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Questions tagged [bosons]

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

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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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What are gauge symmetries corresponding to forces in particle physics?

I understand that color charge is a gauge symmetry, that leads to connection field and force that is strong nuclear force. This is from professor Sean Carroll from TTC course (higgs boson and beyond) ...
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How do I know that gauge fields are bosons?

QED and the Dirac equation have field operators $\psi$ interact with a gauge field $A^{\mu}$. We identify $\psi$ as a fermionic field and $A^{\mu}$ as a gauge boson - the photon. Do we or can we ...
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Suppressed emission of composite particles

If a composite (pseudo)Goldstone boson $\phi$ emerges in a spontaneous symmetry breaking (similar to the mesons of QCD), is the emission of the $\phi$ particle suppressed in high-energy processes, i.e....
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Physics of a Second quantized Hamiltonian?

It is frequently seen that the (Bosonic) Hamiltonian $H=e a^{\dagger}a+f( a^{\dagger}a^{\dagger}+a a)$ is discussed and diagonalized using Bogoliubov transformation. My question is that what is ...
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Simulating the evolution of many-boson states

My task is to simulate the scheme presented in this paper: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.77.062316. In this question: Creating an operator for a polarizing beam splitter, I ...
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Integrals involving Bose-functions (Computational)

In short, I'm looking for some advice/literature how to deal numerically with Bose function. My physical problem is to calculate a coupled set of Self-energies, thermal loop integrals, self ...
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35 views

Definition of Ohmic bath and damping force

I have read the Wikipedia article on quantum dissipation where it is talking about the bath spectral function. The bath spectral function provides a constraint in the choice of the coefficients $...
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How are computed Branching decay modes (for Higgs boson and from a general point of view)

I would like to know how are computed the branching decay diagram, like for example with Higgs boson represented below (source): It seems there are 5 ways of decays for Higgs boson. I suppose there ...
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Two bosons having the same state — how do you know there are two?

So, suppose that photons have the same quantum state. How do we know that there are 'two' photons having the same state, rather than just one? Is there a technical way to guarantee that there are ...
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Diagonalization of Quadratic Fermionic/Bosonic Hamiltonians

I'm currently reading Quantum Theory of Finite Systems by Blaziot and Ripka, and I have a question regarding the first few pages of chapter 3. In particular, the chapter takes on the task of ...
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Frequencies associated with boson/fermion operators

For a Hamiltonian like, $$\hat{H}=\sum_{k}\hbar\omega_{k}b_{k}^{\dagger}b_{k}$$ What does it mean to say that the frequencies $\omega_{k}$ must be positive if $b_{k}$, $b_{k}^{\dagger}$ are boson ...
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Fermoinic and Bosonsic physical Hilbert spaces - are they actually Hilbert spaces?

Consider two identical particles $A$ and $B$. The combined Hilbert space $\mathcal{H}_A\otimes \mathcal{H}_B \newcommand{\ket}[1]{\left|#1\right>} \newcommand{\bra}[1]{\left<#1\right|} $ is a ...
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37 views

Can we have Bose condensation for bosons satisfying a dispersion relation $E=Cp^s$ $\forall$ s?

Suppose a dispersion relation $E=Cp^s$ where $C$ is a constant is known for a collection of massive non-interacting bosons. What is the way to find out whether there will be Bose-Einstein condensation ...
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Bose - Einstein Correlation

I want to study about Bose-Einstein correlations and I have been searching online for many days without any luck. Can any of you suggest me some online materials about this topic? I don't have any ...
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Hard-core bosons and fermions - spinless?

The introduction to this paper about bosonic atoms expanding in an optical lattice says the following: Are hard-core bosons mapped to spinless fermions? Because this link shows the mapping ...
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What experiments can measure the eigenvalues of the particle exchange operator

In a system with two indistinguishable particles, the eigenvalue to the particle exchange operator $\hat{P_{ij}}$ is $+1$ if the two particles are exchange symmetric, ie. bosons, and $-1$ if they are ...
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Bogoliubov approximation, coherent states and particle number conservation

I am slightly confused about an aspect of the Bogoloibov approximation for BEC. In it we take: $$a^\dagger (\vec 0)\approx \sqrt{N_0}$$ $$a(\vec 0)\approx \sqrt{N_0}$$ and find our Hamiltonian in ...
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Why is a collection of non-interacting bosons pathological?

In this lecture titled "Disorder and Interactions: From Spin Chains to Cold Atoms" the speaker Thierry Giamarchi claims that a collection of non-interacting bosons is totally pathological. His argues ...
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Can matter/antimatter “annihilation” produce “dark matter”?

I was thinking about the following reasoning: If a matter and antimatter reaction produces energy, this energy would have particles itself. I found out (reading...) that one (the main?) product are ...
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System of $N$ bosons

What precaution needs to be observed in writing down an expression for the total number of bosons $N$ valid at low temperatures?
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Boson or Fermion

How do you deduce that an atom is a fermion or a boson? Do you determine it from the number of neutrons because "electrons and protons cancel out each other in a neutral atom"? What does this have to ...
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How do you know $W$ and $Z$ bosons are really bosons and not fermions?

It has been always said that $W$ an $Z$ bosons are bosons and not fermions but is there any experimental trial that prove that? Has anyone put two of them in the same quantum state or studies have ...
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Goldstone modes $\hat a^\dagger(k) \left|0\right>$ for small $k$ or $\hat a^\dagger(0) \left|0\right>$

Consider the Hamiltonian: $$H=\sum_{\vec k} \varepsilon (\vec k)a_{\vec k}^\dagger a_{\vec k}$$ with $\varepsilon(\vec k) \rightarrow 0$ as $|\vec k|\rightarrow 0$. I know that this has gapless ...
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178 views

Which $W$ boson is involved in electron capture?

