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According to the Wikipedia page on Radius of Gyration:
One can represent a trajectory of a moving point as a body. Then radius of gyration can be used to characterize the typical distance travelled by this point.
So does it mean that assuming the trajectory of any moving point as a body and finding its radius of gyra... |
Some books assumes molecules flowing in the x direction for a stationary newtonian fluid, it is defined a microscopic control volume and they says in the top cover (of the box) at level $y_0$ molecules of mass m have more momentum $m v_{x+}$ than molecules below $m v_{x-}$, I agree but they also refers to momentum con... |
The definition of Kitaev chain and the solution is in this article:
https://topocondmat.org/w1_topointro/1D.html
The Hamiltonian has the form:
$H = -\mu\sum_n c^\dagger_n c_n -t\sum_n c^\dagger_{n+1} c_n +\Delta\sum_n (c_n c_{n+1}+\text{h.c.})$
I am interested in the case of periodic boundary condition where the fam... |
Suppose you have a pool table (with no pockets) with a ball in the middle and another ball in one corner. The ball in the corner is hit toward the middle ball. The balls collide and each ball ends up on opposite sides of the table. The 'x-position' of each ball along the walls at each end of the table is observed fo... |
I'm trying to solve numerically the motion of a rigid body in a fluid. To this end I have to solve the fluid PDEs, and at every time step the 6 ODEs of the rigid motion degrees of freedom:
$$(m\mathcal{I} + \mathcal{A}) \frac{d\mathbf{U}}{dt} + \boldsymbol{\Omega} \times ((m\mathcal{I}+\mathcal{A}) \mathbf{U}) = m_1 \m... |
I've been thinking about cosmological redshift lately and in particular its effect on the apparent speed of separation. In particular, let's imagine a source which emits light pulses with a period of $\tau_e=1$ to a source a distance $D$ away at present. If a pulse were emitted at some time $T$ then the distance betwee... |
It is well established that ionising radiation is radiation with sufficient energy to remove an electron from an atom. Although since the ionisation energy differs between atoms I'm unclear on how we define at what energy radiation becomes ionising.
So my question is how do we define radiation as ionising or not based... |
From statistical mechanics, one could calculate phase transition of gas and liquid from Van der Waals's equation.
The characterization was from $p(v)\sim v$ diagram, i.e. the compressability.
However, how to characterize the transition from liquid to solid? i.e. from usual experience the compressability of liquid and... |
I am a developer working on a software application which incorporates some basic acoustic simulations. I am trying to assist another developer in implementing equations provided to us by the team's math and science expert (who is unfamiliar with the specific programming language we're using for the project and can't im... |
Question
What qualifies as a "cosmic structure" in cosmology?
See: https://en.wikipedia.org/wiki/List_of_largest_cosmic_structures .
How is the term defined? Does the term focus on the mass/energy within the structure or the "shape" of the structure, geometrically? Is a cosmic structure a geometric region (such as ... |
Image source: https://en.wikipedia.org/wiki/File:Atwood.svg
In setups such as the one shown in the diagram above, why is it that the force on the pulley by the rope is twice the tension in the rope? (in the case where both pulley and rope are massless and frictionless)
I always thought of it as making intuitive sense ... |
Consider the basic schematic for photoelectric effect without battery
Initially, light falls on a plate charging it positively (because it ejects electrons) and those electrons reach the other plate charging it negatively, but since they are connected to each other, the excess of electrons in one is compensated by the ... |
I was told estimation of partition functions without resorting to MCMC was still an open question in physics about a year and a half ago. An example is that say you have some physical model that obeys a Boltzmann distribution: $p(x) \sim \frac {e^{f(x)}}{Z(x)}$. The objective is to calculate $Z(x)$, without resorting... |
Leonard Susskind had recorded many video lectures across many branches of physics and all of can be found on this official website. Pdf versions of three of the video courses (taken and shared by some generous person) are available in the following links to download for free
Statistical Mechanics and Thermodynamics,
G... |
I was just given a question using Bernoulli's principle that gives you the pressure of water (e.g. $1,000,000 \mathrm{Pa}$) in a hose, and asks for the speed of the water after the water has left the hose if all the pressure potential energy was converted to Kinetic energy, I assume you would solve using:
$\text{Pressu... |
I have a question regarding the usage of the centre-of-mass definition (which I thought required the total momentum, $p_T=0$) in the solution to the question given below:
A particular centre-of-mass energy is needed to create a new particle. We will do the calculation in a so-called fixed-target configuration.
