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So i need to show that the, if $\psi$ is left-handed,
$$C\gamma^0\psi^*$$
Is right-handed.
So, we know that, for any $\psi$, $P_L \psi$ is left handed.
Also, for any $\omega$, is right-handed, $P_R \omega$ is right-handed
And so, here, i need to show that
$$P_R C \gamma^0\psi^* = P_R C \gamma^0(P_L \psi)^* = P_R C \gam... |
In many circumstances we take it that when object $A$ applies a force on object $B$ and vice-versa, the two forces are central forces or along the line joining $A$ and $B$. This is used to derive conservation of angular momentum from Newton's laws.
However, people have also said that this isn't always true. In this pos... |
A large number of mechanisms whereby magnetic fields are generated in the early universe involve the breaking of the conformal invariance of the electromagnetic action. Why is it so? What is the problem with a conformally invariant electromagnetic action in regards to primordial magnetogenesis?
|
This is a question about bridging reality to theory after attending a maths lecture on the ising model. I assume that the term "ising model" may be a bit ambiguous, but I think that we considered the simplest possible setup (see the footnote for more details).
I assume that we can not measure the microstate of the syst... |
I want to figure out how much pressure is being imparted on a plate perpendicular to flow in a pipe. Similar to this setup,
Some initial thinking is that I could just measure the static pressure before and after this area and that pressure difference would be a pretty good analog for the psi being experienced by the p... |
A common statement is that post-SSB electroweak gauge bosons are linear combinations of pre-SSB gauge bosons.
It is also usually stated that pre-SSB bosons can also be thought of as linear combinations of post-SSB bosons - it's just a choice of basis, after all.
However, with a choice of basis, there usually comes an o... |
I understand how a bit flip code in a 2D lattice is like a 2D Ising model in Kitaev's 2001 paper Topological Quantum Memory. But generally, can someone explain how quantum error correction connects to those statistical/thermal physics models and what are phase transitions? I understand quantum error correction like sur... |
I've been looking at all this for the last 2 days and I can't sleep anymore unless I understand it. I think I come to the below conclusion. Much appreciated.
Planck says that the below formula returns the following: Energy density of radiation per unit wavelength(I missed other units, not needed for now) is given by:
$... |
Flexible foam has shortest path from Point-A to Point-B. When the foam is not curved (space-time is not curved), the shortest path is Path-1 (straight line - before curving the foam). But if the foam is curved, the shortest path is Path-2. If I think of the foam as space - should the shortest path (or geodesic) remai... |
If I contact electrify some dielectric powder, filter out the negatively charged part and fill it inside a hollow disk made of insulator material and seal it up, will there be an electric field around the disk?
I know Faraday cages don't, but they are metal. My question is about a faraday cage made of insulator materia... |
I want to use quantum Monte-Carlo results to benchmark an algorithm for the Bose-Hubbard model. There are so many QMC methods in the market, so which one is the simplest one? I want the ground state energy, some simple correlation functions. I thought of using the open toolbox of ALPS, but was frustrated by the lengthy... |
here is the topic of the problem:
You are given $2$ baseballs (consider them as perfect solid spheres) have equal properties with mass $m = 0,142kg$, radius $r_0 = 0.037m$ in the space and thay are $1m$ apart (the distance between their centres of mass), both of their initial velocities are $0$, calculate how long th... |
I was solving some physics problems and saw a question that used a formula for current flowing in $LR$ circuit in $t$th second.
The equation is given as:
I was wondering how this equation is derived as I've never seen it being used before.
