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Explanation for strange pattern appear on Bath tub with sand in it

We have a round bathtub with a surface radius of about 15 cm or greater. It so happens that the water that came from the tab has a little sand in it. Today when the water was about half-filled, I just ...
Young Kindaichi's user avatar
4 votes
0 answers
369 views

Is it possible to diagonalize a Hamiltonian with both quadratic and linear terms in the fermi operators?

A quadratic Hamiltonian in the fermi operators is exactly diagonalizable. The most convenient way of describing these Hamiltonians is of the form: $$\mathcal{H}=\displaystyle \sum_{j,k}(\alpha_{jk}a_{...
Arnab's user avatar
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97 views

Principles and methods of measuring the orbital angular momentum of $\rm H$-atom

When we talk about the orbital angular momentum (OAM) of the $\rm H$-atom, we mean the eigenvalues $l(l+1)\hbar^2$ of the OAM operator of the electron $\hat{L}^2$ defined from its classical ...
Soumita's user avatar
  • 577
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0 answers
260 views

Linearised diffeomorphisms on an arbitrary gravitational background Part 2

This question is a follow on from my recent post here, in the sense that I will use the notation introduced there. In that post, I considered infinitesimal diffeomorphisms of a metric $g_{\mu\nu}$ ...
NormalsNotFar's user avatar
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0 answers
186 views

Linearised diffeomorphisms on arbitrary gravitational background Part 1

Consider some spacetime $\big(\mathcal{M},g_{\mu\nu}\big)$ parameterised by local coordinates $x^{\mu}$ ($\mathcal{M}$ is a smooth differentiable manifold equipped with a Lorentzian metric $g_{\mu\nu}$...
NormalsNotFar's user avatar
4 votes
0 answers
283 views

Is there a spatial representation of the fermionic harmonic oscillator?

An answer to another question derives a Hamitonian of the fermionic harmonic oscillator in terms of a pair of position-like and momentum-like operators. These operators are, as expected, defined in ...
Ruslan's user avatar
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4 votes
0 answers
228 views

’t Hooft anomaly matching and massless baryons

In Lectures on Gauge Theory by David Tong there is statement (section 5.6.3 The Vafa-Witten-Weingarten Theorems), that: To invoke the full power of ’t Hooft anomaly matching, we needed to assume that ...
Nikita's user avatar
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4 votes
0 answers
122 views

What is the field value of a quantized fermionic field?

I'm trying to make an analogy with the phonon field. While preparing this answer I've learned that for a chain of atom-like entities, we have a probability density of the phonon field configuration: ...
Ruslan's user avatar
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4 votes
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82 views

Error of $-i$ factor in light cone indices in conformal field theory in Becker's book

In Becker's book of String theory Ch-$3$ I'm getting an error of factor $-i$ in the definition of lightcone indicies after Wick rotation. The convention of the book is following $\sigma_{\pm}=\tau\pm\...
aitfel's user avatar
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4 votes
0 answers
436 views

Is massless QED more "natural" than massive QED?

My understanding is that massive and massless QED share some key physical features including (see this PSE post and 8-4 of Ref. 1): renormalizability charge conservation The key differences of ...
H. T. Tom's user avatar
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0 answers
132 views

Cross product of operators in exponential: numerical solution

Short version: Numerical solution to a quantum system. I have my discretised wavefunction is real space $\psi(\mathbf{r})$ and in momentum space $\tilde\psi(\mathbf{k}) = \mathcal{F} \left [ \psi(\...
SuperCiocia's user avatar
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4 votes
0 answers
93 views

How did I superheat my pasta water?

Last week I had an incident in the kitchen where I almost scolded my face with hot water. What happened: I was boiling some water in one pan and a sauce with veggies and meats in another next to it. ...
supersoaker2000's user avatar
4 votes
2 answers
266 views

What are the maximum spring lengths of a double spring pendulum?

NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram For a single spring, you can simply equate ...
Christoffer Corfield Aakre's user avatar
4 votes
0 answers
213 views

Heisenberg equation of motion and continuum limit

Given the quite simple Hamiltonian $$\hat{\mathcal{H}}=\sum_n\big(\hat{S}_n^+\hat{S}^-_{n+1}+\hat{S}_n^-\hat{S}^+_{n+1}\big)$$ on a 1D spin chain, it basically interchanges two spins lying next to ...
Caesar.tcl's user avatar
4 votes
1 answer
146 views

Quantization of electromagnetic field: from free-space to media

When studying the quantization of the electromagnetic field, one seems to always derive everything for free space (no charges/currents). This involves solving Maxwell's equations to find modes (in ...
dumkar's user avatar
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0 answers
41 views

Finding symmetry from conserved quantity (reversed Noether's theorem) [duplicate]

Is Noether's theorem reversible? For example, given some conserved quantity, can you find the underlying symmetry which leads to the conserved quantity?
Jason M Gray's user avatar
4 votes
1 answer
175 views

Why is the identity not considered when expanding a $2 \times 2$ matrix in the Pauli basis? [closed]

I am aware of the expansion of a two dimensional matrix $M$ in Pauli basis given by $$ M = \sum_{\mu=0,1,2,3} c_\mu \sigma_\mu$$ with $\sigma_0 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$...
user avatar
4 votes
1 answer
355 views

Resources for $\phi^4$ and $\phi^3$ theories

I have recently completed a first course on Quantum Field Theory, referring primarily to the textbooks by Schwartz and Blundell & Lancaster. I now want to explore in more detail the scalar field ...
4 votes
0 answers
114 views

Physical meaning of a mathematical identity

I have found this mathematical identity which is related to the Caderon identities and I want to understand its physical meaning. Let $S$ be a closed surface with unit normal vector $\mathbf n$ and ...
giovanni gajac's user avatar
4 votes
2 answers
188 views

Curvature Singularities in Geodesically Complete Manifolds

Do there exist manifolds which are geodesically complete, and yet have a curvature singularity? While I don't believe this is the case, I have yet to find a proper proof of the same.
Ishan Deo's user avatar
  • 1,568
4 votes
0 answers
348 views

Explicit example of dimensional regularization involving $\gamma^5$

I'm currently reading Collins' book Renormalization, Chapter 4. In section 4.5 he introduces $\gamma$-matrices and the trace operation in an arbitrary dimension $d$. In section 4.6 he then talks about ...
Sito's user avatar
  • 1,205
4 votes
0 answers
60 views

Does bernoulli's principle exert a downward pull on a moving ship?

If you hold a spoon with its convex side next to a column of running tap water, it will be drawn to it, but does this apply to moving ships, where the hull is rounded like the spoon, and the water is ...
Toby Que's user avatar
4 votes
0 answers
213 views

Unitary irreducible representation of $SO(2,2)$

I would like to study the unitary irreducible representations of the Lorentz group $SO(2,2)$, isomorphic to the conformal group in $(1+1)-$dim. I know one could use the highest weight repn theory to ...
physicsuser's user avatar
4 votes
0 answers
176 views

Quantum field theory of electrostatics [duplicate]

I don't understand how anything in electrostatics, including electric potential and magnetic fields, is possible via the exchange of particles. Since particles are essentially fluctuations in these ...
Mike Flynn's user avatar
  • 1,156
4 votes
0 answers
294 views

Topological order and volume-law entanglement

Topological order is a property traditionally most associated with ground states of gapped Hamiltonians. However, using the notion that topological order is fundamentally about a form of "long-...
anon1802's user avatar
  • 1,320
4 votes
1 answer
236 views

Wave-function in geometric algebra, rotors and electromagnetism

I am confused by the appearance of the electromagnetism bivector in the formulation of the wave-function in space-time algebra. David Hestenes suggests that the wave-function can be written as $$ \psi ...
Anon21's user avatar
  • 1,546
4 votes
0 answers
66 views

