Fundamental characteristic property of particles which together with orbital angular momentum acts as the generator of rotations and which doesn't have a classical equivalent but is sometimes compared to and contrasted with classical intrinsic angular momentum.

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2answers
116 views

Why Lagrangian of electromagnetism with Lorenz Gauge evolve Klein Gordon equation?

Simply Lagrangian without a source for Maxwell equation is $$ L = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} $$ Also Lorenz Gauge condition is $$ \partial_{\mu}A^{\mu}=0 $$ and if so I can briefly add this ...
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1answer
41 views

Why does a spinning nucleon generate a magnetic field?

I am trying to understand how NMR works, but I am not sure why a spinning nucleon produces a magnetic field. Is this a consequence of the quark structure inside?
2
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1answer
87 views

Why gamma-matrices are associated with tetrads Lorentz rotation?

In Zee's "QFT in nutshell" in a paragraph "Differential geometry of Riemann manifold" he states that Dirac gamma-matrices are associated with tetrads Lorentz rotation, so Dirac lagrangian in curved ...
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1answer
72 views

Interpretations of Stern-Gerlach experiment

In many textbooks (J.J. Sakurai for instance) S-G experiment is explained through the idea of a collapse of a state of a system. So here, in this discrete case, we can see quantum behavior more ...
2
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1answer
81 views

Where do the quantum fields encode the spin information?

I know basically the difference between Klein-Gordon and Dirac field is spin. But I am not sure where we need to implement this info. The solutions of both equations are the wave packets which ...
2
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2answers
442 views

Tensor Product vs. Direct Product for three spin-1/2 particles

Let us consider three spin-1/2 particles and only focusing on their intrinsic spin $S$. The Hilbert space has then to be $\mathcal H = ℂ^2 ⊗ ℂ^2 ⊗ ℂ^2$. The spin can be described by $V ∈ \text{SU(2)}$ ...
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0answers
101 views

Spin, parity, etc. conservation in decays/reactions

I have a long list of short physics questions I'm reviewing, and there are several that ask about whether certain decays or reactions are allowed. Clearly these questions are testing my knowledge of ...
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2answers
134 views

A conceptual question about spin

I read in Landau's quantum mechanics(section 62) that if the Hamiltonian does not involve spin, the total wave function can be written $$ \psi ( x_1, x_2, ...) \chi ( \sigma_1 , \sigma_2 ,...)$$ in ...
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1answer
57 views

Why $2j+1$ number of states?

In this statement from Modern Quantum Mechanics by J.J. Sakurai: If $j$ is an integer, all $m$ values are integers; if $j$ is a half-integer, all $m$ values are half-integers. The allowed ...
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1answer
49 views

How have the duration of the martian day changed in the past?

There is a panspermia theory which claims that life might have begun on Mars and I currently read a post that the human circadian rhythm is closer to the martian day length (about 25h) than the day ...
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1answer
47 views

How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states. Each one of them can be uniquely determined by total spin and its orientation, we can use ...
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0answers
58 views

Determining Parity of Decaying Quantum System

Show that a particle of spin $1$ cannot decay into two identical particles of spin $0$. The $\rho$-meson has spin $1$ and can decay into two spinless (spin-$0$) $\pi$-mesons, or pions, with ...
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5answers
1k views

Difference between spin and polarization of a photon

I understand how one associates the spin of a quantum particle, e.g. of a photon, with intrinsic angular momentum. And in electromagnetism I have always understood the polarization of an EM wave as ...
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0answers
63 views

Can spin angular momentum be understood as orbital angular momentum in extra dimensions?

It is to my understanding that in Kaluza-Klein theories the mass of particles can be understood as linear momentum in the extra dimensions. Let's consider in $\mathbb{R}^{1,3}\times{}B$ space-time a ...
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1answer
43 views

Spin Hilbert space

I'm currently doing some quantum mechanics and was able to transform my Hamilton operator to something that basically looks like this: $$ H = H_{xy} + \frac{p_z}{2M} + \alpha S_z, $$ where $H_{xy}$ ...
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1answer
205 views

Why doesn't the deuterium nucleus have spin 0?

A deuterium nucleus is composed of a proton and a neutron. Both have spin 1/2 so I would expect the deuterium to have two possible spins: 1 for the triplet and 0 for the singlet. But apparently ...
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0answers
42 views

Why spin-$\frac{1}{2}$ nuclei have zero electric quadrupole moment?