Any resources for further information would help too.
|
There's a horizontally placed rod, fixed on a vertical axis at one end, so it doesn't fall on the ground with acceleration $g$, and stays horizontal, there is a bead (mass $m$) near that end point through which the rod passes, and the bead is free to move along the rod without friction. If the rod has constant angular ... |
I read EM waves carry momentum and can exert pressure, if this is the case can ejecting them be used to generate thrust? Radiation pressure is cited as a real thing but I read about the EM drive and it was shown to not generate measurable thrust.
|
Negative sign is used for electric potential belonging to negative charge but whenever in electrostatics the "negative" sign is referencing for example: force means its attractive or repulsive. Then electric potential is a scalar quantity why do we need to make it so that we need to specify it as attractive or repulsiv... |
A Boeing 747 with a wingspan of 64.4 m is flying in this area due north at 275 m/s. The earth's magnetic field at the plane’s location has a magnitude of 52.5 µT. Although it points north, it is deflected down 64.5° below the horizontal.
a. Determine the induced emf across the plane's wings.
b. Which wing tip is at th... |
When we learned about AC L-R-C circuits, there is a phase difference in the voltage across the inductor and capacitor with the current. We were told that representing these phase differences on the complex plane and extracting the real part can make calculations less complicated. However, I see that the impedance of th... |
I am reading section 4.1.3. of Poisson's book "A relativist's toolkit" and I am a bit perplexed by condition (4.13), namely that the variational principle for General Relativity has to be subjected to the following Dirichlet boundary conditions
$$
\delta g_{\mu\nu}=0
$$on the boundary of spacetime. These conditions fix... |
Picture a chair with 4 perfectly vertical legs joined at the top by a rail between each pair. The top face of each rail is a perfect 90-degree rectangle. If we lean each leg a few degrees towards the centre, the top face of each rail becomes a trapezoid with angles greater than 90-degrees at the 2 outside corners and l... |
For information isospin for $u$-quark = 1/2, isospin for $d$-quark = -1/2 and isospin for $s$-quark = 0.
Lambda Baryon consists $uds$ quarks,therefore sum isospin 1/2-1/2+0=0, It true.
But sum isospin for Sigma Baryon consists $uds$ quarks too isospin equal to 0 ,but data written isospin for it the particle = 1...A co... |
I am analyzing the band gap of $\rm TiO_2$ samples made by ALD and titanium anodization. My doubt is that in the samples made by titanium anodization, two linear regions appear in the Tauc plot, and I am unsure if this results in two different band gaps because the sample contains both crystalline and amorphous phases;... |
My question is wether one can use a one dimensional simulation for the Kronig Penney model in order to study a 3 dimensional crystal. I have seen that the problem of a 3 dimensional crystal can’t be reduced in a trivial way to three 1D problems. For example, supposing a cubic well potential, it can be factorized as a p... |
I have this 5-dimensional metric
\begin{equation}
ds^2= N^2(z)dz^{2} + a^{2}(z) q _{\mu\nu}(x) dx^{\mu} dx^{\nu}
\end{equation}
I'm trying to understand what is meant by a lapse function. Would $N(z)$ be classed as one or, as it does not depend on time but rather the 5th dimension, is it just another warp factor?
|
For a rigid smooth rolling ball rolling down a ramp (as seen above), the acceleration of the center of mass is given by:
$$a_{\text{com}, x} = - \frac{g \sin θ}{1+\frac{I_\text{com}}{MR^2}}.$$
However, if $θ=0$, the acceleration would be zero, meaning that the ball would travel at constant velocity. Why wouldn’t there... |
(The context of this topic is that, section 20.6 of this book derives Maxwell equations from Einstein field equation.)
On page 472~473 (section 20.6) of Misner, Thorne, and Wheeler's book Gravitation, it reads:
Step five: The determinant of the coefficients in the four equations (20.38) for the four unknowns (20.39) h... |
I would like to discuss the nature of the following effect. At whatever angle and with whatever initial speed the particle fly into a uniform gravitational or electric field, over time the directions of the instantaneous velocity and field strength converge. The kinematics and dynamics here are trivial, but I wondered:... |
I'm learning the QM propagator and the first example is of course the free particle: $\hat{H}=\frac{p^2}{2m}$, then the new wavefunction is found by:
$$\psi(x,t)=\int dx_0\;K(x,t;x_0,t_0)\;\psi(x_0,t_0)$$
and $K=\langle x|U(t,t_0)|x_0\rangle;$ Thus evaluating the time-evolution operator and etc we find:
$$\psi(x,t)=\in... |
I am studying the Tight Binding Method (LCAO) to calculate bind structure. I understand the general idea, but I am having trouble calculating the overlap integral. In particular, I am not sure on what criteria to use to decide on what potential to use.
