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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Why are fermionic atoms less prevalent than bosonic ones?

Many atoms have no stable fermionic isotopes. Those that do typically have more stable bosonic isotopes than fermionic ones. Furthermore, the fermionic isotopes of most atoms are lower in natural ...
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Where does the Energy for $W$ and $Z$ Boson Emission come from?

I understand that the Weak interaction is mediated by the $W$ and $Z$ bosons, and that their huge masses are the reason for the Weak interaction's short range. However, I cannot find an explanation ...
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Why Photon gas's Equation of State Diverges?

We know that, for Photon gas, the equation of state is given by $pV=\frac{1}{3}U$; where $p$ is the Pressure, $V$ is the Volume and $U$ is the Internal Energy of the Photon Gas. (see Equation of State ...
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Why is Equation of State of Photon gas different from the Equation of State of Boson gas?

We know that, for Bosons, the Equation of State is given by $pV=\frac{2}{3}U$; where $p$ is the Pressure, $V$ is the Volume and $U$ is the Internal Energy of the Boson Gas. (see Equation of State of ...
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Electron density via bosonization/refermionization

I'm currently trying to understand the rigorous construction of bosonization/refermionization via Jan von Delft. In the constructive approach, we consider a system on a finite $L$ circle and thus in ...
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How to calculate commutator between fermionic terms and bosonic conjugate momenta?

Consider a system which has a three bosonic scalar fields and non-relativistic fermionic part. Let the field operator for the bosonic part be $\phi_k(x)$, $k=1,2,3$, with conjugate momentum $\pi_k(x)$....
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Why does Quantum Harmonic Oscillator treatment to Blackbody Radiation result in Ultraviolet Catastrophe?

Planck, in his treatment to solve Blackbody Radiation, considered that the Electromagnetic Waves inside the Cavity of the Blackbody are Standing Waves due to Oscillating charges on the wall of the ...
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Partition function for the indistinguishable particles using symmetrization of states

In the derivation of the partition function for the the N particle ideal gas, the factor of $\frac{1}{N!}$ does not come naturally. We have to go for symmetrized and asymmetrized state. So, to derive ...
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Planck's assumptions for Treatment of Blackbody Radiation

Planck, in his treatment to solve Blackbody Radiation, considered that the Electromagnetic Waves inside the Cavity of the Blackbodyare Standing Waves due to oscillating charges on the wall of the ...
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Why are single-electron states occupied at $T=0$ in superconductors?

Some textbooks show a density of states where the single-electron states below the Fermi energy are occupied at $T=0$ (see picture). However, I thought that at $T=0$ all electrons are paired. Hence ...
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How are signal strength modifiers calculated?

I've been asked to measure a likelihood function , and to measure "simultaneously parameters" $\mu^{ggF}$ and $\mu^{V \hspace{0.5 mm} BF} $ , and to measure the parameters $\mu^{ggF}$ and $\...
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Can $A_{nm} = |n\rangle \langle m|$ be written in terms of boson operators $b, b^\dagger$? [duplicate]

I am curious whether all operators can be written as a linear combination of product of boson operators $b, b^\dagger$. More precisely, consider the single harmonic oscillator Hilbert space $H$, whose ...
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Why should the wavefunction of two isolated bosons be symmetric?

The question is in the title, Let's say I have one boson (Mike) somewhere on earth and another one (Fatima) somewhere in proxima centauri. They are identical. My friend argues that whatever the ...
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Is it a prerequisite for the usage of the Gross-Pitaevskii equation, to assume a dilute Bose gas?

Is it a prerequisite for the usage of the Gross-Pitaevskii equation, to assume a dilute Bose gas? Or is it also for Bose-Einstein condensates which are not so dilute?
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Equality of Bose Lattice Hamiltonian and Josephson Array Hamiltonian

I am currently reading the paper Boson localization and the superfluid-insulator transition by Fisher, Weichman, and Fisher. Equation 2.1 defines the Hamiltonian of a Bose Lattice gas as $$ H = -\sum_{...
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Relation of spin and force of bosons

Why can odd spin bosons (gluons, photons) both repel and attract, but even spin bosons (gravitons) can only do one or the other? Does the Higgs boson fit this rule, i.e. does it mediate a force that ...
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Are paired electrons not bosonic?

