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22
votes
3answers
722 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 ...
15
votes
1answer
584 views

A reading list to build up to the spin statistics theorem

Wikipedia's article on the spin-statistics theorem sums it up thusly: In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
11
votes
1answer
365 views

What is the reason why anyons escape spin-statistic theorem?

I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem. I've read somewhere (the wikipedia page is ...
11
votes
1answer
330 views

Can the CPT theorem be valid if Lorentz invariance is only spontaneously broken?

Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are ...
10
votes
2answers
341 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 * ...
10
votes
1answer
546 views

Time reversal symmetry and T^2 = -1

I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
8
votes
2answers
212 views

Irrelevance of parastatistics for space dimension > 2

Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal ...
8
votes
1answer
86 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 ...
8
votes
1answer
250 views

Is conservation of statistics logically independent of spin?

If the number of fermions is $n$, we expect the quantity $(-1)^n$ to be conserved, i.e., $n$ never changes between even and odd. This is known as conservation of statistics. In the normal context of ...
7
votes
2answers
2k views

What causes the Pauli exclusion principle (and why does spin 1/2 = fermion)?

It seems to be related to exchange interaction, but I can't penetrate the Wikipedia article. What has the Pauli exclusion principle to do with indistinguishability?
7
votes
1answer
278 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 ...
7
votes
1answer
404 views

Spin-Statistics Theorem (SST)

Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
6
votes
3answers
377 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 ...
6
votes
2answers
447 views

Is there a reason why the spin of particles is integer or half integer instead of 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 ...
6
votes
1answer
575 views

What goes wrong when one tries to quantize a scalar field with Fermi statistics?

At the end of section 9 on page 49 of Dirac's 1966 "Lectures on Quantum Field Theory" he says that if we quantize a real scalar field according to Fermi statistics [i.e., if we impose Canonical ...
6
votes
1answer
472 views

Time reversal symmetry and T^2 = -1

I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
5
votes
2answers
865 views

Why are anticommutators needed in quantization of Dirac fields?

Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
5
votes
1answer
720 views

Why is the majorana particle a fermion?

My knowledge of quantum mechanics is rather limited, but what I always understood was that Bosons have integer spins and Fermions have half-integer spins. My question is very simple: the Majorana ...
5
votes
1answer
206 views

Does there exist a nonrelativistic physical system in which the effective long-distance fields violate spin/statistics?

The nonrelativistic Schrodinger field allows spin independent of statistics, so that you can imagine a nonrelativistic Schrodinger scalar field with Fermionic statistics, or a Schrodinger spinor field ...
5
votes
0answers
48 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 ...
4
votes
1answer
188 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 ...
4
votes
1answer
133 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 ...
4
votes
1answer
153 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. ...
4
votes
2answers
313 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 ...
3
votes
2answers
387 views

Example of a wavefunction that cannot be represented by a single Slater determinant

I know that in general, interacting fermions cannot necessarily be described by a single Slater determinant. Can anyone provide a simple example of a state that has no such representation?
3
votes
2answers
298 views

Why is fractional statistics and non-Abelian common for fractional charges?

Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
3
votes
4answers
4k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
3
votes
1answer
72 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 ...
3
votes
1answer
54 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) ...
3
votes
1answer
275 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 $(s,0,0,..,0)$ ...
3
votes
0answers
76 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?
3
votes
0answers
93 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 ...
3
votes
0answers
67 views

Question about the derivation of an equation in full replica symmetry breaking solution

Using replica method and saddle point method, the free energy of a magnetic system can be expressed as $$-\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
2
votes
1answer
363 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?
2
votes
1answer
2k views

Partition function of bosons vs fermions

I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively. What's the difference between ...
2
votes
2answers
267 views

Fermion Field of Standard Model

Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
2
votes
1answer
242 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 ...
2
votes
1answer
199 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 ...
2
votes
2answers
282 views

Why Pauli exclusion instead of electrons canceling out?

To quote Wikipedia, The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state ...
2
votes
2answers
236 views

existing bounds on maximum density achieved by a Bose condensate

As we know, fermions are subject to exchange interactions that limit the densities they can achieve. However bosons (simple or composite) are not constrained by this, which implies physical phenomena ...
2
votes
1answer
69 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?
2
votes
1answer
186 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 ...
2
votes
1answer
227 views

NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms

From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
2
votes
0answers
43 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
0answers
55 views

Spin-Statistics Theorem - Proof [duplicate]

Is this proof of spin-statistics theorem correct? http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf This proof is probably a simplified version of Weinberg's proof. What is ...
2
votes
0answers
275 views

Proof of Spin-statistics theorem [closed]

Is this proof of spin-statistics theorem correct? http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf This proof is probably a simplified version of Weinberg's proof. What is ...
2
votes
0answers
118 views

Ising Hamiltonian for relativistic particles

An Ising system is described by the simple Hamiltonian: $$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$ Here the $x_i$ are spins (+1 or -1 in units ...
1
vote
1answer
138 views

Does the Higgs mechanism address the spin statistics problem?

Since the Higgs mechanism is so intimately tied to binding together massless chiral fermions, does it happen to have anything to say about the spin statistics issue? I'm actually assuming the answer ...
1
vote
1answer
92 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
1answer
429 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. ...