8
votes
4answers
2k views

Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula ...
7
votes
3answers
274 views

What are the main differences between $p p$ and $p \bar p$ colliders

I know that it is somehow related to the parton distribution functions, allowing specific reactions with gluons instead of quarks and anti-quarks, but I would really appreciate more detailed answers ! ...
7
votes
1answer
179 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
2
votes
1answer
22 views

Energy levels in molecules

I apologize in advance if this turns out to be a duplicate question. As far as I can understand, if you bring two or more atoms together their wave functions begin to interfere and, since there ...
1
vote
2answers
121 views

Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
-3
votes
1answer
31 views

Overloading stresses wooden planks beyond their elastic range, causing them to fail? [on hold]

info: In a video on youtube in an unsafe way a car is boarding a ship going over two wooden planks. It looks to me that there two 2x10" wooden boards support a 5,000 lbs car/truck (a not so light ...
3
votes
1answer
193 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
0
votes
1answer
19 views

Coulomb barrier in nuclear fusion

Suppose there exists an alpha particle in the nucleus. Within a radius of 2 femtometer, the dominating force is the nuclear force but beyond this radius, the Coulomb force becomes the effective ...
1
vote
2answers
458 views

How does this chair move?

I have a chair like this(shown in figure). I was kneeling on the part where we sit. I just gave a sudden push to the part where we rest the back, without moving my legs. I found that the chair is ...
-1
votes
1answer
21 views

Central Force - Trajectory [on hold]

There is a central force $\vec{F}(\vec{r})=f(r)\vec{e_r}$. 1.1.: The trajectory/flight path is defined by $r=r(\phi)$, compute $f(r)$. 1.2.: The path is defined by $u=u(\phi)$ with ...
2
votes
2answers
39 views

'Doppler redshift' Vs 'Cosmological redshift'

It is not difficult to understand the differences between 'Doppler redshift' and 'Cosmological redshift' conceptually. But how do astronomers distinguish them when doing observations?
0
votes
0answers
12 views

Derivation of the kinetic energy of decay product [on hold]

By conservation of momentum: $$M_{\alpha }V_{\alpha }+M_{Y}V_{Y}$$ By the conservation of energy: $$(\frac{1}{2})M_{\alpha }V_{\alpha }^{2} + (\frac{1}{2})M_{Y }V_{Y }^{2}$$ Here I begin the ...
0
votes
1answer
61 views

Question about scalar product of 2 four-vectors

I'm looking for help to prove that $\mathbf{a\cdot b}=-ab\ cosh \ \theta$, where: $a=\sqrt{\mathbf{-a\cdot a}}$, $b=\sqrt{\mathbf{-b\cdot b}}$, and $cosh \ \theta$ is $\gamma$, for a Lorentz ...
17
votes
1answer
847 views

Causality and how it fits in with relativity

I was talking to my teacher the other day about Einstein's spacetime and there's one thing he couldn't explain about the nature of Cause. I may be being stupid or just unable to comprehend, thanks for ...
6
votes
2answers
288 views

Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson ...
2
votes
4answers
148 views

Physical reason why the derivative of a wavefunction has to be continuous?

Question What is the physical reason (i.e. without any maths) that the derivative of a wavefunction (except with infinite potentials) has to be continuous? Other info I know that in the classical ...
1
vote
3answers
21 views

How can we be sure that a new frequency standard is better than the old one?

Lets assume for this question that at one point in scientific history everyone was running along well with their cesium frequency standards, and someone has a brilliant idea and builds an active ...
0
votes
2answers
168 views

Dielectric constant of water

I need the dielectric constant of water from $10^{-2}$ Hz to $10^4$ Hz. As stupid as it may seem, I cannot find much info. I've googled for days. All I can find is close to GHz. And the only info ...
0
votes
1answer
19 views

Notation of polarization of light

Upon my research of polarization of light I stumbled upon the following formula: What do the three dots mean? I have never seen them before. Edit: Found this notation in the book "Nonlinear fiber ...
2
votes
1answer
54 views

Minimizing the Lagrangian action of an impossible problem

I'm working my way through Structure and Interpretation of Classical Mechanics (SICM), and am stuck on an exercise in Section 1.4: Exercise 1.6. Minimizing action: Suppose we try to obtain a ...
4
votes
3answers
393 views

Explaining a quote by Weinberg about the signifcance of symmetry groups in physics

When skimming through a book, I found this quote: The universe is an enormous direct product of representations of symmetry groups. —Steven Weinberg I am a mathematician (so I know only basic ...
1
vote
1answer
28 views

Seeking Reference on Transport of Momentum by Diffusion of Mass

I'm looking at continuum mechanics from the perspective of De Groot and Mazur's "Non-Equilibrium Thermodynamics" - the first reference that I've come across that seems to do a good job of bringing ...
0
votes
1answer
47 views

Getting to spins of arbitrary direction

Let me rephrase this question: Let us assume we know that symmetry transformations always look like this: $$U(s)=e^{iKs} $$ with a hermitian Operator K. This tells us that for very small $s$: ...
0
votes
2answers
34 views

Is the light from the stars within our galaxy redshifted?

I know that metric expansion does not happen within a galaxy. But is the light from stars in our galaxy somehow redshifted? Also, everyone says that our galaxy isn't expanding. But is there a slight ...
0
votes
1answer
20 views

Does the electron confinement energy vary with temperature?

