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 a field $\phi$ obey both the scalar relation and the fermi relation?

Let $L_{\text{scalar}}=\frac{1}{2}\eta^{\mu\nu}\partial_\mu \phi \partial_\nu \phi$ be the scalar lagrangian and $L_{\text{fermion}}=i\psi \gamma^u \partial_\mu \psi$ be the fermionic lagrangian. Can ...
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Strange material, Bydrogen

Let's take a hypothetical scenario in which you manage to make a meta material in which the bulk of the mass is made of by a central negative nucleus and that has a single spin 1 boson whizzing around ...
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Formation of fields with momentum operator

Ok. Weinberg says that in their QFT book Vol 1 on pages 238 and 239 that we can construct any bosonic (A,A) field from scalar ((0,0)) field if we form operator of 2A partial derivatives (momentum ...
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zero spin particles' spin states

We know that the full wave function of spin particles have two parts. One is the spin part and another is the spatial part. Let's assume I have given a wave function which is the spatial part: $$\...
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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 ...
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37 views

Creation operator on coherent state and issue with commutation relations

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 ...
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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. ...
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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\...
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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 ...
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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}$...
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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^...
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Grand Canonical derivation of Bose-Einstein and Maxwell-Boltzmann statistics

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: $$\...
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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 ...
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111 views

Bogoliubov transformation for bosons (matrix calculation)

I'd like to know if there is a general numerical method of diagonalizing the bosonic quadratic Hamiltonian below $$H=\sum_{i,j=1}^NT_{ij}b_i^\dagger b_j+\frac{1}{2}\sum_{i,j=1}^N\left(U_{ij}b_i^\...
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Bose–Einstein Condensation in one dimensional harmonic oscillator [duplicate]

I was given that there is Bose gas with spin 0 in one harmonic oscillator so the energy levels are: $\epsilon_{n}=\hbar\omega n$ Can this gas go through Bose Einstein Condensation? I think yes, ...
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Spacial Wavefunction Symmetries and Identical particles

I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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Difference between fermions and bosons in Statistical Mechanics

I am an undergraduate student in Physics and Mathematics. I am now preaparing for my final exam in Statistical Mechanics and I would like some help in a particular point. So here it goes: In the ...
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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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Single atom states with energy 0, probability and occupation number fermions and bosons

Two mutually non-interacting atoms are trapped in a double-well potential in equilibrium at a temperature $T$, such that an atom can only occupy two possible single- atom quantum states, $Ψa(x)$ and $...
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70 views

Pauli Exclusion and Black Holes [duplicate]

Pauli exclusion principle states that 2 identical electrons cannot be in the same state, where state includes a spacial component. I have heard that, in order to avoid being in the same state, in a ...
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Spin 0 boson interaction

I have a question regarding the interaction of two spin 0 bosons in a shared harmonic oscillator. What would their first excited state be? I'm thinking that the total state has to be symmetric so ...
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119 views

Goldstone bosons when SSB potential has two fields

A theory consists of two complex scalar fields $φ_0$ and $φ _1$ with a symmetry-breaking potential $$V(|φ_0|^2 + |φ_1|^2).$$ How many Goldstone particles will there be in the theory?
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Orbital angular momentum for single particle in particle physics

I am taking an introductory course in particle physics and am quite confused about conservation of angular momentum at a vertex. This trouble arose specifically when considering the decay $\pi^0 \...
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Pauli Exclusion Principle and Quantum States [closed]

We know that two identical fermions cannot be in the same state together because of the Pauli exclusion principle. My questions are: Can two bosons (for example, photons) be arbitrarily close ...
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Probability of finding a particle in a two/three particle system

Let us consider a system of 2 identical particles, 1 and 2. Let, $ψ_a(1)$ is the amplitude of finding particle 1 at state $a$, and $ψ_a(2)$ is the amplitude of finding particle 2 at state $a$. Let N.F ...
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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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The importance of phase when defining fermions and bosons

In my lecture on indistinguishable particles, my lecturer is trying to illustrate to me the notion of particles being indistinguishable when considering that when we swap two particles in a box the ...
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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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Distribution of photons emitted by atoms

I am currently revising quantum gases, and a small but confusing thought experiment has been bugging me for a while. I understand the bookwork stuff on photons and how a photon gas in a blackbody ...
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Are composite bosons superradiant scattering candidates?

Massive bosons can experience superradiant scattering in an ergosphere. This can in principle be used as a power source. However, elementary massive bosons ($H^0,\,W^\pm,\,Z^0$) are short-lived. Are ...
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Bosonic commutation relations for force carriers?