A parti... |
The definition of refraction which I found on wikipedia is
In physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium.
But in the below case, there is no change in direction of light. So, is this also refraction?
|
I was looking a few videos on youtube and I came across a video named the speed of light is nothing related to light. In the video, it was said that speed of light is actually speed of causality so what actually is causality?
|
If there is a point charge inside a shell conductor for example, making a Gaussian surface around the point charge will tell me there is a non-zero flux, meaning non-zero electric field inside, but how is that possible if electric field inside any conductor is zero because charges on the inner surface redistribute to c... |
I came across with the following questions in reading Altland and Simons page 186
https://books.google.cl/books?id=0KMkfAMe3JkC&pg=PA188&lpg=PA188&dq=Pauli+paramagnetism+altland&source=bl&ots=8Z4XEHF2MB&sig=ACfU3U1GnQUI-hZqDQLRe808zjVzTAVbnQ&hl=es&sa=X&ved=2ahUKEwijwPaD4qXpAhWWEbkGHdhuCWQQ6AEwAHoECAoQAQ#v=onepage&q=Pau... |
I'm reading a magazine article on 3d orientation and want to know what the mathematical issue is and where to read about it, preferably a theorem title that I can google or a topic and textbook:
It’s possible to prove that no three-scalar parameterization of 3D
orientation exists that doesn’t suck, for some suitably... |
Mass M is fixed to the end of a rod of length l and negligible mass that is pivoted to swing from the end of a hub that rotates at constant angular frequency ω, as shown in the drawing. The mass moves with steady speed in a circular path of constant radius. The problem is to find α, the angle the rod makes with the ... |
Consider a current-carrying ring as shown, having no resistance. Now, we can say that the fields around this would be constant. Thus, we must expect this system not to radiate energy. Considering it in another manner, the charges present inside are moving on a curved path with drift velocity. Their motion is thus acce... |
Suppose I have an operator given as $$T_a \psi(x) = \psi(x+a)$$ Is there a way I can get the operator in Dirac bra-ket notation. I am a newbie to QM. Please do give me hints.
|
Consider a grounded spherical shell conductor (radius $R$) with a point charge $q$ inside a distance $a$ from the center. In order to calculate the electric field inside we can place an image charge with charge $q'=-q\frac{R}{a}$ and position $d=\frac{R^2}{a}$ but if we apply Gauss law around the sphere, the electric ... |
What does it mean when without flow, the pressure must be transmitted normal to solid boundaries and arbitrary surfaces in a fluid?
Also, the pressure at a point is the same regardless of orientation of the area upon which it acts?
|
I have been taught that an electron has a wave-particle duality nature and an electron behaves as a wave when traveling.
I do also know that a wave is some kind of vibration, either it be a vibration of a vector field, or of a particle.
My questions is: If an electron behaves as a wave and a wave means some sort of vi... |
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume. If at all a cavity is carved inside the sphere...will the field inside the cavity be equal to zero or will a field exist?
But my textbook says that the cavity will have a uniform electric field inside it. Can... |
Maybe not a very sensible question, but I would like to know, whether there exist topological field theories (TQFT) with propagating degrees of freedom, or, conversely, theories without propagating degrees of freedom, which are not topological?