Is that always an approximation, and thus the decision is taken bas... |
Assuming that there is an observer S in a train that is equipped with a cannon moving to the right relative to another observer S' in a train moving to the left relative to S, which is also equipped with a cannon.
Note: the situation assumes force of gravity = 0.
At some point the S train fires a cannon ball towards S'... |
One way to write the action for a particle moving in curved spacetime is to use the proper time as a parameter and the metric tensor as a function of the coordinates. This leads to an action that is proportional to the length of the geodesic followed by the particle. Another way to write the action is to use a differen... |
Sabine Hossenfelder says time dilation is due to acceleration in the twin's paradox. Is this true?
At 12 minutes into this video https://www.youtube.com/watch?v=ZdrZf4lQTSg, Hossenfelder states, "This is the real time dilation. It comes from acceleration."
Looking at the equations for time dilation, time dilation come... |
DFT calculations with GGA functionals result in bulk germanium being metallic. Has anybody ever tried to correct this result by computing the bandgap with DFT+U in Quantum ESPRESSO?
I tried but failed. I suspect this is due to the fact that the states near the gap aren't related to the 3d shell that receives correction... |
I am currently studying the basics of Quantum Electrodynamics, and I have learned from this that photons are the quanta of excitation for given field modes. In other words, when a photon is absorbed, the amplitude of oscillation at that frequency for the EM field goes down by a fixed amount. However, when I imagine a s... |
The concept of a wave packet is universally introduced in introductory QM classics in order to "localize" a particle in free space (i.e. $V(x) = 0$ in the 1-Dimensional Schrodinger Eq.). Many textbooks use the example of the Gaussian wave packet most often written as
$$\psi(x,t=0) = e^{-ax^2} \cdot e^{\imath k_{o} x} ... |
I performed a thought experiment.
Consider a body $A$ and another body $B$.
Body $B$ is moving at velocity $v$ in direction $x$ with respect to $A$. This implies that body $A$ is moving at velocity $v$ in direction $-x$ with respect to $B$.
If work is done on body $B$, its velocity increases to $(v+dv)$ with respect to... |
Is it right to think that an isolated electron is always in an eigenstate of the spin observable along $some$ axis? For instance, even if the electron is not in an eigenstate of $S_x, S_y,$ and $S_z$, there would be some axis $i$ so that the electron is in an eigenstate of $i$-spin. Is that right?
|
In the theory of Bravais lattices, it is immediate to associate with each set of primitive unit vectors a primitive unit cell (see e.g. here). It is (probably) not hard to show that this map is an injection from the set of sets of primitive vectors to the set of primitive unit cells. But is this a surjection, or does t... |
If an object B does NOT move away from us, doesn't matter whether it's 10 km or 5,000,000 km away from us, I think redshift wouldn't happen.
Now, if the object is moving away from us, it's said that redshift happens. As we know, redshift is the increase in wavelength. I wonder if this is happening due to the speed, le... |
hope you are well,
So , in my physics class we use graphical method to determine the radius of curvature and as we know this method isn't very accurate, so when I watch a YouTube video I find this relation:
So is this relation always true? Because I was able to find it before watching the video, but with the condition... |
I was reading Prof.Tong's notes where everything went smooth until when he just stated that for Kruskal coordinates $$U=-\exp(-u/4GM), V=\exp(v/4GM),$$ the horizon $r=2GM$ of Schwarzschild metric becomes $U=0$ or $V=0$. For reference, $u=t-r_\star,~v=t+r_\star$, where $$r_\star=r+2GM\ln|\frac{r}{2GM}-1|.$$
He proceeded... |
Why is the binding energy of the electron in atomic hydrogen not the same as the ionization energy of hydrogen? The binding energy is $\approx 13.605874\text{ eV}$ (accounting for fine structure, see also the value in Griffiths'), and the ionization energy is $\approx 13.59844\text{ eV}$ NIST.
