Homework Statement
(a) Calculate the Conserved currents $$K_{\mu \nu \alpha} $$ associated with the global lorentz transformation and express them in terms of energy momentum tensor.
(b) Evaluate the currents for $$L=\frac{1}{2}\phi (\Box +m^2)\phi$$. Check that these currents satisfy...
this is a small part of a problem on tidal forces and I wasn't sure what the question asks as it seems to me that more information is needed. Am I right or is there something im missing? the question goes as:
"A spacecraft approaches a neutron star of radius 10 km and mass 1.5 times mass of...
Homework Statement
A cylinder of permeability ##\mu## is placed in an external field ##B_0##. find the strength and direction of magnetic field inside the cylinder for:
a) when axis of cylinder is parallel to external field.
b) when axis of cylinder makes an angle ##\theta _0## with external...
Homework Statement
Point transformation in a system with 2 degrees of freedom is: $$Q_1=q_1^2\\Q_2=q_q+q_2$$
a) find the most general $P_1$ and $P_2$ such that overall transformation is canonical
b) Show that for some $P_1$ and $P_2$ the hamiltonain...
Homework Statement
If in a system with i degrees of freedom the $$Q_i$$ are given what is the best way to proceed for finding the $$P_i$$ so that we have an overall canonical transformation. say for a two degree freedom system we have $$Q_1=q_1^2 $$ and $$ Q_2=q_1+q_2$$
Homework Equations...
Homework Statement
Two photon of energy ##E_1 ## and ## E_2## collide with their trajectory at an angle $\theta$ with respect to each other.
a) Total four-momentum before collision?
b) square length of 4-momentum in lab frame (LB)and in center of momentum frame (CM)?
c) 4-momentum of two photon...
Homework Statement
A potential satisfies ##\nabla^2 Φ = 0## in the 2d slab ## -\inf < x < \inf ##, ##-b < y < b ##, with boundary conditions ## Φ(x, +b) = +V_s(x)## on the top and ##Φ(x, b) = -V_s(x)## on the bottom, where[/B]
##V_s (x)= -V_0 for -a<x<0##
##V_s (x)=+V_0 for 0<x<a##
(a) what...
Homework Statement
Suppose a linear operator L satisfies <A|L|A> = 0 for every state A. Show that then all matrix elements <B|L|A> = 0, and hence L = 0.
Homework Equations
##<A|L|A>=L_{AA} and <B|L|A>=L_{BA}##
The Attempt at a Solution
It seems very straight forward and I don't know how...
Homework Statement
A potential ##\phi(\rho, \phi ,z)## satisfies ##\nabla^2 \phi=0## in the volume ##V={z\geqslant a}## with boundary condition ##\partial \phi / \partial n =F_{s}(\rho, \phi)## on the surface ##S={z=0}##.
a) write the Neumann Green's function ##G_N (x,x')## within V in...
I can't think of a situation where we can utilize greens function without the presence of a point charge. lets consider the following equation:
\Phi=\frac{1}{4\pi \epsilon} \int dv \rho(x')G_{N} (x,x')+ \frac{1}{4\pi} \int da F_{s}(\rho , \phi) G_{N} + <\phi>_S
Here we see that a volume...
in the paper written by Jose Torres-Hernandez in 1984 titled as : "Photon mass and blackbody radiation" in the first page he writes for the partition function:
lnZ=λ \sum_{normal modes} e^{-βε_l} = \frac{-λπ}{2} \int_{ε_0}^∞ n^2 ln(1-e^{-βε}) \frac{dn}{dε}dε
i really don't understand...
consider energy for a damped electric oscillator . ("f" indicates the dipole moment of the oscillator)
in the absence of the damping force
U= \frac{1}{2}kx^2 +1/2 (\frac{d^2x}{dt^2}) ^2
and the energy conservation tells us dU=0.
but if there is damping force we get the following...
the problem is on page 26 of "relativistic quantum mechanics and field theory" by Franz Gross.
consider the lagrangian density:
L=(1/2)[(∂ψ/∂t)^2 -(∂ψ/∂z)^2 -m^2ψ^2]
a) find the momentum conjugate.
b) find the equation of motion for the fields and the solution. use periodic boundary...
Hi guys! I'm a third year physics student. and I'm studying mathematical physics and particle physics. I thought of doing some research in the field of theoretical physics but the problem is I don't know which subject is most appropriate for me to do research in. I will appreciate it if someone...