By definition, the correlation functions and observables in TQFT do not de... |
I would like to understand the concept of Black Body through this question : can we say that the radiator of our home is a black body ?
|
I'm a High School student learning the kinetic theory of gases, and this is something I'm a bit confused about. So say there's a container covered with a piston. When you lower the piston and therefore decrease the volume, what happens to the root mean square speed? If I think about it, when the piston is lowered, ther... |
$R_\xi$-gauges are said to be a generalization of the Lorenz gauge. I dont quite get why we add the term
$$
\mathcal L_{GF} = - \frac{(\partial_\mu A ^\mu)^2}{2\xi}\tag{1}
$$
to the Lagrangian. If i calculate the EOM for the electromagnetic field $A^\mu$ adding the "gauge-breaking"-term (1) so for the Lagrangian
$$
\m... |
To be specific, let us consider the double-well potential. If we study quantum mechanics, i.e. a particle in such a potential, then we know that there is no spontaneous symmetry breaking but a energy-level splitting. The ground state is presumably a superposition of the local minima. Now if we consider a quantum field ... |
I am given the bipartite swap operator $\mathbb{S}_\text{AB} = \sum_{i,j=1}^{d} |i_\text{A}j_\text{B}\rangle \langle j_\text{A}i_\text{B}| $ that swap the states of two qubits relative to a fixed basis {$|i_\text{A}\rangle \otimes |j_\text{B} \rangle$} and am supposed to diagonalize it. The task is explicitly to not d... |
As far as I have known, our center of the Milky Way, the supermassive black hole Sagittarius A*, weighing 4,000,000 times the mass of our sun, had erupted 3.5 million years ago, the explosion of relativistic jets so powerful that it had struck the Magellanic Stream 200,000 light years away.
However, I am unable to find... |
Let $u_{ik}$ denote the $i^{th}$ component of the position vector of the $k^{th}$ particle. Then kinetic energy of the system of $N$ particles is given by:
$$T=\frac{1}{2}\sum^N_{k=1}\sum^3_{i=1}m_k\dot u_{ik}\dot u_{ik}$$
Next, since $u_{ik}=U_{ik}(q_1, ... , q_n, t)$, we may write,
$$\dot u_{ik}=\frac{\partial U_{ik}... |
I wanted to prove this identity for the general value of $\lambda$
$$
\sum_{n=0}^{\lambda-1} (-1)^n{\lambda-1 \choose n} {\partial^{\left(\lambda-1-n \right)}{\partial_-}^{\left(n \right)}}\left( \bar{\Phi}\; \partial_{-}^{\left(\lambda-n \right)} \partial^n \bar{\Phi} \right)\;=\;\sum_{n=0}^{\lambda-1} (-1)^n{\lambda-... |
In his TASI notes Oliver DeWolfe starts with the KG equation on the Poincaré patch metric
$$
ds^2=\frac{r^2}{L^2}(-dt^2+dx^2)+\frac{L^2}{r^2}dr^2.
$$
When we use the ansatz$$
\phi(r\rightarrow\infty,x,t)=\frac{\alpha(x,t)L^{2\Delta_-}}{r^{\Delta_-}}+\dots+\frac{\beta(x,t)L^{2\Delta_+}}{r^{\Delta_+}}+\dots
$$
on the KG ... |
I know that decay might correspond to one of the two following decay chains:
$$ B^{+} \rightarrow f_2^0 \pi^+ , \text{followed by } f_2^0 \rightarrow \pi^+ \pi ^- ;$$
or
$$ B^{+} \rightarrow \rho^0 \pi^+ , \text{followed by } \rho^0 \rightarrow \pi^+ \pi ^- ;$$
where $f_2^0$ and $\rho^0$ are short-lived intermediate p... |
Although Peskin & Schroeder treats Wilson's approach to renormalisation theory in some depth, I don't get one of its main points. According to P&S (p.401):
Imagine that we wish to compute a correlation function of fields whose momenta $p_i$ are all much less than $\Lambda$. We could compute this correlations function... |
In the magnetic gun a conducting rod is placed on a two rails connected to a voltage source, so that a current can flow in the rod. Magnetic field $\vec{B}$ is applied perpendicular to the rail-rod plane.