A pair of electrons has spin 0 which makes any such system a boson rather than a fermion. The Pauli exclusion principle does not apply therefore to paired electrons and any such two electrons can ...
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Why are phonons bosons if they cannot occupy the same eigenstate?

I am reading the The Oxford Solid State Basics and on pages 82-83 it appears the following: If a classical harmonic system (i.e., any quadratic Hamiltonian) has a normal oscillation mode at frequency ...
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Qualitative difference of excitations in Fermi VS Bose superfluids

Assume that we have an electrically neutral interacting gas (or liquid) of Bose or Fermi particles in a superfluid state. For simplicity, assume that the particles interact via an assigned central ...
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Feynman diagram

In this picture first diagram, can't the gluon be a $Z$ boson? Similarly, can't the $Z$ boson in the second diagram be a gluon?
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Free boson CFT: how the zero mode $\phi_0$ acts on the Hilbert space?

In the Section 6.3 of the yellow book, free boson CFT is constructed. We have operators $a_n, \bar a_n$ for $n\neq 0$, as well as the zero modes $\phi_0$ and $\pi_0$. Among the zero modes, $\pi_0$ is ...
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Can a Bose-Einstein condensate be made of any boson?

Can a Bose-Einstein condensate be made of any boson, or even two different types of bosons. Since none have to obey the Pauli exclusion principle, if so, how can we predict how one would like?
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Further insight into the pairing tensor for many-body bosonic systems

According to Blaizot and Ripka's "Quantum Theory of Finite Systems", the generalized density matrix is given by $$R = \begin{pmatrix} \rho & \kappa \\ -\epsilon \kappa^* & 1-\epsilon ...
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Why at high energies, Fermi-Dirac and Bose-Einstein distribution behaves as Maxwell-Boltzman distribution? What is the physical explanantion?

I was searching for the reason that why at higher energies, the FD and BE distributions behave as MB distribution. In Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles by Eisberg and ...
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Homotopic Paths and Spin-Statistics

I am currently reading Schwartz' book on QFT, Section 12.2 on Spin and statistics. He shows, that in 3D there are only two inequivalent ways to exchange two indistinguishable particles. More formally, ...
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Why is there no stars made of bosons?

Consider the white dwarf (or similarly neutron stars), which can be modeled as a star made of degenerate Fermi gas: A white dwarf, also called a degenerate dwarf, is a stellar core remnant composed ...
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Gauge boson layout in $\rm SU(5)$ GUT unification

It is known that the theory of the Great Unification $\rm SU(5)$ GUT encapsulates the gauge groups of the standard model to one large group $\rm SU(5)$. But is it possible to show schematically how to ...
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Argument for Fermions and Bosons as eigenfunctions of particle exchange operator $P$

Some time earlier, my prof took me through an argument leading to emergence of fermions and bosons by the application of particle exchange operator on the multiparticle wavefunction. I will try to ...
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Exact ground state energy of the noninteracting one-dimensional Bose Hubbard model? [closed]

The Hamiltonian of Bose-Hubbard model reads as $$ H = -J\sum_{<i,j>}a_i^\dagger a_j + h.c. + \frac{U}{2}\sum_i n_i(n_i - 1) $$ In the non-interacting case where $U=0$, what is the ground state ...
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Representation of Bosonic Hopping Operator in Bargmann space

In the Segal-Bargmann representation, the bosonic canonical operators can be mapped to differential operators via $a\to z$ and $a^\dagger \to \partial_z$ such that the number operator can be written ...
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Why can we choose spin-1/2 degrees of freedom to commute?

Edit 2: The previous title of this question was "Why are qubits bosonic?" Thanks to the answers that have been provided so far, I now realize I asked my question in a sloppy way. The ...
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Eigenstate of a Hamiltonain diagonalized using a paraunitary matrx

I have a question regarding the definition of energy eigenstates of Hamiltonian that can be diagonalized using paraunitary matrices. From quantum mechanics, energy eigenstates are defined by, $$ \...
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Some questions about the compact boson in David Tong's notes on Gauge Theory

The notes can be found at http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html. In Sec. 7.5.1, T-Duality, around Eq. 7.51, it says that the Bianchi identity $\partial_\mu(\epsilon^{\mu\nu}\partial_\...
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System of distinguishable fermions

I've started reading many-particle systems in Quantum mechanics, and came across the concept of identical particles vs distinguishable particles. However, I'm wondering, what happens in case of a set ...
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Do quantum measurements destroy the symmetrization requirement?

