All Questions
234,133
questions
4
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89
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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 ...
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_{...
4
votes
0
answers
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 ...
4
votes
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}$ ...
4
votes
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}$...
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 ...
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 ...
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: ...
4
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0
answers
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\...
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 ...
4
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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(\...
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.
...
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 ...
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)$$
on a 1D spin chain, it basically interchanges two spins lying next to ...
4
votes
1
answer
146
views
Quantization of electromagnetic field: from free-space to media
When studying the quantization of the electromagnetic field, one seems to always derive everything for free space (no charges/currents). This involves solving Maxwell's equations to find modes (in ...
4
votes
0
answers
41
views
Finding symmetry from conserved quantity (reversed Noether's theorem) [duplicate]
Is Noether's theorem reversible? For example, given some conserved quantity, can you find the underlying symmetry which leads to the conserved quantity?
4
votes
1
answer
175
views
Why is the identity not considered when expanding a $2 \times 2$ matrix in the Pauli basis? [closed]
I am aware of the expansion of a two dimensional matrix $M$ in Pauli basis given by
$$ M = \sum_{\mu=0,1,2,3} c_\mu \sigma_\mu$$
with $\sigma_0 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$...
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 ...
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.
4
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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 ...
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 ...
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 ...
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 ...
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-...
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 ...
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 ...
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 ...
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) ...
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.
...
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:
$$G(i, j, \tau) \equiv\left\langle e^{-\frac{i}{2}\left[\hat{\Phi}_{i}(\tau)-\hat{\Phi}_{j}(0)\right]}\right\rangle_{0}$$
$\...
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 ...
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 ...
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 ...
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 ...
4
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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 ...
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-...
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 ...
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 ...
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 ...
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:
$$
p^{\mu} q^{v} \Delta_{\sigma \lambda}^{\mathrm{tr}}(r) \Gamma_{\mu \nu \lambda}(p, q, r) =\frac{1}{\widetilde{Z}\left(p^...
4
votes
0
answers
116
views
Why is the speed of light in vacuum frequency-independent?
I recently came across this paper: Mainland & Mulligan, Foundations of Physics 50(5), 457–480, "Polarization of Vacuum Fluctuations: Source of the Vacuum Permittivity and Speed of Light" ...
4
votes
1
answer
169
views
Sudarshan's dynamical maps
This is a question about an equation in a paper by E.C.G. Sudarshan, P.M.Matthews and J. Rau. The authors introduce the concept of dynamical maps - objects that determine the time evolution of density ...
4
votes
0
answers
147
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Source of hierarchy problem for fermions and bosons
In the beginning of a SUSY course, we computed $1$-loop level corrections to the mass of a bosons $\phi$ and a fermion $\psi$ in the theory
\begin{align}
\mathcal{L} &= \bar{\psi}(i\gamma^\mu D_\...
4
votes
0
answers
85
views
First order quantum string action
Considering this post: Quantum String action the action given is of the lowest order but the effective action, for low energies, is given by:
$$ S_{ef.}= -\frac{1}{2k^2} \left( S^{(0)}+ \alpha S^{(1)} ...
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 ...
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 ...
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 ...
4
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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 ...