The ionization energy for... |
I am currently studying Magneto-optical trap(MOT). When a photon absorption takes place, there is a transition of an atom from an initial state to a final state (more accurately an electron in the atom goes to an excited state). We can consider the superposition of the two states as a new state with frequency $\Omega=\... |
I am reading about this apparatus at Wikipedia: https://en.wikipedia.org/wiki/Magneto-optical_trap
And there is the following sentence which I don't understand:
"As atoms travel away from the field zero at the center of the trap (halfway between the coils), the spatially-varying Zeeman shift brings an atomic transitio... |
Say we have a string of fixed size on a violin. If I were to play it open (without pressing down on it) it would vibrate at a certain frequency. If I were to play it whilst pressing down on the middle, it would obviously vibrate at a different frequency. Is this because I have changed the length of the string that is a... |
The differential relations for Helmholtz free energy are
$$S = \left.-\left( \frac{\partial F}{\partial T} \right) \right|_{V,N}$$
$$P = \left.-\left( \frac{\partial F}{\partial V} \right) \right|_{T,N}$$
$$\mu_i = \left.\left( \frac{\partial F}{\partial N_i} \right) \right|_{T,V,N_{j\ne i}}$$
These are valid for a sin... |
I know that in a reversible isobaric process, the enthalpy change of the system is the change in heat for that system. What happens if the process is not reversible? I.e only the outside pressure is constant, for example atmospheric pressure?
For example, in a container with a movable piston on the top, a gas phase che... |
I have started going through A. Zee's "Einstien Gravity in Nutshell" after a good number of years away from studying physics (perhaps too many) and I have been stuck on a derivation that I would appreciate some assitance in.
In the solution to Exercise 3 in Chapter I.1, Zee finishes the Newtonian derivation of the def... |
Based on my understanding in frictionless banking, the vertical component of the normal force must be equal to weight force for the horizontal component be the centripetal force. This means that the normal force has to be greater in magnitude than the weight force. However, a given for centripetal motion is that the ca... |
I am using Kittel's book. It says that the relationship between the distance of donor level to the bottom of conduction band is related to the ionization energy, but it does not say why.
|
Modelling the impurity as a hydrogenic system in a uniform dielectric of permittivity $\varepsilon$, the donor ionization energy is given by a modification to Bohr's result for the hydrogen atom:
$$E_d=\frac{e^4m^*}{32(\pi\varepsilon\hbar)^2}$$
Here $m^*$ is the effective mass of the donor electron.
If we interpret thi... |
The vector representation of Coulomb's law uses a vector between the position vectors of the charges at rest. However, my teacher and a few books use the convention that vector $\vec r_{21} = \vec r_1 - \vec r_2$, while other books use the convention that,
$ \vec r_{12} = \vec r_1 - \vec r_2$. Which is correct? Or can ... |
In my experiment, I have a signal y(t) that should be given by a continuous sum of exponential decays:
$y(t) = \int_a^b n_0(E) \exp[-t/\tau(E)] {\rm d}E$
However, I see just a single exponential decay. My ansatz is that what I observe is the following:
$N_0 \exp(-t/\bar{\tau}(E))$
, where $N_0 = \int_a^b n_0(E) \,{\rm ... |
In Bailin & Love (Chapters 5-6) a formula very similar to the LSZ reduction formula is derived before any discussion of renormalization (Ch. 7).
They construct a generating functional for the S-matrix as a path integral over asymptotically free fields (those which tend to the in- and out- fields in the adiabatic limit)... |
I'm reading Conceptual Framework of QFT by Anthony Duncan, and at the bottom of page 77 he says
The translation of a physical system by displacement $\vec a$ is of course effected by the unitary operator
$$U_{trans}(\vec a) = e^{-i\vec a \cdot \vec p}$$
where $\vec p$ is the total 3-momentum vector for the system.
I ... |
When we bring a charge -Q close to a plate some positive charge is induced on the near surface of the plate to this external charge and some negative charge on the other farther surface. I believe this happens because of the electric field produced by -Q.