The rod length is $d$ and the mass is $m$ , the raillength is $l$ . What should be the current through the rod in... |
I recently had a discussion with a friend of mine who is like me studying physics. And we might got used to a misconception about the Lagrange-Formalism in field theory. In common field theory books one just states that the action is given by
$$
\mathcal S[\phi] = \int \mathcal L (\phi(x), \partial_\mu\phi(x),x)\, \tex... |
assumption: Warmer gas rises. (under gravity)
assumption: A volume of gas cannot have uniform temperature, because gas with fully uniform temperature (all molecules having the same speed) has lower entropy than gas with 'somewhat random' temperature distribution (molecules move at different speeds).
Imagine the follo... |
We all know we need a centripetal force to do a circular motion, but is it the same case for rotational motion? If it is not, then how does the velocity vector changes without applying force? If yes, then how does a rotating body remain in rotational motion in space without any force?
|
This question, I solved quite theoretically differentiating the equation of given graph $$(v=mx+v_0)$$
taking $m$ as slope of given line. Note that $m$ is a non-zero negative number. Thus $$a=m^2x+mv_0$$ which means that acceleration as a function of distance when graphed should have a positive non-zero slope and a neg... |
I read in fluid dynamics that the potential energy stored in the molecule of water due to the attraction by the other molecules is negative. Can energy be negative and what does it mean to have negative energy??
|
What is meant by "current flows in a superconductor forever" ? What if a superconductor is applied with a voltage and current flows but then the circuit is disconnected.
In this case the superconductor has open terminals. There will be no path for the current to go from the conductor. So how can we say in this case th... |
There are some arguments in my country from a population that they are "religious". Then, their argument is that there is a perfect balance in universe and solar system.
Hence they say that Earth will collapse when the orbit of Earth shifts 1 meter towards the Sun. Is there a something like this?
What is the mechanis... |
I understand quantization as a map from Symplectic Manifolds $M$ (either finite dimensional or not) to Hilbert Spaces $H$, along with a rule that attach to every function $F$ in $M$ a hermitian operator $A_F$ in $H$. Dirac proposed that the map should satisfy the rule $-i\hbar[A_F,A_G] = A_{\{F,G\}}$, where $[A,B]:=AB-... |
We all know that air is a fluid as it can blow and we say that the cause of this blow is pressure difference but my question is what creates this pressure difference? Is it related to Earth's motion or something else?
|
East-facing condos/apartments are considered more valuable than west-facing condos by some due to perceived superior light quality and lower peak temperature. My assumption is total solar heat gain through east- and west-facing windows is equivalent (i.e., orientation, size, glazing are all equivalent). With this assum... |
My question differs from these questions:
When is $\Delta U=nC_V \Delta T$ true?
Because here he asks to distinguish between $C_P$ and $C_V$ and not why it's always $C_V$
Work done in adiabatic process
Here the answer is "just because it is always the case"
Is there no mathematical proof for this? What is the real ... |
Frisbees normally generate lift because their "wing" is moving through air,
so what would happen if I just get the frisbee spinning without pushing its
center of mass forward? Assume there is no gravity so there is no falling
"parachute effect".
Let's define a frisbee as a 2D cross section which is rotated about the y... |
If I connect a neutral body to a charged body (suppose it is negatively charged) with a conducting wire, how will the neutral body get charged - by induction or by conduction?
|
I want to find the probability of a particle travelling a distance greater than 0.5mm before it decays. I know the mean lifetime of the particle at rest and it's momentum components.
I know how to calculate the average distance of the particle before decay but not how to calculate the probability of it travelling a sp... |
I know that temperature can be found as a quantity proportional to some quantity which increases monotonically with "hotness". And we can use various methods such as mercury column, gas thermometer and resistors to do so.
