The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
1answer
71 views

What is the difference between Bosonic and Fermionic symmetry protected topological phases (SPT)

I am reading the paper ``Braiding statistics approach to Symmetry Protected Topological Phases'' by Levin and Gu. In this paper two spin models considered describe spin-1/2 particles in (1+2) ...
3
votes
1answer
52 views

What does it mean that a Cooper pair behaves as a boson but respects the obligations of fermions?

I refer to the fact that it has integer spin, but antisymmetric wavefunction. How is this possible?
0
votes
1answer
21 views

Connection between singlet, triplet two-electron states and the Slater determinant

I'm confused about a number of things concerning two-electron systems and spin. Here is (perhaps too much) exposition, skip to "the problem" if you want: Consider the helium atom in the simplified ...
1
vote
0answers
64 views

Is there a simple man's perspective of Pauli’s exclusion principle [closed]

I've been pondering over a questions from a while. Please forgive me if I am being too naive. We all know that because of Pauli's exclusion principle no two electrons can populate one state. This ...
3
votes
1answer
70 views

Stern-Gerlach experiment with Bosons

I'm new to this forum and I'm studying semiconductor physics at the moment. I just wanted to ask a thing about the concept of spin: when it was studied for the first time, in the Stern-Gerlach ...
1
vote
0answers
41 views

Fermi momentum and Fermi energy

I have some confusion about the concept of fermi energy/fermi momentum. Is the fermi momentum always defined as $\sqrt{2mE_F}$ ,where $E_F$ is the fermi energy, or the fermi momentum depends, as ...
1
vote
0answers
38 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
2
votes
1answer
70 views

Which quasiparticles follow which statistics [closed]

Let me say beforehand that I know this is an ill-defined question, but I believe it is useful anyway. For these common quasiparticles: Phonons Holes Plasmons Excitons Plasmon-polaritons What ...
1
vote
1answer
64 views

Derivation of Fermions anticommutation rule

How one might derive fermions anticommutation rule? For bosonic particles, there is no ordering issue, and its commutation relation could be easily derived. However, for fermion, is there any easy way ...
3
votes
1answer
212 views

Why must fermions be antisymmetric? [closed]

I have read that fermions cannot exist in the same state simultaneously. I understand why indistinguishable particles with an antisymmetric superposition of states can't exist in the same state ...
2
votes
0answers
40 views

dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b$, then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
4
votes
0answers
71 views

Correct way to define parity of two parafermions

I am checking the literature on parafermions and it seems that people define the parity of two parafermions to be $\gamma_{a}^{-1}\gamma_{b}$. Is this definition always valid? How does one come up ...
3
votes
1answer
106 views

Why must the supersymmetry generators be spinors?

I have read in a few places (for example, at page 5 here) that the supersymmetry generators must be spinors. Quoting the reference mentioned The generator of the symmetry must relate two types of ...
0
votes
1answer
258 views

Ising model with metropolis algorithm around critical temperature

I'm trying to simulate Ising model using metropolis algorithm. Boundary conditions are periodic. I know how the algorithm works and I have written the code myself. Everything works as it should except ...
2
votes
0answers
32 views

Intrinsic CPT phase

Under charge conjugation C, spatial inversion P and time reversal T transformations, there are possible intrinsic phases (more for this on Chapter 9, The Quantum Theory of Field v1 by S. Weinberg): $$...
1
vote
0answers
82 views

Relation between representations/classifications

Generally a quantum system can be characterized in the following way: its states form a representation space for every symmetry group of that system. The representation has to be unitary (or anti-...
0
votes
0answers
83 views

Quantizing field with anti-periodic boundary condition

This is a naive question about a possible toy model in QFT. In particular, I am trying to find a simple model where spin-statistics theorem holds. One can construct a 1+1 dimensional classical ...
1
vote
2answers
49 views

In which part of physics can we utilize the rotational antisymmetry of certain wave functions?

Just a quick question - I fail at Googling this topic since I do not remember clearly, in which case (e.g. for what type of particles) is the wave function antisymmetric in terms of spatial rotation $...
5
votes
1answer
76 views

Spin, statistics and neutron stars

So a thought occurred to a friend of mine the other day: in a neutron star, neutrons are prevented from sitting directly on top of one another due to the Pauli exclusion principle, what with neutrons ...
1
vote
1answer
114 views

Spin statistics

I have a very intrinsic question about quantum field theory and even more general, why in 3+1-dimensional spacetime, we have only two statistics for particles to obey? Therefore why we have only two ...
11
votes
1answer
299 views

What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
3
votes
1answer
116 views

Permutations of two identical particles in two dimensions

In three spatial dimensions there are only two possible statistics: Bose-Einstein and Fermi-Dirac. This is the fact related with the statement that first homotopic group of 3-dimensional configuration ...
1
vote
0answers
48 views

Pauli's exclusion principle? [duplicate]

What is the idea behind Pauli s exclusion principle? Why should an electron or any particle having non integral spin obey this principle?
1
vote
1answer
242 views

anti-symmetric spin wave function of $|^3\text{He}\rangle$

Consider $|^3\text{He}\rangle$ in the ground state (2 protons and 1 neutron). Assume the spatial part of the wave function is symmetric. I have to construct the spin part of the wave function. This is ...
9
votes
3answers
2k views

Is there a reason why the spin of particles is integer or half integer instead of, say, even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...
1
vote
1answer
77 views

kitaev-honeycomb : can't get wilson loop squared to yield +1

I'm new here, loving this website and I'm having some difficulty with the wilson-loop operator in kitaev's honeycomb model. problem statement The Kitaev model (Kitaev, 2006 is the original paper) ...
5
votes
1answer
202 views

Is Romer's letter on our search for the elementary proof of the spin-statics theorem out of date today?