But when the plate is grounded why don't electrons flow from/int... |
After answering this question, I am now confused about whether the change in enthalpy equals the total amount of heat that flows in a system:
$$\Delta H=Q_\mathrm{net}^\mathrm{in}=Q_\mathrm{rev}^\mathrm{in}-Q_\mathrm{irrev}^\mathrm{out}$$
or the total amount of heat that flows in and out a system:
$$\Delta H=Q_\mathrm{... |
So i need to find the eigenfunctions (in momentum space) of the harmonic oscilator unidimensional.
We know that $(m=\hbar=1)$, in position space, $\psi(x) \propto e^{-x^2} H_n(x)$.
Now, basically the equation in momentum space, for the harmonic oscilator hamiltonian $H = \frac{p^2}{2} + \frac{x^2}{2}$ is equivalent in ... |
For simplicity, let us consider the 2D case. Suppose O is a five-fold axis or point. If $P_0$ is another five-fold axis, then by the rotation symmetry around O, we can get in total five five-fold axes, $\{ P_0, P_1, P_2, P_3, P_4\}$. Now we can rotate the system around these five points, and we will generate many more ... |
This is a dumb question, but I am pretty certain that water vapour has higher energy than water as you do work in raising the intermolecular potential energy. However, water vapour molecules at 100$^{\circ}$C have the same kinetic energy as water at 100$^{\circ}$C and since internal energy for an ideal gas is only its ... |
In all the flow dynamics textbook I have consulted the gas flow is driven by pressure gradients. Is there a way to analyse a molecular gas flow when also temperature and density gradients exist?
|
If a body with mass is a finite distance away from another body with mass, then they possess a gravitational potential energy. Consider that both the bodies didn't have any energy previously, but when they are in one another's gravitational influence they are gaining gravitational potential energy. Is this energy comin... |
In the International Physics Olympiad problem 1998: rolling of a hexagonal prism:
it states that conservation of angular momentum is applicable since the total external torque is 0. How is this the case? Wouldn't there be a torque due to the gravitational force about the axis of rotation of the hexagon? Is it because ... |
I am currently reading about Clifford groups/gates and am having trouble understanding how a transformation can or cannot preserve conjugation. For example, Clifford transformations preserving conjugation for Pauli operators.
|
I know that the Faddeev-Popov path integral is gauge invariant. But how does one show that
\begin{equation}
I = \int \mathcal{D}\mathcal{A}_\mu \bigg|\frac{\delta\mathcal{G}}{\delta{\omega}}\bigg|\delta(\mathcal{G}) \exp(- S_\text{YM}[A_\mu])
\end{equation}
is independent of the gauge choice $\mathcal{G}$? Here $\omeg... |
How to calculate the static spin structure factor in a system with a large unit cell? I know the basic definition of it, however, I am not sure what change would happen for a large unit cell.
The static spin structure factor is a quantity of interest in condensed matter physics, which provides information about the spi... |
How do one compute the $3n-j$ symbols using the young tableau method,for a $U(n)$ ?
Edit
$3j$ symbols were first introduced by Wiegner which are related to C.G. coefficients, similarly $6j$ symbols are related to racah coefficients, similarly there are $9j$ symbols and so on, for short 3n-j symbols. They are useful in ... |
I'm doing a physics lab and I have a question that asks me to linearize the expression of time (it gives me the equation for time) in function of the mass.
I don't want any solution, just want to know what linearization means in physics (I know its something graph related).
|
This might be a dumb question, but I've been trying to figure it out for a while now. If you got two plate capacitors placed in parallel in a grounded box, one with a potential of -1, and one with potential +1, how can i solve the Laplace equation inside the box?
