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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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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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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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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Bosonic qubits using BEC versus usual qubit implementations based on energy levels

All condensate atoms in a BEC (say like Rb, etc) effectively occupy the lowest energy-state. If it is that the case, then how are such bosons in a BEC encoded as a qubit? In particular, when Grover ...
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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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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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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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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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Bosonization and Commutation Relation

I'm playing a bit with bosonization $ψ→:e^{-φ}:$ and $ψ^*→:e^{φ}:$ in the sense that $$ \Bigg\langle 0_\mathrm{F} \Bigg|∏_{i=1}^nψ(z_i)ψ^*(w_i)\Bigg|0_\mathrm{F}\Bigg\rangle = \Bigg\langle 0_\mathrm{...
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Spin state of two distinguishable bosons

I was reading about the $C$-parity of a particle-antiparticle pair. Since charge conjugation has the effect of swapping the particle and antiparticle, the $C$-parity can be found from the symmetry of ...
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451 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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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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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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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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58 views

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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2k views

Why bosons have integer spin and fermions have half-integer ones?

Due the fact that the fermions are the "block particles" and the bosons are the "carriers" I just came out with the question that, why the "block particle" have half-integer spin and the "carriers" ...
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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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475 views

Finding states of a system of 2 identical bosons (including spin)

I'm trying to find the ground state and first excited state for 2 identical bosons in an infinite square well. I know that both states are degenerate and the spatial and spin parts of the wave ...
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941 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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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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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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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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Meaning of the chemical potential for a boson gas

My lecturer told me that the mu is the Chemical potential is zero or negative, in the following example, mathematically it acts as a Normalisation constant. But is there any Physical insight about why ...
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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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183 views

Qubits from fermions?

I'm confused about qubits and fermions/bosons. I would like to look at a specific example: Take an electron (which is a fermion) with its spins as a qubit system. A spin up state is the $\lvert 0 \...
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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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1answer
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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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21 views

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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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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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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142 views

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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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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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 ?