Why are force carriers bosons? The easiest answer that I can give myself is that the gauge field $A_\mu$ is introduced like this: $$ \partial_\mu \rightarrow D_\mu = \partial_\mu+ieA_\mu, $$ so it ...
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Difference between $W^-$ and $\pi^-$

Maybe it's a very naif question, but what is the difference between a $W^-$ and a $\pi^-$? I mean they both change a $d$ into a $u$ right? $d \rightarrow u W^- \quad \text{and} \quad d \rightarrow ...
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A proof that Heisenberg's and Euler Lagrange's equations are equivalent in QFT [closed]

I asked this before (link, link) but I think people didn't understand what I was asking, so I am going to try again . Thanks for everyone that helped so far. In QFT, Heisenberg's equation is ...
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Can I distinguish a Bose-Einstein Condensate of composite bosons from one of elementary bosons?

The only requirement for an ensemble of particles to undergo a transition into a BEC is to be bosons. But two fermions also make a bosons. Are there physical, measureable implications of a BEC being ...
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Do anyonic statistics only arise from spatial degrees of freedom?

Elementary texts on quantum mechanics justify the existence of fermions and bosons using the simple argument that if we have a state of two indistinguishable particles $|a,b \rangle$, where $a$ and $b$...
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Do macroscopic bodies also show quantum nature at extremely low temperatures?

If we consider atoms or molecules and cool them to extremely low tempertures, will they also show quantum nature. Will their wave nature also get dominated? And if they are bosons, will they become a ...
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Example of phenomenon that occurs because Bosons don't obey exclusion principle

I am writing an essay targeted at undergrad level, non-science audience and I am trying to find another real world example of what is possible due to the fact that bosons are not subject to Pauli ...
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Will more than one composite boson can stay in the same energy state if constituent fermions has moderate entanglement?

Let say we consider two distinguishable fermions(bi-fermions) in compact form. The case when both fermions are existing as free fermions, they will obey Pauli exclusion principle. In other case if ...
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super bunching effect of bosons

Let say we consider a $N$ pair of elementry bosons (i.e $N$ composite bosons). At very low temperature these bosons will condense into the ground state. If we find the mean occupation number $\langle ...
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Why do composite bosons form a BEC?

I found this question here but it does not fully answer my question. The answer there was that "composite bosons can occupy the same state when the state is spatially delocalized on a scale larger ...
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What is the criteria of trapped ideal gas to form Bose-Einstein condensate (BEC)?

If we have ideal gas of bosons in a trapped harmonic potential, is the only necessary thing for BEC is a temperature less than the transition temperature? Or is there any other things we should keep ...
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What are soft theorems in context of scalr fields

What are soft theorems ? I tried reading Weinberg’s paper but couldn’t understand it, are there any resources on this ? I am very interested in the case of scalars.
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Wave function of a system of two identical fermions

In N. Zettili's 'Quantum Mechanics Concepts and Applications' [chapter 8, solved problem 8.3], we have to find wave function and ground state energy of a system having two identical fermions and in ...
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Can we consider oscillation of air column in the wind instruments as phonons subject to Bose- Einstein statistics ?

A flute is a wind instrument, which could be modelled as a resonance cylinder open at both ends. Any cylinder resonates at multiple frequencies. A skilful player produces a standing wave in the flute ...
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What is the super-bunching effects of composite boson?

What is the super-bunching effects of composite boson ?
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Can we ever “measure” a quantum field at a given point?

In quantum field theory, all particles are "excitations" of their corresponding fields. Is it possible to somehow "measure" the "value" of such quantum fields at any point in the space (like what is ...
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Is possible to replace the photon as a force carrier of electromagnetic force with a sfermion-fermion relation pair model?

force carriers or messenger particles or intermediate particles are particles that give rise to forces between other particles. I read that A field’s spin is determined by how it transform if you ...
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Relation between entanglement and average number of modes that are taken by constituent particles of coboson

Let we have composite boson made of pair of fermions, and fermions are entangled with each other. The state of composite boson can be written as $ \sum_m \sqrt{\lambda_m} a^{\dagger}_m b^{\dagger}_m |...
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Indistinguishable particles and symmetrization of wavefunction

For 2 indistinguishable particles, we take the wave function to be $$\psi\pm (r_1,r_2) = A[\psi_a (r1)\psi_b (r2) \pm \psi_b (r1)\psi_a (r2) ]$$ where fermions get a - sign and bosons get a + But, if ...