Many thanks for any help, and if needed, I can send some... |
We know velocity of a planet in an elliptical orbit is given by:
$$v^2 = GM * (\frac{2}{r} - \frac{1}{a})$$
in an elliptical orbit. [Here r is distance between particle and sun] source
We also know, areal velocity in an elliptical orbit is given by
$$\frac{dA}{dt} = \frac{1}{2}vr$$
By putting value of velocity in this ... |
I was solving a question of rotational motion given below:
Four point masses, each of mass $m$, are fixed at the corners of a square of side $L$. The square is rotating with angular frequency $ω$, about an axis passing through one of the corners of the square and parallel to its diagonal. The angular momentum of the s... |
Why it is not possible to determine intrinsic parity of the $^+$ mesons from the $^+ → ^+ ^0$ decay?
|
I am trying to work through a proof of causality in special relativity using the Lorentz transformations, but there is one assumption that is necessary for the proof that I don't see as correct.
The question I am working on specifically asks: "In frame S, event A causes event B and therefore occurs before event B. Show... |
To calculate the entropy change of the universe when a closed system undergoes an irreversible process, one must choose a reversible process and calculate the following integral
$$\Delta S=\int \frac{\delta Q_\mathrm{rev}}{T}$$
However, it contradicts the fact that during reversible processes, $\Delta S=0$. Am I misund... |
As the question title says, I want to know how to measure the partial pressure of a gas (in a vessel containing a mixture of many gases). I wonder how to measure it? Please help me answer this question
|
The definition of degeneracy and density of states (DOS) looks resembling to each other, what is the relation and difference between these two concepts? And is there a mathematical relation or formula between these two physical quantities?
|
THE PROBLEM
Suppose we are in stationary conditions, in which case the following Maxwell Equations hold:
$$
\underline{\nabla} \cdot \underline{B} \equiv 0 \\
\underline{\nabla} \times \underline{B} = \frac{\mu_0}{4\pi} \underline{J}
$$
Let $\phi(\underline{x}):=R\underline{x} + \underline{a}$ be an isometry of $\Bbb R... |
I learnt that pure rotational force can be caused by only couple force , two forces acting in opposite direction which are equal in magnitude in 2 different points at a system.
But I am trying to understand how a couple force is created in this steel ruler as shown in this video
The scale is bent in a way such that onl... |
I understand that Cosmic Microwave Background Radiation Map provided by WMAP survey in HEALPix pixelization format is nothing but an array of temperatures associated with the cmb radiation coming from each line of sight i.e. we have a temperature value for each pixel of the map. The map array values are something like ... |
I'm reading Statistical Physics of Particles by Mehran Kardar for my Statistical Mechanics class. In the Interacting Particles section, he discusses about writing the partition function $Z$ in terms of the cumulant expansion for the interacting potential $u(\vec{q_1},...,\vec{q_N})$:
$$\ln{Z}=\ln{Z_0}+\sum_{l=1}^{\inft... |
For thin accretion disks the radial pressure gradients are taken to be negligible and so only the gravitational force is considered. Why is this assumption justified?
|
So, we know from Noether's theorem that the translational symmetry of space (nothing changes if our physical system is located in a different position) implies the conservation of a quantity we call momentum.
We also know that conservation of momentum is equivalent to Newton's third law.