Mean value of $[x,p]$ on an eigenstate of $x$ [duplicate]

The canonical commutation relation states that $$[x,p] = i \hbar\ \mathbb{I}$$ if we imagine to be in a one dimensional space. If we take the mean value of the commutator over an eigenstate of the ...
Francesco Musso's user avatar
4 votes
0 answers
266 views

Defining particles by their commutation/anti-commutation relations

In my studies of many-body physics, I have encountered three types of particles, which can be defined based on their commutation/anti-commutation relations. Fermions, defined by raising/lowering ...
Solarflare0's user avatar
4 votes
0 answers
247 views

Conformal Killing Group volume in string amplitude calculations

In string amplitude calculations, the volume conformal Killing group (CKG), if finite, can enter into the calculations when the number of external vertex operator insertions is less than the (complex) ...
Yuan Yao's user avatar
  • 813
4 votes
0 answers
131 views

Does the theory of holographic superconductors have any application?

I recently became aware of the relatively novel concept of holographic superconductors, and I was wondering whether anyone here has read something about experimental application of these theories. ...
xabdax's user avatar
  • 239
4 votes
0 answers
128 views

How to calculate the "vortex" correlation function in 2D free system?

I want to calculate the following correlation function in 2D square lattice: $$G(i, j, \tau) \equiv\left\langle e^{-\frac{i}{2}\left[\hat{\Phi}_{i}(\tau)-\hat{\Phi}_{j}(0)\right]}\right\rangle_{0}$$ $\...
Merlin Zhang's user avatar
  • 1,572
4 votes
0 answers
266 views

Interpretation of Feynman's propagator

What is the interpretation of the Feynman's propagator $$D(x-y) :=\langle 0 |\phi(t,x)\phi(t',y)|0\rangle~?$$ As far as I understand, it is the following. $|D(x-y)|^{2}$ is the probability density of ...
MathMath's user avatar
  • 1,113
4 votes
0 answers
47 views

Equivalence between path integral formalism and operator formalism on curved spacetimes and radial quantization for a 2D boson field

We know that the path integral formalism and operator formalism are equivalent on flat spacetime. I am wondering whether we can also make it explicit on a curved spacetime. Let us consider a concrete ...
Yuan Yao's user avatar
  • 813
4 votes
0 answers
29 views

Why aren't common magnets made of magnetite, $\rm Fe_3O_4$? Instead of ferrite, $\rm Fe_2O_3$?

Why are common, simple, cheap magnets like refrigerator magnets made (usually) of hematite ($\rm Fe_2O_3$) in some form, like 'ferrite', instead of the more magnetic and magnetizable magnetite ($\rm ...
Kurt Hikes's user avatar
  • 4,373
4 votes
0 answers
260 views

No-interaction theorem in classical relativistic mechanics

In classical relativistic Hamiltonian mechanics there is a so-called "no-interaction theorem" (see, for example, this article for a proof). Roughly, it states that if we have an $N$-body ...
Aleksandr Artemev's user avatar
4 votes
0 answers
41 views

Are atoms' most precisely known electronic transition frequencies determined theoretically or experimentally?

In principle, the electronic transition energies/frequencies for a given species of atom can be calculated by solving the time-independent many-body fermionic Schrodinger equation for $n$ electrons in ...
tparker's user avatar
  • 47.4k
4 votes
0 answers
213 views

Why is the Jordan-Wigner transformation an example of an S-duality?