And by calibrating all of this to the different phase transistion states of water, we can get a un... |
I was reading Superselection Sectors, Klaus Fredenhagen and in the introduction it states
"The existence of superselection rules leads to the following picture of the quantum mechanical state space: The Hilbert space of quantum mechanical state vectors is a direct sum of orthogonal subspaces".
Physically it makes se... |
How did Planck solve the UV catastrophe? From online sources, I've seen that this had to do with quantization of energy. Somehow I cannot wrap my head around this.
Can any of you please explain? Thank you for your time :)
|
I watched this recent KITP webinar on Nonequilibrium thermodynamics for active matter yesterday. I saw that KLD(Kullback-Leibler divergence) is used as a measure to quantify irreversibility in the active matter systems like biological ones. KLD is defined in our case as below:
$$
D(P_f||Pr) = \int dp dq P_f(q,p;t) \ln... |
When the bus is stationary the passengers are also stationary. When the bus starts moving the part of the body (lower part) in contact with bus starts moving, but due to inertia the upper part remains stationary and thus he gets reclined back. If he is standing he will fall backward.
I cannot understand that how lower ... |
I have been working on a way to prove that the base unit of SI is not enough for numerical computations to make sense. What I mean by that is let's say you're given units of angular velocity to be [1/s] and if you want to calculate angular displacement it's not enough(you need a unit of an angle like rad, grads, deg). ... |
It is well understood that Einstein’s General Theory of Relativity explains how gravitational effects appear to occur instantaneously at a distance. Mass warps spacetime and so objects simply follow straight lines in this warped 4D spacetime. But at what “speed” does spacetime warp?
Gedankenexperiment: Suppose an elect... |
I know that if a photon with a certain energy $E_1$ is absorbed by an electron, for example we are talking about Hydrogen atom, if this energy $E_1$ is equal to the difference in energy between two different levels, the elctron jumps on the excited state $n$.
If the photon has an energy inconsistent with the difference... |
I'm having trouble finding the potential inside an insulated sphere by setting the potential at the center of the sphere to 0 and then integrating from there.
I know that if I set the reference voltage to infinity, then the potential outside the sphere is $kQ/r$ and the potential inside is $(kQ/R) * (3-r^2/R^2)$. Howe... |
From the 0th law, Thermal equilibrium is when there is no heat transfer between two objects. So I want to ask is temperature the only "potential"-esque quantity which should be equalized for stop of heat flow? If temperature is the only one then why is it the only one? Could we prove this?
|
I am asked to show that the SSH-Hamiltonian for a semi-infinite chain with intralattice e interlattice hopping $u$ and $t$, respectively, given by
$\hat{\mathcal{H}}=\sum_{n=1}^{\infty}u\hat{c}_{n,A}^{\dagger}\hat{c}_{n,B}+t\hat{c}_{n,B}^{\dagger}\hat{c}_{n+1,A}+ h.c.$
commutes with the edge-mode operator
$\hat{c}_{L}\... |
Suppose we have the $L$-loop amplitude of the form
$$\mathcal{I}_L=\int \prod_{i=1}^L \frac{d^D q_i}{(2 \pi)^D} \frac{1}{q_i^2} \frac{1}{(p-\sum_{i=1}^L q_i)^2}.$$
Introducing Feynman parameters to merge the denominators as usual, we may write the amplitude in the form
$$\mathcal{I}_L = (N-1)! \int_0^1 \prod_{j=1}^{L... |
The Aharonov-Bohm effect concerns the electromagnetic fields, where a quantum particle can feel the effect of an electromagnetic field in regions where it vanishes, through the electromagnetic potential 4-vector $A_\mu$.
What is the analog of this in the case of general gauge fields? I would also like to know what is t... |
In quantum mechanics, a good way to model dissipation of energy is to couple your system with a heat bath. This heath bath can be represented by a chain of harmonic oscillators. The Hamiltonian of the coupled system can be written as:
\begin{equation}
H = H_s + H_b + H_{int}.
\end{equation}
where $H_s$ is our system of... |
What is the difference between the center of mass and center of gravity of a rigid body?
In which cases are they the same point and in which cases are they different points?
|
How do branes come into existence according to string theory?
Also what are branes made out of?
|
In the question shown, why can i only get the correct answer by assuming conservation of angular momentum about the point of contact P.I get the wrong answer for angular velocity of the rolling cylinder if I conserve the angular momentum of the system about
1.The center of mass of the cylinder
or
2.Say a point at the ... |
The receiving ability of a dipole antenna is much greater than what is attained when doing calculations involving a plane wave interacting with its actual size.
Why is this? How can an antenna pull energy from a surrounding area beyond its physical interface?
|
When I say electric field, I'm referring to the electric field that causes the movement of charge in the wire.
I have learnt about currents and resistances, but I have never really had an understanding of how the voltage across a conductor actually causes current to flow.
Well there must be an electric field to cause t... |
Fiber optics make use of total internal reflection for transmitting signals through them. Associated with fiber optics are many kinds of losses such as loss of signals due to light rays entering at angles more than the acceptance angle.
If in theory, we could make fibers that are "mirrored" on the inside which would r... |
I've been told that in a DC circuit with a battery the negative terminal of the battery "pushes" electrons in nearby atom away of it and those by themselves cause electrons in other atoms to move, but this convention but this way of thinking brought me some problems in understanding voltage.
I mean voltage is defined a... |
I'm a computer science student, so please be patient with my simple understanding of physics.
I heard that if we have a proton, then it does not have a definite position until we measure it.
Suppose we have two protons, A and B, and we put them near each other. We then perform a sequence of measurements of the position... |
I’ve had trouble understanding exactly why there is not more mixing of plasma at the core of the sun with the outer layers.
I understand the difference between the radiative zone and the convective zone.
However, even $without$ convection, a plasma should mix at a fairly high degree with everything around it.
So there ... |
Does the $c$-theorem imply that in two dimensions all RG-Fixpoints are CFTs? Or does it just imply that the monotonously decreasing function $c$ coincides with the central charge if the fixpoint is a CFT?
|
Let's say we have a frame of reference at rest $R'$ and a frame of reference uniformly accelerated $R'$ with a constant acceleration $\alpha$.
I understand that we can show that the coordinates $(x',ct')$ in the Minkowski spacetime diagram are :
$$
\begin{equation}
\begin{array}
xx'(\tau) = \frac{c^2}{\alpha}\left(\cos... |
If I cycle and lean to one side (left in this case) while making a turn according to this website,
I won't fall because "the frictional force also produces a clockwise torque that will cause the rider and bicycle to tip clockwise to the right.", this seems right.
However in case I'm cycling in a straight line without... |
The picture (taken from a textbook) shows how quantum tunneling occurs with electrons.
Why does the de-Broglie wavelength of the electron change when doing this? It does not make intuitive sense to me that the speed of the electron would change after tunneling
|
How should I proceed to find a formula $\lambda(t)$ for the thickness of and ice sheet in terms of
The diference $T_{a}(t)-T_w(t)$ of the temperatures of air above the sheet and water below
Thermal conductivity ($k$) and entalphy of fusion ($h$) of ice
Im new to "modelling" this stuff so I haven't made any real progr... |
Temporal component of the four-accelaration is:
$$\mathbf{A}_t = \gamma_u^4\frac{\mathbf{a}\cdot\mathbf{u}}{c}$$
that, multipliying by the rest mass, should give a value of the temporal component of the four-force of:
$$\mathbf{F}_t = m_0 \gamma_u^4\frac{\mathbf{a}\cdot\mathbf{u}}{c} = \gamma_u^4\frac{\mathbf{f}\cdot\m... |
When we first started introducing the basic concepts of statistical mechanics we assumed the conservation of energy. Conservation of momentum and angular momentum had to be disregarded because the rectangular box broke both translational invariance and rotation invariance (i. e. the Lagrangian of the system is not tran... |
Following $[1]$ we realize that, in order to construct a covariant derivative, we must to compare two possible covariant derivatives such as: $(\bar{\nabla}_{a} - \nabla_{a})\Omega_{b}$, where $\Omega_{b}$ is a covector field. Now, the difference of the covariant derivatives defines a tensor field called $C^{c}_{ab}$ w... |
I want to understand how the degeneracy of an operator is related to the existence of a complete set of commuting operators that includes it. I know that if a set of operators commute, they possess a common eigenbasis. My question is, can you always find an operator that commutes with a degenerate operator to form of a... |
Electric potential is the amount of work done in bringing a unit charge from infinity to a point. Here we take infinity as a reference point.
The unit charge might have higher or lower potential energy depending on the value of electric potential(volts).
But the "principle of superposition" says that a charge might ha... |
Can a fusion reactor like ITER maintain it's fusion reaction and generate net output electrical power continuously; so long long as fuel is supplied, or does the reactor need to be shut down periodically and the reaction stopped so that it can be cooled down? If there is a cool down period for a reactor could anyone pl... |
When I read about past events in the universe (i.e. big bang, formation of the sun and planets, etc) future events (i.e. sun becoming a red giant) and distant objects (black holes, nebulas, galaxies, etc), it appears to me that a big assumption is always made:
The laws of physics observed from earth today are the same ... |
Imagine a stick with 2x lenght. with mass of m.
And COG is half way through. This stick in space. No gravity and friction exist
I pushed the stick from one end point. Do stick start rotating? Or it just go forward without rotation because there is no pivot?
|
Hopefully you guys can solve this hypothetical for me.
Suppose I have a laser which emits light at frequency $530\mathrm{THz}$ with a very narrow spectral width $1\mathrm{Hz}$.
From signal theory, as far as I understand, this represents a carrier which my eyes perceive as color green.
Now I modulate this laser with a ... |
I’m wondering how to contract a product of gamma matrices like
$$(\gamma^5)_b^{~~d}(\gamma^5\gamma^{\mu})_{ad}$$
Is this just $$(\gamma^5)_b^{~~d}(\gamma^5\gamma^{\mu})_{ad} = (\gamma^5\gamma^5\gamma^{\mu})_{ab}$$
Or have I slaughtered the algebra? Help much appreciated
|
This is a purely hypothetical question, but I was wondering whether its possible to design a useful engine which makes use of both an isothermal process and a piston. Thinking about this, the issue that I came across was that in order to perform an isothermal process, we must have $PV = constant$. Now, we will need the... |
(I called them see through mirrors because I don't know what their actual name is)
I have seen a lot of pictures of glass-like materials which reflect light from on side, and from the other side, they transmit light.
What i want to say is -
Let side A and side B be the two sides. Side B will reflect all (almost all) ... |
When reading about the Wu-Yang monopole, it seems to me that the method that Wu & Young used (using patches and gauge transformations to cover $S^2$) is more systematic and general than Dirac's method for the Dirac monopole analysis (and for reaching the Dirac quantisation condition), but it overall seems to me that th... |
We know that graphene is the strongest metal on earth. It has very high tensile strength. The inter-planar bonds are van der waals force but the covalent bond across the plane between C-C atoms is what gives them the strength. If the covalent bond is soo strong, then, when we mechanically exfoliate graphene, why does i... |
Since your are weightless in space, your arm has no weight, right? Does this mean that bending it in space requires no energy? Why or why not?
|
Does anyone know whether $(x,y)\rightarrow (-x,-y)$ is an inversion transformation or not?
I know that the standard inversion (parity) transformation in two dimensions should be something like $(x,y)\rightarrow (x,-y)$ which only flips an odd number of spatial coordinates. However, if we have a plane embedded in three-... |
With Faraday's law, is it standard convention to leave off the negative sign? Or are answers with negative EMF acceptable (generally speaking)?
|
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