So my question is: Does the phy... |
The Langevin equation for a Brownian particle without the friction term is:
\begin{equation}
m\dot{v}=F(t)
\end{equation}
Where $F(t)$ is the random force acting on the Brownian particle due to collisions with the heat bath particles. With the usual assumptions that:
\begin{equation}
\langle F(t)\rangle=0, \langle F(t)... |
In some manipulations in the free electron theory, one initially has the energy density $u$ of the system as a function of temperature and it's desirable to have the entropy density $s$ (both volumetric densities). The starting point is generally the identity
$$\left(\frac{\partial u}{\partial T}\right)_n = T\left(\fra... |
From here, like in the textbook I am using (Nelkon and Parker 7th edition), they decided to use Resistance 2 as the numerator. Why not resistance 1? I initially thought that the resistance choosen should depend on the direction of flow of conventional current, but my textbook does not consider this as a factor in deriv... |
Black body is an object, hence it's made of atoms. Depending on what atom it consists of, that's how the emitted spectrum should be in my opinion. If it contains hydrogen, absorbed light on black body would excite electrons and electrons of hydrogen can only produce certain wavelengths. Hence, there must be dark lines ... |
I am reading this article discussing quantum field theory. The author mentioned that 'a particle has a certain spin because its underlying field has a respective spin'. I think intuitively this makes sense because particles are excitations of the underlying quantum field. However, I was thinking if I can come up with a... |
About unpolarized electromagnetic field, are the electric and magnetic fields still can be distinguished from each other? Are there pictures that show the orientations or angles of electric fields and magnetic fields if the electromagnetic field is unpolarized? I prefer pictures because mere calculations do not show an... |
In some phenomenology papers in particle physics, often the cross section is shown as a function of some parameter of the model given a certain centre of mass energy of a specific collider. However, sometimes the product (?) of two colliders is shown, (collider1)x(collider2). What does that mean? Is this some kind of... |
I rub a piece of glass against some silk. Normally, left in open air, it would lose its acquired charge. What will happen if after rubbing, I immediately seal it inside a sphere made of insulator material (kind of like a "Faraday cage", but not metal)? Will the glass piece stay charged forever? Assume that no air enter... |
Often one finds in physics textbooks that arguments will be made "to order $n$". I am not sure on what the procedure or argument ought to be when we have some denominator dependence though. As an example, consider the function of temperature
$$f(T) = T\frac{c(T)}{u(T)}$$
where $c(T) = A_cT + B_cT^3 + C_cT^5...$ and $u(... |
The Schwarzschild horizon $r=2GM$ should have normal vectors proportional to $$\nabla^\mu r=g^{\mu \nu}\delta^r_\nu$$ Isn't it? Then I fail to understand how could one have Killing vector field $\partial_t$ being normal to the surface.
More generally, given a surface $$\Sigma:f(x)=0,$$ how could we tell if there is a ... |
Are all rates in physics a scalar, a vector or both?
It seem to me like all rates in science are vectors.
Examples of rate that are vectors are rate of charge flow, rate of heat transfer, rate of mass flow, rate of change of displacement and rate of water entering a water tank (+ve for water entering the tank and -ve f... |
I am uncertain how the first law of thermodynamics $\Delta U=Q+W$ works for reversible and irreversible processes.
I understand $U$ is a state function, ie. the value of $\Delta U$ does not depend on whether the process is reversible or not.
For any process, the change in a system's entropy can be written as
$$\Delta S... |
Consider a certain amount of liquid, and also a solid body of certain mass. The solid is at a lower temperature than the liquid. The goal is to cool the liquid by submerging the solid, and they can't dissolve. The liquid doesn't solidificate either.
The solid can be divided into pieces, and these can be submerged one b... |
Imagining a non-embedded manifold that forces a reformulation of the tangent space at a point as partial derivatives of any arbitrary smooth functions on the manifold along a parameterized curve is mind-blowing. However, the idea of a derivative along a path integral being akin to a velocity or a tangent is helpful.
Un... |
According special relativity, the clock ticks slower on spaceship moving at relativistic speed because the light travels a longer diagonal distance with respect observer on ground.
If light is a wave then how it gains the velocity of spaceship? such that it travels in a diagonal.
can light make an interference pattern... |
I have a worked example from a recorded lecture and lecture notes which I am having difficulty with regarding Rectilinear Motion in Mechanical Dynamics.
When I asked my lecturer about the following, I was advised that since velocity is a function of time and not a single constant scalar, one cannot treat the units as c... |
The electronic properties of (crystalline) solids is typically described in terms of the electronic band structure, which reveals many properties of the electronic structure such as the band gap, electron- and hole effective masses etc. For some of these concepts to be well-defined, however, it is necessary that the ba... |
The QED Ward identity for the vertex reads
\begin{equation}
q^\mu\Gamma^\mu(p,p')=\Sigma(p)-\Sigma(p')
\end{equation}
with $q=p-p'$. In the limit $q\rightarrow 0$,
\begin{equation}
\Gamma^\mu(p,p)=\frac{\partial}{\partial p_\mu}\Sigma(p).
\end{equation}
These identities can also be proven diagrammatically, and relate s... |
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