Do quantum measurements destroy the symmetrization requirement? The symmetrization requirement requires that the combined wave function of a system of particles be either symmetric under an exchange ...
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How does the Higgs boson get its mass? [duplicate]

I understand that Higgs boson gives other particles mass. But how does it get its own mass? Does it interact with another field?
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Can two or more bosons concretely exist at the same exact point in space at the same time?

Is it just the probability of finding the 2 particles in the same volume is the same or is it that they can really exist concretely as each other in the same point in time. Also related is, can two ...
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Two-particle states of bosons

I'm reading Advanced Quantum Mehcanics of Schwabl and I'm having a hard time trying to reproduce this calculation (page 57). Consider the following general two-particle state: $$\displaystyle{|2\...
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Difference between BEC and Superfluidity. Why is considered superfluid helium not a BEC?

I have not a clear idea what the difference between a BEC of weakly interacting bosons and superfluid is. My second question that could help me understand this difference is: why do alkali atoms form ...
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Multinomial theorem and binomial factor (case for Bosons)

I am trying to understand the meaning behind the binomial factor and multinomial theorem when dealing with problems in statistical mechanics, mostly combinatoric related problems. This is the problem ...
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Thermal average of this operator

Anyone know how I might work out what something like this $$\frac{1}{Z}Tr(e^{-\beta H_{B}} (\hat{a} + \hat{a}^{\dagger}) e^{V_{n}(\hat{a}^{\dagger} - \hat{a}) - V_{n'}(\hat{a}^{\dagger} - \hat{a})})$$ ...
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If photons have also particle properties why should they not collide with each other?

If photons have also particle properties why should they not collide with each other? Collisions between fermions are possible as collisions between fermions and photons(bosons) except collisions ...
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1 vote
1 answer
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Compactified Boson on the cylinder vs. on the Torus

I am a little bit confused if there is a difference between the compactified boson on the torus and on the infinite cylinder. In the big yellow book from Di Fransesco et altera, the formula for the ...
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Why does the weak interaction ineract solely with left handed particles?

So let me elaborate, my problem is that I don't fully understand why the weak interaction is a chiral theory - I would like an answer with the Lagrange density and the Higgs field. I also want to know ...
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2 votes
3 answers
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How can two bosons having mass be in the same place at the same time?

I'm fairly new to this topic, so please excuse any amateurism. I'm confused about how a boson (i.e a particle that does not obey Pauli's exclusion principle) can have mass. For example, W and Z bosons ...
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Inner product of bosonic coherent states [closed]

In the notation of Altland and Simons, we have bosonic coherent state: $$ |\phi\rangle = \exp \left(\sum_i \phi_i a_i^\dagger\right) |0\rangle. $$ On page 159, they use $\langle0|\phi\rangle = 1$ ...
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Where is the error in my calculation for a simple bosonic system?

$ \newcommand{\ket}[1]{\left|#1\right\rangle} $I was doing some calculations and I came across something that confused me and maybe you can explain to me where my reasoning is wrong. Let's say I have ...
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3 votes
1 answer
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Why there aren't classical field associated with fermions?

In A Introduction to Nuclear Physics by GreenWood, It's written Bosons are particles that obey Bose-Einstein statistics and are characterized by the property that any number of particles may be ...
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Identical particles

I am reading Quantum Mechanics from Griffiths (for the first time); in chapter 5 (2nd ed.) page-179 it is written: Now I really is not able to understand what Griffiths exactly wants to say by the ...
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1 vote
1 answer
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How does one integrate the Fermi-Dirac distribution using the zeta function?

I've seen in my physics book that: $$n=\frac{g}{2\pi}\int_0^\infty\frac{E^2dE}{e^{E/T}\pm1}$$ Regarding the number density of a relativistic gas of either bosons ($-1$) or fermions ($+1$). The ...
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