Why spin-$\frac{1}{2}$ nuclei have zero electric quadrupole moment? How to calculate in general?
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0answers
42 views

Parity of magnetic susceptibility $\chi(\omega)$

It is well known that real and imaginary parts of magnetic susceptbility, defined as $\chi=\chi'(\omega)-\mathrm{i}\chi''(\omega)$, ought to be even and odd to frequency $\omega$ respectively, ...
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0answers
20 views

Spin statistic in spontaneous parametric down-conversion

In a spontaneous parametric down-conversion a photon will be converted into two photons with half energy and correlated polarization. How the spin from the ingoing photon will be transfered to the ...
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0answers
30 views

What is the physical process in paramagnetic resonance

In our QM lectures, Prof introduced an phenomenon called paramagnetic resonance, which described an electron precession in an $z$-direction magnetic field. I didn't quite understand this phenomenon, ...
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1answer
134 views

Heisenberg Hamiltonian for spin-spin system

I wonder how we should conclude the following Hamiltonian (I mean the 32-18 in the picture below, written in solid state physics by Ashcroft & Mermin.) for spin-spin system? (It is in chapter 32 ...
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2answers
128 views

What's the connection between the spin of the photon and the polarisation of light?

In view of wave-particle duality, the spin of the photon must have a counterpart in the wave picture: is this polarisation?
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2answers
95 views

How are the components of the spin vector defined?

How do we distinguish between the $x$, $y$ and $z$ spin components? More precisely: how do we define the $z$ component? (according to what, it is the $z$?) for measuring the $x$ component how ...
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1answer
54 views

Gordon decomposition of Dirac current for massless electron?

We know Gordon decomposition of Dirac current is applicable only for massive (nonzero mass) Dirac particles. Is there an analog for massless Dirac particles? (I have made an attempt to answer ...
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0answers
46 views

Spin of an operator in supersymmetric theories

How exactly is the spin of an operator in the context of a supersymmetric theory defined? For example, in page 25 of [1], $\mathcal{N} = 2$ supersymmetry is defined to have operators $J, G^{+}, G^{-}, ...
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1answer
145 views

Spin operators commutation

Why do the spin operators $ S_{x1}$ and $S_{x2}$ of two particles along the $x$-axis commute i.e $S_{1x}S_{x2}-S_{2x}S_{1x}=0 $ ?
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1answer
67 views

How can black holes have electric charge and spin? [duplicate]

If the star's mass supposedly collapses into a single point, and it ends up having "said" zero volume, then how can people say that the hole has a specific spin or that it can have an angular ...
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2answers
290 views

Why photon only have helicity other than spin? [duplicate]

When learning angular momentum in quantum mechanics, a spin 1 particle have 3 states. Then I saw from sakurai's modern quantum mechanics that photon's two polarization are just like spins, but with ...
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0answers
28 views

What is the difference between antiferromagnetism and spin density wave?

It seems that antiferromagnetism can be treated as a special case of spin density wave with wavelength equals to twice of the unit cell. Is that so?
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0answers
24 views

Two state Hubbard modell

I am given the two state Hamiltonian $$ H = U \sum_{j \in \{L,R\}} n_{j \uparrow}n_{j \downarrow} - t \sum_{\sigma \in \{\uparrow,\downarrow\}}(a_{L \sigma}^{\dagger}a_{R \sigma} +a_{R ...
2
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1answer
62 views

The spin and weight of a primary field in CFT

A primary field in Conformal Field Theory transforms as $$\phi (z,\bar{z}) =\left(\frac{dz}{dz'} \right)^h \left(\frac{d\bar{z}}{d\bar{z}'} \right)^\bar{h}\phi (z',\bar{z}') $$ under a conformal ...
8
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2answers
246 views

Does the lagrangian contain all the information about the representations of the fields in QFT?

Given the Lagrangian density of a theory, are the representations on which the various fields transform uniquely determined? For example, given the Lagrangian for a real scalar field $$ \mathscr{L} = ...
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4answers
99 views

Conceptualization and modelling of spin

I'm trying to get a decent understanding of the Bell inequality, and so am trying to understand spin both conceptually and mathematically. When I picture spin, I imagine a sphere rotating about its ...
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0answers
125 views

Why doesn't the 1 dimensional ising model have a transition temperature?