The Jordan-Wigner transformation allows one to map a spin theory to a fermionic theory and, according to wikipedia, it is an example of an S-duality. In turn, according to the wiki page for the S-...
FriendlyLagrangian's user avatar
4 votes
0 answers
196 views

Derivation of Born's Approximation in 1D

I'm studying Quantum Mechanics and I'm curious about something related to Scattering Theory: Griffiths has a derivation from the Green's function to the Born's approximation in 3D but I was wondering ...
smartcookie16's user avatar
4 votes
0 answers
225 views

Marrying Statistical Mechanics and Differential Geometry

Recently, I have been trying to get a more thorough understanding of the mathematics at the fundaments of theoretical physics. I liked V.I. Arnol'd's introduction to mechanics and the book by Ratiu ...
4 votes
0 answers
64 views

Two photons Rabi oscillation

Assuming we have a 2 level system (e.g. an atom with 2 energy levels) and the lifetime of the upper level can be neglected, if we make the atom interact with a laser at a fixed frequency, we would get ...
JohnDoe122's user avatar
4 votes
0 answers
464 views

Symmetry factors for feynman diagrams from complex scalar interaction term

My question regards a quantum field theory with an interaction term $${\mathcal{L_{int}}=-\frac{\lambda}{4}\phi^\dagger}^2 \phi^2.$$ It's claimed in the solutions to a problem sheet that the one-loop ...
Nick Ormrod's user avatar
4 votes
0 answers
428 views

Slavnov-Taylor identities and the Ward identity

Suppose we have a vertex $\Gamma$ that satisfies the Slavnov-Taylor identity: $$ p^{\mu} q^{v} \Delta_{\sigma \lambda}^{\mathrm{tr}}(r) \Gamma_{\mu \nu \lambda}(p, q, r) =\frac{1}{\widetilde{Z}\left(p^...
Akoben's user avatar
  • 2,395
4 votes
0 answers
116 views

Why is the speed of light in vacuum frequency-independent?

I recently came across this paper: Mainland & Mulligan, Foundations of Physics 50(5), 457–480, "Polarization of Vacuum Fluctuations: Source of the Vacuum Permittivity and Speed of Light" ...
A. P.'s user avatar
  • 3,231
4 votes
1 answer
169 views

Sudarshan's dynamical maps

This is a question about an equation in a paper by E.C.G. Sudarshan, P.M.Matthews and J. Rau. The authors introduce the concept of dynamical maps - objects that determine the time evolution of density ...
Amey Joshi's user avatar
  • 2,235
4 votes
0 answers
147 views

Source of hierarchy problem for fermions and bosons

In the beginning of a SUSY course, we computed $1$-loop level corrections to the mass of a bosons $\phi$ and a fermion $\psi$ in the theory \begin{align} \mathcal{L} &= \bar{\psi}(i\gamma^\mu D_\...
xpsf's user avatar
  • 1,042
4 votes
0 answers
85 views

First order quantum string action

Considering this post: Quantum String action the action given is of the lowest order but the effective action, for low energies, is given by: $$ S_{ef.}= -\frac{1}{2k^2} \left( S^{(0)}+ \alpha S^{(1)} ...
MicrosoftBruh's user avatar
4 votes
2 answers
726 views

Why is $mg$ split into components instead of the tension in vertical uniform circular motion?

I am a beginner physics student. I am trying to prove that the magnitude of the tension varies sinusoidally as an object P travels around the circle or something of that sort. Thus, I am evaluating ...
user avatar
4 votes
0 answers
165 views

Renormalization in non-perturbative QFT ($n$-point function)

How does one do renormalization if one can exactly calculate the $n$-point function of QFT? Take for example QED when doing renormalization We calculate $2$ and $3$ point function Expand them in ...
aitfel's user avatar
  • 2,973
4 votes
1 answer
168 views

Interfering alternatives and identical particles in Feynman and Hibbs

I am currently self-studying Feynman and Hibbs, and in his first chapter, Feynman talked about 'alternatives' like the various possibilities or paths an experiment can take. He defined two different ...
coffeynman's user avatar
4 votes
0 answers
333 views

What is the current status or resolution of Greisen–Zatsepin–Kuzmin (GZK) cosmic-ray paradox?

The Greisen–Zatsepin–Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. A number of ...
ann marie cœur's user avatar

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