The following link provides a letter to the editor by Robert H. Romer who writes, In a 1994 "question" in this journal, Neuenschwander asked whether anyone had yet met Feynman’s challenge of ...
3
votes
0answers
83 views

Is there a reasonable lower bound for free energy per site of the 2D Ising model in the presence of an external field?

Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}}, $$ is ...
2
votes
1answer
81 views

Angular momentum of anyons

Why is it true that anyons can have angular momentum taking any real value? Why aren't they restricted to the $j(j+1)$ integer values most are familar with?
3
votes
0answers
93 views

Has the existence of anyons been experimentally verified?

I've been wondering whether there has been any experimental evidence for the existence of anyons or are they just objects of purely mathematical interest?
2
votes
1answer
408 views

Does Fermi-Dirac Statistics explain anti-particles?

I wondered whether the Fermi-Dirac Statistics describes the anti-fermion particles. Does it include the anti-particles?
4
votes
1answer
254 views

Anyons only in 2+1 spacetime dimensions - better explanation

Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason that the paths for exchange in 3D are deformable into each other while in 2D,...
4
votes
2answers
753 views

Spin-statistics theorem proof details

Recently I have read one book where there was some incomprehensible proof of the Pauli's spin-statistics theorem. I want to ask about a few details of the proof. First, the author derives ...
5
votes
1answer
229 views

Does This Really “Prove” Spin-statistics Theorem?

In quantization of scalar field theory we impose commutation relation between the field operators by hand and similarly we impose anti-commutation relation between Dirac field operators by hand. As a ...
5
votes
0answers
215 views

What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
7
votes
1answer
447 views

Double connectivity of $SO(3)$ group manifold

Is there any physical significance of the fact that the group manifold (parameter space) of $SO(3)$ is doubly connected? EDIT 1: Let me clarify my question. It was too vague. There exists two ...
30
votes
3answers
2k views

Idea of Covering Group

$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence? I heard that this fact is related to the description of bosons and fermions. But how does it ...
2
votes
0answers
96 views

Spin-statistics theorem on spaces with non-integer dimensions

What would be the spin-statistics relation for particles in a space with non-integer dimension, $ 2 \lt D \lt 3 $? In other words (cf. stackexchange questions here and here), what is the first ...
3
votes
1answer
84 views

an Abelian complex statistical phase from exchanging non-Abelian anyons?

We have some discussions in Phys.SE. about the braiding statistics of anyons from a Non-Abelian Chern-Simon theory, or non-Abelian anyons in general. May I ask: under what (physical or mathematical) ...
14
votes
2answers
592 views

Braiding statistics of anyons from a Non-Abelian Chern-Simon theory

Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function: $$ Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * j(\...
2
votes
1answer
493 views

Why do electrons couple in atoms?

In describing electron states in hydrogen, we have a very "simple" picture, at least in intro-quantum. But this only has one electron! As we permit more electrons, we also have things like the ...
1
vote
1answer
104 views

What spin-statistics is a magnetic monopole expected to obey?

What statistics (or spin) is a magnetic monopole expected to have? Does it depend on the theory used?
1
vote
2answers
1k views

What is the significance of electron spin quantum number?

Somewhere I read that spin quantum number is a particularly interesting theory of quantum mechanics as what it really implies is that particles like electrons do not come back to the initial state of ...
1
vote
0answers
77 views

Time reversal invariance and statistics

To what extend does the behaviour of time reversal invariance depend on the statistics of the particle under consideration? More explicitly: To what extend does the action of the time reversal ...
1
vote
1answer
525 views

Some limiting cases of the Heisenberg XXZ model (1/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
3
votes
1answer
688 views

Symmetric transverse traceless tensors of rank $s$ and $(s,0,0,..,0)$ representations of $SO(n)$

Can someone help see this connection as to why a spin $s$ (an Integer) particle is to be thought of as a symmetric transverse traceless tensor of rank $s$ and that they lie in the $(s,0,0,..,0)$ ...
6
votes
1answer
225 views

What is the the Ehrenfest-Oppenheimer rule on the statistics of composite systems?

Ehrenfest 1931 gives an argument to the effect that the application of the spin-statistics theorem to composite systems is valid, but only as an approximation and under certain conditions. ...
2
votes
1answer
282 views

Can one prove the full spin-statistics theorem from the spin 0, 1/2 and 1 cases?

Using second quantization for scalar field, spinor field and vector fields, we can get commutation and anticommutation relations for the birth and destruction operators of the fields, which leads us ...
6
votes
2answers
538 views

Is the symmetrisation postulate unnecessary according to Landau Lifshitz?

The symmetrisation postulate is known for stating that, in nature, particles have either completely symmetric or completely antisymmetric wave functions. According to these postulate, these states are ...
2
votes
1answer
447 views

Explanation of Superconductivity

I can't get a definitive explanation of why superconductivity happens and I am getting mixed explanations from my textbooks. I will tell you what I know and hopefully you can correct any ...