I was introduced the electron confinement energy. At room temperature thermal energy of a particle is about $k_B T$, where $T=298K$, giving about $25meV$. I was told that $E_\text{confinement}=50emV$, ...
0
votes
1answer
81 views

On Thermodynamics of Spontaneity of the Reduction-Oxidation Chemical Reactions

According to the first and second law for a closed system containing different chemicals we have \begin{align} &\delta Q - \delta W = dU = T dS - p dV +\sum_i \mu_i d N_i\\ ...
2
votes
0answers
47 views

What are the quantum dimensions of the primary fields for SU(N) level k Kac-Moody current algebras?

The CFT of the $\mathrm{SU}(N)$ level $k$ Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields. I ...
-1
votes
1answer
30 views

Time dilation: reference frame [on hold]

So I'm calculating how long it will take for half of some muons to decay for in a stationary observers frame of reference. They have a half life of 2.2 * 10^-6 and are moving at a speed of .98c ...
-3
votes
0answers
10 views

What is the energy levels of 1d hydrogen by using WKB? [on hold]

I need to find the energy levels of 1d hydrogen using WKB and $V(x)=-1/x$? can you help me please?
0
votes
2answers
54 views

Are spherical coordinates distances or angles?

I've become confused about spherical coordinates when dealing with electric fields. The way I always understood spherical coordinates is something like the below picture. To define a vector, you give ...
2
votes
2answers
94 views

Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
12
votes
4answers
244 views
+100

Black Body Golf Balls

The surface of a golf ball has about 35% more surface area (than a similar sphere) due to its dimples. So my question is simple, given identical radius, ideal black body material, and temperature: ...
0
votes
1answer
25 views

Concentrations of carriers in semiconductor

For a given semiconductor at a given temperature $T$ with doping levels of acceptors $N_A$ and donors $N_D$ and intrinsic carrier concentration $n_i$ without any external biases, how can I calculate ...
2
votes
1answer
500 views

Force required to move a fluid out of piston at depth

I have a cylinder filled with water in it at the bottom of the ocean. Say 100 meters down. In this cylinder is a piston that moves up and down. Its job is to squish the water out the bottom of the ...
1
vote
0answers
17 views

Polchinski equation 11.2.7

In Polchinski's string theory volume 2, when discussing the GSO projection for the heterotic string he says: In the IIA and IIB superstrings the GSO projection acted separately on the left- and ...
0
votes
1answer
44 views

How do I calculate the energy flux for this toroid?

My question is how do i calculate the total energy flux through the walls of the torus in this situation? The Poynting flux is given by $\vec{N} = \frac{1}{\mu} ( \vec{E} \times \vec{B})$ but the ...
2
votes
1answer
16 views

What is the value (order of magnitude) of electric charge density of the atom and the nucleus?

The mass density of the nucleus is constant. But what is the electric charge density of the nucleus and the atom (any order of magnitude)?
0
votes
1answer
100 views
+50

single photon/electron double slit experiment, resetting the detector material after each impact

What is the experimental (*) outcome of a single photon/electron double slit experiment under the constraint that after each detection the detector material is reset to the original state ie, in the ...
2
votes
2answers
120 views

Far Field Diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the fraunhoffer diffraction integral, or simply by the ...
2
votes
1answer
151 views

Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
-1
votes
0answers
5 views

With what frequency triangle swings if it shuns from equilibrium? [on hold]

Guide V-shaped is with no friction in the swivel bearings A and B (see Fig.) Of the magnet with a vertical magnetic field of 0.8 T. The weight of the guide is 50 g, the length AB 4 cm, and the length ...
1
vote
2answers
89 views

Speed of light paradox [duplicate]

If I send two rockets from the Earth in opposite directions, at, say, 60% of the speed of light relative to the Earth, then relative to each other they are travelling at 120% of the speed of light. ...
-1
votes
0answers
9 views

What voltage is induced between the endpoints of bar, if we swing it by an amplitude [on hold]

After a long horizontal conductor carrying current of 10 A is vertically suspended 2m long insulated conductive rod. We swing it by an amplitude of 10 cm. (a) in the direction of the wire; (b) in ...
0
votes
0answers
21 views
0
votes
2answers
40 views

How do vinyl records work?

I know that vinyl records save the sound as ups and downs on the record plate surface. Let's say two people with different voice timbers say "I like vinyl records" with the same level of voice. It ...
1
vote
1answer
10 views

does the internal energy and enthalpy of the GAS changes in a free expansion process?

when a balloon kept in an evacuated room is punctured and the ideal gas in the balloon goes on to fill the entire room,does the gas perform any work in this expansion, and is there in any change in ...
0
votes
1answer
180 views

Mean-free-time between collisions and drift-velocity

In a physics text book I need help to make sense of the part highlighted in yellow: This is out of context of course, so just to make it clearer: $\tau$ is the mean free time of the electrons in a ...
6
votes
2answers
235 views

Motivation to introduce von Neumann algebras in addition to $C^*$algebras?

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be ...
3
votes
1answer
61 views

What are the latest findings on the topology and size of the universe?

The paper G. Aslanyan & A.V. Manohar, The Topology and Size of the Universe from the Cosmic Microwave Background, JCAP 06 (2012) 003, arXiv:1104.0015, uses the 7-year WMAP data. Has any ...
0
votes
1answer
49 views

Explanation of Interference of Electromagnetic Waves

There is a question on a test which goes like this: "Given two electromagnetic waves, one of wavelength 6.0 X 10-7 m and the other of wavelength 7.0 X 10-7 m, travelling in space. When the two ...

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