributions follow:$n_i=\frac{1}{e^{\beta(\epsilon_i-\mu)}+c}$. Are there distributions with different $c$ other than FD/BE?

Quantum statistical distributions play a pivotal role in describing the behavior of particles in different quantum states. The well-known Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann ...
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Derivation of hypercharge neglecting squared amplitude for WZ helicities in paper

I am trying to get from equations (20) and (21) in this paper to equations (13) in this one. I will start with my attempt at deriving this for the LL case. (With $F$ from equation (4), $g_2-g_1$ from (...
J.N.'s user avatar
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Interacting identical bosons

Say we have two spin-1 bosons on a ring of circumference L, where they interacts according to the potential $g\delta(x_1-x_2)$ (g is a real number). What is the degeneracy of the first excited state? ...
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Can not follow derivation of $WZ(0, 0)$ amplitude in paper

i am re-reading this paper and trying to follow the derivation of equation (21) from equation (15). Maybe someone can tell me where i am going wrong. So the original equation 15 is: $$M(0,0) = F\frac{\...
J.N.'s user avatar
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1 answer
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What's happening in this approximation for the equation of state of an ideal gas of bosons

The way we arrived at the equation of state for an ideal fermion gas was to approximate the right handside of $$\beta PV=\sum_{\vec{p}}\log{(1+fe^{-\beta\frac{p^2}{2m}})}$$ as $$\frac{V}{h^3}\int \log{...
Lourenco Entrudo's user avatar
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Fourier transform of the Heisenberg antiferromagnetic model

I have a short question about the Fourier transform of the antiferromagnetic Heisenberg model. The Hamiltonian, written in terms of bosonic operators, is: $$ \widehat{H} = -NJ\hbar^2s^2 + J\hbar^2s \...
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Does the completeness relation for vector bosons hold also in this form?

Consider a generic Spin-1 vector field (massless) $A^{\mu}$, we know that the solution for its equations of motion can be built as $$A^{\mu}(x)=∫ d^{3}kN_{k}(\epsilon^{\mu}(\stackrel{\rightarrow}{k},\...
Filippo's user avatar
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Confusion about spin in 1 dimension

If spin should not be defined for particles in 1 dimension since we can't do rotations in 1d, like it happens for the orbital angular momentum, then why can we talk about fermions in a 1 dimensional ...
abc's user avatar
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Mermin-Wagner theorem and SSB in 2D: is there sound in low dimensional solids

The Mermin-Wagner theorem states that there cannot be any spontaneous symmetry breaking happening in systems with short range interactions below dimension 3. Moreover, we know that Goldstone boson, ...
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Why do we only consider commutators and anticommutators in QFT?

While studying canonical quantization in QFT, I observed that we quantize fields either by a commutation or an anticommutation relation \begin{equation} [\phi(x), \phi(y)]_\pm := \phi(x) \phi(y) \pm \...
Ishan Deo's user avatar
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WZW primary fields / correlations in terms of current algebra?

Cross-posted from a Mathoverflow thread! Answer there for a bounty ;) Given the $\mathfrak{u}_N$ algebra with generators $L^a$ and commutation relations $ [L^a,L^b] = \sum_c f^{a,b}_{c} L^c $ , the ...
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Is it possible to construct theory where fermions are force carriers?

Supersymmetry is a model based on symmetry between bosons and fermions. Bosons carry force and they are described by potentials. Fermions are matter particle and they are described by wavefunctions. ...
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What mathematics indicate that the vacuum of the universe is metastable?

As I understand it, the meta stability of the universe's vacuum depends on the electroweak force, which depends on the mass of the top quark and the Higgs boson. But I don't understand this fully. Can ...
PhysicsNoob's user avatar
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Can the Keldysh occupation function have a zero for bosons or a pole for fermions?

In the Keldysh framework for nonequilibrium dynamics of quantum systems we learn that there are essentially two Green's functions that characterize a system: the retarded Green's function $G^R(\omega)$...
Jonathan Curtis's user avatar
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Changes due to Chargeless Bosons

Do chargeless bosons (i.e. Z boson and photon) change any properties in particles they interact with besides energy, momentum, and angular momentum/spin?
18th Shard's user avatar
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Is it theoretically possible to get a fermion fields from compactifying a bosonic field theory?

It doesn't seem impossible to me that compactifying a purely bosonic field theory could result in spinor fields. For example, the spin groups (the double covers of $O(n)$) have representations in $2^{...
user avatar
1 vote
3 answers
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ELi5- How do pions hold nuclei together if they are so short-lived?

I need help understanding how particles do what they do and maintain the structures they maintain if so many of them exist for such a short time? In the case of the nucleus and pions, pions only exist ...
blacktopshaman's user avatar
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Bosonic Gas vs Ideal Gas

Bosonic Gases and Ideal Gases have these properties in common: They are composed of indistinguishable particles. The particles of both gases do not obey the Pauli Exclusion Principle. As far as I ...
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Does the Pauli exclusion principle apply to mesons?

According to the Pauli exclusion principle, two identical fermions cannot occupy the same quantum state simultaneously, but two bosons can. Mesons are bosons, but composed of two quarks, and quarks in ...
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If the bosons in a certain interaction can be outside of their mass hyperbola, how can we know the mass of the particles?

As far as I know, the virtual particles that appear in Feynman diagrams are allowed to be outside of their mass hyperbola, namely \begin{equation} k^2 = \omega^2 - (\vec{p})^2 = m^2 \end{equation} So ...
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Why not use Bose-Einstein Statistics to derive the Planck's blackbody radiation law?

While deriving the Planck's radiation formula, why do we use MB statistics when we calculate the average energy of oscillators? Shouldn't we use BE? Is this because temperatures concerned are very ...
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