Consider a 1 dimensional chain of spins that are able to either have the value $\sigma =$ $+1$, $-1$, from now on referred to as up and down. For the Hamiltonian $H = J \sum_{i,j} \sigma_i \sigma_j$ ...
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0answers
37 views

Difference between the 1/2 representation of $SU(2)$ and the (1/2,1) representation of $SU(2)\times SU(2)$? [closed]

What's the difference between the $j = 1/2$ representation of $SU(2)$ and the $(j,j') = ( 1/2 , 1 )$ representation of $SU(2)\times SU(2)$?
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1answer
85 views

Does the $\bf{1+3}$ representation of $SU(2)$ also represent $SU(2)\times SU(2)$?

I'm a bit confused about this following issue concerning representations of $SU(2)$. Denote by 1 the 1-dimensional representation of the group $SU(2)$ (=the spin 0). Similarly, denote by 2 and 3 the ...
2
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1answer
106 views

Why does dot product equal to one? (Pauli spin matrices)

I was reading these lecture notes (NB: PDF): For spin-1/2, the rotation operator $$ R_\alpha^{(s)}(\mathbf n)=\exp\left(-i\frac{\alpha}{2}\vec\sigma\cdot\mathbf{\hat n}\right) $$ can be ...
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0answers
27 views

Coupling a ferromagnet to an antiferromagnet

Consider a system composed of a thin film of FM material on top of an AFM material. From my research I found that pinning of the FM material occurs when we cool the system from $T_N<T<T_C$ to ...
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3answers
83 views

Pions, parity, spin

Pions have odd parity ($P=-1$) which means their wavefunction is anti-symmetric $\psi(x)=-\psi(-x)$. According to Spin-Statistics theorem fermions (spin 1/2 particles) have anti-symmetric ...
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1answer
126 views

How do I derive the eigenvalues of the 1D Heisenberg model? (Bethe Ansatz)

I've been trying to work through Introduction to the Bethe Ansatz I (by Michael Karbach and Gerhard Muller) in spare time and I am having trouble deriving the eigenvalues given in equation (5) for ...
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0answers
57 views

Polarization sum rule for Rarita-Schwinger field

There are Rarita-Schwinger equations: $$ \tag 1 (p\!\!\!/ - m)\psi_{\mu} = 0, \quad \gamma_{\mu}\psi^{\mu} = 0, \quad i\partial_{\mu}\psi^{\mu} = 0. $$ So the polarization sum $D_{\mu \nu}(p) = ...
0
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1answer
52 views

Why is the unitary matrix relating the gamma matrices and their complex conjugates antisymmetical?

In Messiah's Quantum Mechanics Vol. II, properties of the Dirac matrices are derived. There is so-called fundamental theorem, which states that, Let $\gamma^\mu$ and $\gamma^{'\mu}$ be two systems of ...
2
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1answer
53 views

Infinite Larmor precession

Say an isolated electron (meaning it's not part of an atom) is at rest and we turn on a homogeneous magnetic field around it. The electrons' spin undergoes the Larmor precession (except in the case ...
2
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1answer
344 views

How can pseudospin be a vector? (Graphene)

In graphene science, I don't understand how one interprets pseudospin as a vector. I thought 'pseudospin' was the vector of Pauli matrices. So how can it be a vector that one can plot for example in ...
8
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3answers
1k views

What do the Pauli matrices mean?

All the introductions I've found to Pauli matrices so far simply state them and then start using them. Accompanying descriptions of their meaning seem frustratingly incomplete; I, at least, can't ...
4
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1answer
137 views

Misuse of $\mathbf J^2$ in classifying Poincare reps

$SO(1,3)$ has an infinite number of representations, classified by the Casimir invariant $p^2$. $SO(3)$ also has an infinite number of representations, classified by the Casimir invariant $\mathbf ...
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1answer
83 views

Entangled vectors in hilbert space

We consider a system of two particles of spin $\frac{1}{2}$, each described by the two-dimensional one-particle Hilbert space $\mathcal{H}$. Let $|\pm\rangle\in\mathcal{H}$ denote the eigenvectors of ...
0
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1answer
99 views

No need for spin?

Here's a cool idea: we don't need spin: recall that a quantum field arises from an attempt to construct an object that transforms unitarily under $SO(1,3)$ (i.e. by choosing a representation). A ...
3
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2answers
62 views

Behavior of Ortho- and Para-hydrogen in a Magnetic Field

At low enough temperature, at equillbrium, the dihydrogen molecule is predominately parahydrogen, with the spins of the two protons opposite. Does an external magnetic field alter the ortho-para ...
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1answer
41 views

J-coupling constants and nuclei with zero total angular momentum

The Wikipedia page on J-couplings states that Scalar or J-couplings (also called indirect dipole dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect ...