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Here, $\rho$ is the resistance at temperature ($T$) and ($R$) is the resistance at a given temperature. Also, will the value of $α$ become negative if the resistor is cooled?
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Consider, a box with $N$ particles each of mass $m$, arranged at time $t=0$ to be moving parallel to the $x$-direction, with mean velocity v and mean distance l. The particles are spheres of mean radius r. Assume, the collisions are elastic and head-on, collisions occur when two particles move along the same direction,... |
Electromagnetic waves follows superposition principle. So that we can simply add the fields of waves to calculate the final field. Then let's think there are two waves that are moving through x-axis and y-axis. If we control the phase difference well, we can make a situation like figure.
In the figure with some $t=t_0... |
The two point correlation function for the Ising model is defined as $\left[\langle\sigma_i\sigma_j\rangle -\langle\sigma_i\rangle\langle\sigma_j\rangle\right]$. Then the sum over $i$ $j$ of that function gives:
\begin{equation}
\sum_{ij}\left[\langle\sigma_i\sigma_j\rangle -\langle\sigma_i\rangle\langle\sigma_j\rang... |
I would like to know the complete equations for a collision of two perfectly elastic/rigid balls.
I have seen something along these lines:
$$m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'$$
but I think there is missing one parameter, namely how much one ball touches the other.
In other words, if the collision is direct or... |
so i just learnt about about the derivation of Kinetic Gas Equation! In that derivation, and i have a question which i am trying to find the answer for but i can't find it anywhere on the internet!
In the derivation when we are deriving the formula for force on a particle, we first find that change in momentum after hi... |
Imagine a closed loop in the shape of a trefoil knot (https://en.wikipedia.org/wiki/Trefoil_knot). How should one calculate the flux through this loop? Normally we define an arbitrary smooth surface, say, $\mathcal{S}$ whose boundary $\partial{\mathcal{S}}$ is the given loop and calculate the flux using its integral de... |
I am currently studying the textbook Modern optical engineering, fourth edition, by Warren Smith. Section 1.5 Interference and Diffraction says the following:
Now if the waves arrive at C in phase, they will reinforce; if they arrive one-half wavelength out of phase, they will cancel. In determining the phase relation... |
In the chapter calorimetry of class 10 I read that heat energy is the total energy content of a body, that is sum of the kinetic energy of the molecules and their potential energy due to the attractive forces between them.
But why is it that just because a couple of molecules are moving randomly and rapidly they need ... |
I will be surprised if no one asked this before and I would be happy if it is answered already although I haven't located it just yet!
From Einstein's original paper "Does The Inertia of a Body Depend on it's Energy Content" 1905. I am wondering if maybe my original thinking is not right. I always thought that energy i... |
I recently got into a debate about the classical villain or hero move of lifting an adversary by the neck. We've all seen the one-arm or even two-arm lift and i made the case that even two arms against a wall would be a close-to impossible feat by any human but of course the relative strength and weight has a say in th... |
I'm looking for references covering the following topics: path integrals in statistical mechanics and Wick rotations, second quantization, fermionic systems and Ising-like models and mean field theory. I have a background in quantum mechanics, statistical mechanics and thermodynamics.
|
I come across the terms "equations of motion" and "field equations" all the time, but what is the difference? For example, general relativity is described in terms of the Einstein field equation $G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu}$ and particle dynamics are governed by the geodesic equation (of moti... |
First off, a Michelson interferometer does work. It can measure tiny length differences. Here is a video showing one in action.
I must have misunderstood how it works. Here's what I think is happening:
The light beam is split in two. The different paths may be different lengths. They are then recombined, and so they ma... |
From Wikipedia's energy efficiency in transport, I gathered the following data for a person riding a bike:
65 kg person riding at 4.5 m/s requires 110 kJ/km, which equates to a continuous power output of 495 W. I assumed the mass of the bike was 10 kg, so total of 75 kg.
I want to convert these numbers into energy per ... |
We know that 2d semiconductors have time-reversal symmetry breaking' properties.
How can I check the spatial inversion symmetry properties and time-reversal symmetry of materials?
Please explain it easily.
|
In spin 1/2 system with TR symmetry , the Berry curvature must vanish. Because Berry curvature is odd. How to prove it?
\begin{equation}
\langle\partial_{-k_x}u^{I}(-k)|\partial_{-k_y}u^{I}(-k)\rangle-x\leftrightarrow y=-\langle\partial_{k_x}u^{II}(k)|\partial_{k_y}u^{II}(k)\rangle-x\leftrightarrow y
\end{equation}
\be... |
In regular Newtonian physics, we use $ x(t) - t$ graph to under position of a particle but why is it that in special relativity that we switch up the axis notation? I was seeing the lecture by Leonard Susskind and, after one hour, I came under the impression that it is just a relabelling of an the axes because, I think... |
Why do gas bubbles initially stick to the walls of the bottle in carbonated drinks? And what happens when we open the cap? How do they separate from the walls?
|
We have the equation of motion in polar coordinates:
$$\frac{d^{2}\vec r}{dt^2} = (\frac{d^2 |\vec r|}{dt^2} - |\vec r|\cdot (\frac{d\theta}{dt})^2)\hat r + (|\vec r|\cdot \frac{d^2\theta}{dt^2}+2\frac{d\theta}{dt}\cdot\frac{d|\vec r|}{dt})\hat \theta.$$
For example, we have a pendulum that is consisted by a rigid rod... |
Variational approximation
Variational methods are an important technique, frequently applied for the approximation of complicated probability distributions, with the applications in statistical physics and data science.
Suppose we have some complicated distribution $P(x)$, from which we cannot infer the partition funct... |
I'm talking about the mechanics which uses the minimisation of integral of $L=T-V$ to deduce motion paths.
I've read it is a more generalised version of Newton's formulation because it can be used with generalised co-ordinates.
But when we say $\vec{f}=\frac{d\vec{p}}{dt}$, we are simply referring to a law independent ... |
The main problem I am having is what Actually remains constant in the two cases. Is it the average force, or the time period for which the force is exerted? any helpful hints would be appreciated.
Note : This is not a homework question; I was asked this by a friend and am trying to intuitively figure out the answer.
|
Say speed is the magnitude of velocity then:
\begin{align*}
v &=\left|\vec{v}\right|\\
\frac{D}{\Delta t} &= \left|\frac{\Delta \vec{x}}{\Delta t}\right|\\
\end{align*}
since $\Delta t$ is always positive, we get:
$$D = \left|\Delta \vec{x}\right|$$
which is not true.
$D$ = distance travelled
$\Delta \vec{x}$ = displac... |
Why couldn't the photon be the graviton? How sure are we that the photon could not fill the role of gravitons?
|
Suppose I represent 2 forces as vectors and set 3 points there proportionally (divide the 2 vectors by 3).
If I now draw the connections according to Pappus' Hexagon theory, does the intersection line give the vector of the resulting forces (orientation)?
|
When solving the Schrödinger equation for the hydrogen atom, textbooks invariably work in a more constraint situation, whereby not only an eigenfunction for the Hamiltonian operator $\hat{H}$ is sought, but one which is simultaneously an eigenfunction for $\hat{L}^2$ and $\hat{L}_z$. My question is why we do this?
A si... |
The title pretty much explains itself, could someone recommend me a textbook on fluid mechanics for someome who knows nothing about it? I've already learnt some vector calculus and I'd like to learn fluid mechanics so I can use them.
|
As far as I understand it the Higgs field leads to the creation of rest mass for certain elementary particles but does it explain the phenomenon of resistance to acceleration associated with rest mass?
|
Why does the commutator of two operators evaluated at different times vanish? Take for instance a fermonic field $\psi_\sigma (\vec{x},t)$, which satisfies the well known anti-commutation relations at equal times
\begin{equation}
[\psi_\sigma (\vec{x},t),\psi^\dagger_{\sigma'} (\vec{x}',t)]_+ = \delta^{(3)}(\vec{x}-\v... |
Non-physicist asking.
I have a hollow enclosed 1cm-sided cube. It is filled with N mols of an ideal gas.
(1) What is the probability that for one infinitesimal moment, all the gas will occupy half of the box, leaving a vacuum at the other side.
(2) What is the probability that it will stay this way for a specified leng... |
For having studied both classical and quantum optics, I regard Maxwell's equations as the grand "cheat sheet" from which (almost) all optical/photonic phenomena can be derived. Yet, I also know that wave-particle duality extends to all other fields and particles in the standard model. I'm therefore left with a nagging ... |
If I leave a bar of a radioactive material (e.g. uranium-235) for its half-life time, how will the bar look after halving its mass?
Will it:
stay the same size, but be lighter?
shrink in size as to keep the same density?
be filled with small holes (like cheese or bread)?
have turned into a small pile of uranium dust a... |
For example, if you were to roll a piece of paper into the shape of a hollow cylinder and then try to return the paper to its original, flat shape, it would naturally roll to the cylinder when you let go. Why would an originally flat surface, when changed to posses two curves roll?
|
This is a follow-up question to the accepted answer to this question: Leibniz Rule for Covariant derivatives
The standard Leibniz rule for covariant derivatives is $$\nabla(T\otimes S)=\nabla T\otimes S+T\otimes\nabla S$$
so for $T\otimes\omega\otimes Y$ this would translate to $$\nabla(T\otimes\omega\otimes Y)=(\nabla... |
In the Laser Interferometer Space Antenna (LISA) mission proposal document, section 4.2 (page 17) there is a formula for the test mass acceleration noise level:
\begin{equation}
S_a^{1/2}\leq 3\cdot 10^{-15}\frac{\rm m\cdot s^{-2}}{\sqrt{\rm Hz}}\sqrt{1+\left(\frac{0.4~{\rm mHz}}{f}\right)^2}\sqrt{1+\left(\frac{f}{8~{\... |
If electrons move through the wire because of the force applied by the electric field that attracts them from negative terminal to positive terminal and this force is setting them to motion in a direction not opposing to the direction of the force, why don't they gain potential energy as there is work being done on the... |
What is the highest electric field known in nature?
To add clarity, as requested: an electric field is measured in V/m, Volt per meter.
What is highest value that has been measured or observed?
What is the highest value that is suspected?
There are two candidates situations and systems where one can search.
(1) Microsc... |
It is well known that the electric field inside the cavity of a conductor is zero. The same can't be said in case of a non conductor. Although its easy to show that the field inside a concentric sphere + spherical cavity combination is zero everywhere inside the cavity, when we change the shape or position of the cavit... |
We know that the objects are made up of atoms. We also know that we cannot see atoms with the help of light as the wavelength of light is too big in comparison to atom. So, my question is then: how can we see objects with the help of light if we cannot see atoms?
|
How does a gas bubble detach from a wall (say, for example, bubbles which form when water in a vessel is heated) it was sticking to?
I have an idea...
It is that when we increase the internal pressure by introducing heat into the system... the ends of the thin film (the layer formed by surface molecules) which connect ... |
In the EM Lagrangian, the QCD Lagrangian, and the charged and neutral weak current Lagrangian, there is always a $\psi$ term and its adjoint $\bar{\psi}$.
The $\psi$ term can represent a Dirac spinor for EM, or a Dirac spinor $\otimes$ color space for QCD. AFAIK, it represents just a Dirac spinor for the weak currents ... |
Current is defined as charge/time and the only use of current is to see how much charge passes through an area in 1 second, and current depends on voltage.
So even if we change current as charge/area or charge/volume it shouldn't be wrong, right?
|
I've been searching for the derivation of planar moment of inertial but I can't find it anywhere $(I = \iint y^2dA)$. I don't understand why there's a $y^2$ term in there but I do understand that you divide up the body into smaller parts which is why you integrate over the entire body. I also can't understand how they ... |
I had a lot of problems imaging the current in an AC generator.
I fully understand the principal of it and how it depends on a magnetic field repeatedly cutting another one and how to use Fleming's right hand rule, I only still have trouble imagining why emf changes when the wire is in different positions.
Anyway it's ... |
I am watching a Science Channel program on the collapse of massive stars and it got me wondering... What is the distribution of heavier than iron elements in the universe. (It is my understanding that some of these elements are formed by the shock wave compressing the outer layers of the star as it explodes)... This ... |
We have an isolated assembly of N indistinguishable harmonic oscillators, each has energy $\epsilon_i=\hbar \omega/2 + n_i \hbar\omega$, where $n_i$ is a non-negative integer. If the total energy of the system is $E=N\hbar\omega/2 + M\hbar\omega$, ($N\gg 1$) then each micro-state must satisfy
$$
\sum_{i=1}^{N}\epsilon_... |
Why and how is the supercurrent generated in a superconductor in response to an applied magnetic field? Does it flow only along the surface? If yes, why?
|
If velocity of a straight wire and magnetic field make acute angle and the wire lies in the same plane, is there an EMF developed in the wire? It is a thin wire. The velocity is perpendicular to it. I thought that there is no EMF because magnetic force is perpendicular to length and so charge separation does not take p... |
According to the literature, the square lattice has $C_{4v}$ symmetry. This point group does not contain inversion. However, the square lattice is obviously inversion-symmetric.
Is this because inversion can be constructed by composing two mirror operations?
|
I have read this question:
Why doesn't diamond glow when hot?
This is because of Kirchhoff's law of thermal radiation. The corollary from it is that emissivity of a material is equal to its absorptivity.
Does any material glow, under appropriate conditions?
a body must absorb and emit identically at a given wavelen... |
Say there are two particles in the x axis. Initially, with high probability one staying at $x=-1$ and going to the right, and the other $x=1$ going to the left. Will they collapse when both arriving at $x=0$?
If one does not use the Born rule, one has only a combined $\psi(x_1,x_2,p_1,p_2,t):\mathbb{R}^4\times\mathbb{R... |
My Question is That?
There are a variety of gases that are in our atmosphere. They all together create an atmospheric pressure. why this pressure exist I mean look at outside the earth there is nothing more than a huge empty space. Is Gravity pull sufficient to bind this pressure together ? or Is there any other factor... |
I know many scientist gives many theory to explain structure of atom and that's Quantum mechanics explained very well. Even Schrondiger eq. to get idea where electron more probable is around a nucleus give just a probability. I am beginner so plz.. guide me why there is so rat race behind the position of electron ? I d... |
Conformal gravity theories are alternatives to GR which are conformally invariant. That is, if $g_{\mu\nu}$ is a metric solving the field equations of the theory, then so is $\Omega^2 g_{\mu\nu}$ for any nonvanishing function ("conformal factor") $\Omega$. Some people study the possibility that such a theory might actu... |
A short question, because the math got me confused.
If in my inertial reference frame, I see a dude going away from me at a speed $v$.
Then, from his frame of reference (which is also inertial) he also sees me moving with speed $v$. No matter how close he is to the speed of light.
Is that correct ? $$dx/dt = v = dx'/dt... |
On page 355 of principles of physics by Resnick walker and Halliday, the author writes:
Work must also be done on the system (at the input end) to push the entering fluid into the tube and by the system (at the output end) to push forward the fluid that is located ahead of the emerging fluid. In general , the work don... |
It has been said that falling into a black hole and crossing the event horizon would appear as "nothing out the ordinary" for the in-faller (especially for a super-massive BH, but lack of strong tidal forces is not my concern here).
When falling towards the event horizon (actually towards a collapsing star because the ... |
Is there any relation between drift velocity and area velocity?
And how I can to find area velocity for electrons in a magnetic field?
|
Is there a formula for how long it takes light to catch up with a constantly accelerating object given initial distance?
|
Time can be calculated from a modified kinematics quadratic formula using the initial velocity, displacement, and acceleration. However, the acceleration vector isn't limited to 1 axis.
When applying a quadratic kinematics equation you get 2 roots. However, since acceleration isn't along 1 axis there are 3 quadratic eq... |
This might be a dumb question, just into my physics docos. Trying wrap my head around how mass translates to gravity and effect on space time.
So many docos say the higgs boson is the particle that interacts with the higgs field and gives matter mass. They show imagery of matter passing through the higgs field, experie... |
In Quantum mechanics, before we get to Slater determinants and all that, it is said that many-particle wavefunction for the case of non-interacting particles is just a product of all the particles' individual wavefunctions. There is certainly a good reasoning to assume so: since the particles are independent, they are ... |
I am studying an article which is about quantum gravity (M. Martellini, "Quantum Gravity in the Eddington Purely Affine Picture," Phys. Rev. D 29 (1984) 2746). I have come to eq. 2.11a which is
\begin{equation}
\overline{\nabla}_{\rho}\overline{K}_{\alpha\beta}=0
\end{equation}
where, $K_{\mu\nu}$ is Ricci tensor
\begi... |
I've been thinking about star trek 2009 and star trek Picard in which they happen to talk about a sun inside a fictional solar system which goes supernova destroying a particularly important planet to a militaristic alien species. This got thinking, could you know in advance whether it be in days/weeks/months/years/dec... |
I have a doubt regarding the Riemann tensor in a LIF. The general expression of the Riemann tensor is:
$R^{\alpha}_{\beta \mu \nu} = \Gamma ^{\alpha}_{\beta \nu, \mu} - \Gamma ^{\alpha}_{\beta \mu, \nu} -\Gamma ^{\alpha}_{\kappa \nu} \Gamma ^{\kappa}_{\beta \mu} +\Gamma ^{\alpha}_{\kappa \mu} \Gamma ^{\kappa}_{\beta... |
When revisiting Ohm's Law, I wondered why (I know it's experimentally derived) the voltage change between two points would depend on current. I could understand this dependence with total energy dissipated in moving a current across a resistor but I can not understand why the P.D. (i.e. the work done per unit charge) d... |
I have a question that would probably be easy for you.
If we could put an elevator together with its shaft on a scale and have its motor pull it up, lets say for 50 floors.
will the reading on the scale be less while the elevator is traveling?
I'm not talking about fluctuations that will be caused by inertia as it's st... |
I'm, trying to integrate
$$
m\ddot{r} = -\frac{\partial V(r)}{\partial r}
$$
To arrive at $E=T+V$.
I'm capable of getting to
$$
\frac{1}{2}m\dot{r}^2 + \text{constant} = -V +\text{constant}
\\
\frac{1}{2}m\dot{r}^2 + V = \text{constant}
\\
T+V = \text{constant}
$$
but I'm not sure what conservation law, boundary condit... |
I knew that one liter of helium would lift approximately 1 gram of mass. However, I could not find how to calculate how high would that 1 gram go. Imagine if we have a helium balloon (ignore the weight of the balloon skin and string linking the balloon to the mass) lifting a gram of mass, how high would that balloon go... |
Rubidium-87 was the first and the most popular atom for making Bose–Einstein condensates in dilute atomic gases. Even though rubidium-85 is more abundant, rubidium-87 has a positive scattering length, which means it is mutually repulsive, at low temperatures. This prevents a collapse of all but the smallest condensate... |
This question has been asked two times
Similar question 1
Similar question 2
Now my question will be different from all those questions, since I will be asking where exactly I am having trouble understanding the working of an atomizer rather than just asking explain the working of atomizer.
While deriving equation of... |
The a particle with the potential $V(x^2+y^2)$ undergoes an active transformation where
$x\rightarrow x+y\delta$
$y\rightarrow y-x\delta$
The exercise was to prove that the Lagrangian of the system remains the same even after the transformation, but I don't understand how the potential energy remains the same.
A soluti... |
Given a 2D crystal Hamiltonian $H(k_x,k_y)$ in terms of momenta $k_x$ and $k_y$, how do I use the rotation operator $R_n(\theta)=e^{-i \theta \vec{J}\cdot\vec{n}}$ (or otherwise) to find the Hamiltonian's possible $n$-fold rotational symmetry.
I know that if $H(k_x,k_y)$ has $n$-fold rotational symmetry, then $R_n(\the... |
After reading a comment by @Stian Yttervik to one of the answers in this question that goes as
I would add that in both cases, the resultant products are in sum lighter than its reactants - and that is the whole trick about it. $E=mc^2$
"both cases" in this context was fission and fusion.
Below is part of page 196/1... |
The definition of centre of mass on Wikipedia is given as
This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.
How can I prove that such a point is the weighted average of the radius vectors of all discrete masses mathematically?
Also see this question.
|
Though this seems obvious, the longer the string length, the longer the time period. But my question is why does this exactly happen, and how do you explain it with equations?
|
The first equation of motion is $v = u + at$.
The second equation of motion is $s = ut + \frac{at^2}{2}$.
If we divide the second equation of motion by time $t$, why don't we get the first equation of motion where has $1/2$ come from?
|
Suppose $F$ is independent of velocity,so Newton's law can be
expressed as : $m \ddot{\mathbf{x}}(t)=\mathbf{F}(\mathbf{x}(t)) .$
Then an energy function of the form $$ E(\mathbf{x}, \dot{\mathbf{x}})=\frac{1}{2} m|\dot{\mathbf{x}}|^{2}+V(\mathbf{x}) $$
is conserved(i.e for any solution of Newton's equation $E$ is a
c... |
I need to know what would happen if I increased the earth's size by a small percentage to make a fictional world similar to earth. So my thought process is this: My thinking started with increasing the earth's time zones or to increase the number to time zones.
At first I wanting to add 4 more hours making the planet ... |
Air molecule has $6$ degrees of freedoms: it can move up & down, left & right, front & back, rotate along $x$-axis, $y$-axis, $z$-axis. But I heard about graviton, a hypothetical particle can have up to anywhere from $2$ to $10$ degree of freedom.
How and why do certain particles be restricted to less than $6$ degree o... |
The original question I was asking was Why does a body not rotate if force is applied on the centre of mass?.
The obvious answer is that the torque ${\bf r}\times{\bf F}$ is zero as ${\bf f}$ is zero at the centre of mass, but that defeats the purpose of my question. Why is the centre of mass so special that we take to... |
In the following the basis vectors are assumed to be varying functions of position. This means that when a vector appears under the differentiation operator, both components and basis vectors will, in general be differentiated according the the product rule. An underline indicates a particular term is to be held consta... |
If a train was made to utilize the ground effect, (or plane made to follow a rail) not to have any contact with the ground other than air, would the rail need to be so heavily built since the air is distributing the weight?
Keep in mind the fastest train's full weight is still supported by a rail suspended with magnet... |
Let's say that a particle moves horizontally with a velocity of $v_x$ and vertically with a velocity of $v_y$. Now, when we represent these two velocities and their resultant velocity using the head to tail method, we draw a horizontal arrow which represents $v_x$ and we draw a vertical arrow whose tip is at the head o... |
In potential flow theory there are simple analytical models (formulas) for velocity-field of elementary features (like source, sink, dipole, vortex etc.)
Is it possible to write simple analytical expression for flow (i.e. velocity field $\vec v(\vec r)$) inside ascending mushroom cloud (i.e. bouble of hot air creating... |
I am confused about a sentence in Polchinski's String theory chapter 8 p 255 when he works out the example of the full $T$-duality with two compact dimensions. He writes
"A simultaneous $T$-duality on $X^{24,25}$ acts as $\rho\rightarrow -1/\rho$ with $\tau$ invariant."
Here $\rho$ and $\tau$ are two complex fields t... |
I had some trouble finding this information, so I believe it would be interesting to have a post in here explicitly mentioning the issue described on the title. Furthermore, I would like to ensure my line of thought is correct.
In Classical Mechanics, it is simple to show that the Euler-Lagrange Equations for a Lagrang... |
I'm a chemist, first off, and I'm trying to self teach myself some graduate statistical mechanics from "Statistical Mechanics: Theory and Simulation" by David Chandler. The first chapter is on classical mechanics and I'm confused about the form of the Euler-Lagrange equation given in generalised coordinates, specifical... |
I am looking for a recent paper in which the signal-to-noise ratio for the ground based advanced LIGO/VIRGO interferometers is discussed, on the same line of this paper (dated 2006 by E. Berti et al.) about the SNR for LISA.
I have found this old paper (dated 1997, by Flanagan & Huges) which estimates the SNR for LIGO/... |
Poincare in science and hypothesis wrote:
When we say force is the cause of motion we talk metaphysics, and this definition, if we were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover, that suffices; it is not at all necessary that it teach w... |
Why do we take the relative velocity instead of the absolute velocity in the analysis of flow rates? More particularly when we write down momentum, isn't the 'velocity' term which we multiply with the mass, the absolute velocity of the body with respect to some inertial frame?
I am aware that we could shift between di... |
We know that magnetic field is produced by a current carrying wire with time varying current? My doubt is that- do the electrons in motion cause the magnetic field or is it due to some another reason?
|
In book Renormalization Group and Fixed Points there is formula for scaling of correlation function:
But this formula contradict my understanding of scaling of correlation functions.
For free theory we have:
$$
\langle \phi(x) \phi(y) \rangle = \frac{1}{(x-y)^{d-2}}
$$
$$
\langle \phi(sx) \phi(sy) \rangle = s^{2-d }\... |
While studying the unit of electrostatics, I came across the formula $$C=\dfrac QV,$$ Where C refers to the capacitance of the conductor, $Q$ refers to the charge present on the conductor and $V$ refers to the potential of the conductor. I don't understand what is meant by the potential of a conductor. Isn't electric p... |
In The renormalization group by Matthew Schwartz the is very interesting picture of RG for dimension and dimensionless couplings:
Topology of such diagrams is very different. But this pictures describe the same system.
How from these pictures to understand, that these pictures describe the same system, but for differe... |
From Leonard Susskind's book The Theoretical Minimum.
"A particle in two dimensions, x and y, has mass m equal in both directions. It moves in a potential energy $V = \frac{k}{2(x^2+y^2)}$. Work out its equations of motion. Are there circular orbits? If so, do they all have the same period? Is the energy of the system... |
Einstein explicitly states in "Zur Elektrodynamik bewegter Körper" that the only two postulates he requires for his derivation of the Lorentz transformations are 1) the principle of relativity and 2) the constancy of speed of light (the so-called 2nd postulate).
Many physicists since then, the first being Wladimir Igna... |
The value of the Hubble parameter determined locally from the Type Ia supernovae is found to be greater than that determined from the Cosmic Microwave Background (CMB) radiation. This is known as the 'Hubble Tension' or even 'Crisis in Cosmology'.
Why is this a problem?
If we assume that the Universe is accelerating, t... |
On page 33 of these notes by David Skinner, it is claimed that
[starting from a connected graph and removing the bridges] tells us how to compute $\Gamma(\Phi)$ perturbatively from the original action: $\Gamma(\Phi)$ consists of all possible 1PI Feynman graphs that may be constructed using the propagators and vertices... |
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