I am learning about Electron Capture. $$p+e\to n+\nu_e$$ My question is whether the $W^+$ boson or the $W^-$ boson is involved in this transfer. I can consider this two ways: 1) Since the electron ...
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255 views

Imaginary Frequency in Bosonic Hamiltonian

I'm doing some calculations for my Thesis involving a Bosonic Hamiltonian of the form: \begin{equation} H=\sum_{\vec{k}}\alpha\ a^{+}_{\vec{k}}a^{+}_{-\vec{k}} + \beta\ a^{+}_{\vec{k}}a^{-}_{\vec{k}}...
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Does the field (force-carrying) of a gluon or boson have a magnetic-like shape? Not spherical

The challenge of force-carrying boson is that many experiments generate results that are not consistent. Hence, quantum statistics. It is established that things like 'strong nuclear interaction/...
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Two particles in a harmonical potential (indistinguishable particles)

In statistical mechanics, we are going to find the difference between the canonical partition function for distinguishable particles and indistinguishable particles. For understanding this prinicple,...
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1answer
222 views

Spin of a neutral pion

I was going through the book High Energy Physics by DH Perkins. In the decay $\pi^{0}\rightarrow 2\gamma \ (photon)$, the possible spin components of the system of photons $S_z$ can be $0$ or $2$. A ...
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68 views

Why the $\beta^-$ decay releases $e^-+\nu_e$ and not $\tau$ or $\mu$ generations?

The $\beta^-$ decay is \begin{equation} n \rightarrow p + e^- + \bar\nu_e \tag{1} \end{equation} It can be broken down into \begin{align} d \rightarrow & \ u + W^- \tag{2}\\ W^- \rightarrow &...
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Exercise on bosonic vacuum

Consider bosonic canonical transformation, generated by operator $S = e^{\lambda (a^{\dagger})^2}$. Show, that \begin{equation} b \equiv SaS^{-1} = a - 2\lambda a^{\dagger}. \end{equation} ...
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What Makes a $W$-Boson a Gauge Boson?

I understand that in beta decay, a quark changes its flavor and emits a $W$-Boson, and this $W$ (is the W Boson virtual, by the way?) quickly decays into an electron and an electron antineutrino or ...
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Trace with Boson operators

I want to compute the following trace $$ \operatorname{tr}(\exp(-\sum_k\varepsilon_k a_k^\dagger a_k)a_i a_j) $$ with bosonic operators $a_i,a_j$. I think the result will be proportional to $\delta_{i,...
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59 views

Fock space-Weyl Algebra

I am new to quantum physics, help me out please on this question. I am confuse about how to compute the norm of the states describe below: Given the operators $a_m, a_m^{\dagger}, m=1,2,\dots, M$, ...
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What makes common matter what it is compared to, for example, Electromagnetic Fields?

Last week, I discussed with some friends (we are all Physics Students) what are the differences between photons and electrons that account for the differences between light and matter. One team argued ...
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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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Calculating density of states given energy levels and degeneracy

In my statistical mechanics class, my professors did a problem in which he calculated the density of states, however I am having trouble justifying his approach. I did the problem beforehand in an ...
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“Excitatonium” is made of electrons and the holes they leave — so how can they be bosons?

My understanding is that solid matter is made out of fermions (which are subject to the Pauli exclusion principle, which is why they're solid) and bosons (which are not subject to Pauli exclusion and ...
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190 views

How bosons do not violate conservation of energy?

As far as I understand bosons are energy packets which carry forces: e.g. Higgs bosons carry gravity. What I don't understand is, for example if we have an isolated object which constantly releases ...
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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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141 views

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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Mass softening for high-energy interactions?

It is well known (see, e.g., eq. (2) in this paper) that the coupling $g$ of composite, fermion-bilinear bosons (e.g. pomerons) to fermions (e.g. quarks) decreases above the compositeness scale $\mu$ ...
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3answers
214 views

Are bosons matter?

The title explains the question. Are bosons matter? As I have seen, there are three answers to this question: No, only fermions are matter. Yes, but only those with mass. Yes, all bosons are matter. ...
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1answer
343 views

Eigenvalues of the exchange operator determined by the particle type (boson or fermion) in a two particle system

While dealing with a two particle system in QM (the particles are identical), the net wave function of the system would be simply the product of the wavefunctions of the individual particles in the ...
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1answer
120 views

Fundamental string theory questions

Can anyone answer some basic string theory questions for me? The Veneziano Amplitude is celebrated for predicting the scattering amplitude of mesons and for practically giving birth to string theory....
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Interpretation of antiferromagnetic magnons dispersion relation

The dispersion relation of magnons in a ferromagnetic 1d lattice is \begin{equation} \omega(k)=\omega_0\big[1-\cos(ka)\big] \end{equation} where $\omega_0$ is a constant and $a$ is the spacing ...
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28 views

Efimov physics: $N$-body “fundamental forces”?

Can Efimov trimers or generalizations be understood as "fundamental" 3-body interactions (or $N$-body) or are they just special dynamics driven by scale invariance, as suggested by Efimov himself?
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Efimov physics: beyond trimers!

Is it possible to get $N$-body $N$-mers in a similar way we get trimers in usual Efimov physics?
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70 views

Action of Field Operator on Ket

I've very little experience with field operator notation so am trying to get to grips with the fundamentals. I'm asked, if state $|\Psi \rangle$ has the wavefunction $\Psi(x_1,...,x_N)$, then what ...
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2answers
64 views

Difference between particle and state

I have recently started studying particle physics, and I was surprised by the description of hadrons. At first I was told that the $\Delta^0$ baryon was composed by one up and two down quarks, and ...