Im following Weinberg's QFT volume I and Im tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8):
S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' ...
Hey there! I've recently been looking at calculating amplitudes, densities of states and scattering cross sections in QFT, but am having a little bit of trouble with the exact form of the cross section - particularly with factors of ##2E## for the energies of the incoming and outgoing particles...
Hi all,
I'm trying to find a mathematical way of showing that given a complete set $$\left |a_i\right \rangle_{i=1}^{i=dim(H)}∈H$$ together with the usual property of $$\left |\psi\right \rangle = ∑_i \left \langle a_i\right|\left |\psi\right \rangle\left |a_i\right \rangle ∀ \left...
Homework Statement
Approximately 4% of the intensity of light is reﬂected at a glass-air boundary. Classically one expects roughly 8% of light to be reﬂected from a thin glass plate (4% at the front and back boundary). Outline brieﬂy what quantum theory predicts for a single photon instead of...
In the following there is a proof, for positive values of ##a## only, of (8.18) of Kaku, reference 1, I quote'
$$\int_{-\infty}^\infty~\mathrm{d}p~e^{iap^2+ibp}=\sqrt \frac{i\pi}{a}e^{-ib^2/4a}~~~~~~~~~~~~~(8.18)$$
'. Kaku says this result can be proved by completing the square.
$$iap^2+ibp =...
I learned that stimulated absorption, spontaneous emission and stimulated emission are three fundamental concepts in the process of radiation. Among these three concepts, I found stimulated emission really hard to comprehend, it says when atom in its excited state is stimulated by external...
Dear physics forums,
What is the physical interpretation of imposing the following constrain on a Hamiltonian:
Tr(\hat H^2)=2\omega ^2
where \omega is a given constant. I am not very familiar with why is the trace of the hamiltonian there.
Thanks in advance,
Alex
I have taken a couple of graduate level courses in quantum mechanics and I have decided to read Sakurai's Modern Quantum Mechanics from cover to cover, partly because I liked his style and I have heard a lot of people talk highly of it. But I recently realised that the second edition of the same...
Homework Statement
Show that ##d^4k## is Lorentz Invariant
Homework Equations
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Under a lorentz transformation the vector ##k^u## transforms as ##k'^u=\Lambda^u_v k^v##
where ##\Lambda^u_v## satisfies ##\eta_{uv}\Lambda^{u}_{p}\Lambda^v_{o}=\eta_{po}## , ##\eta_{uv}## (2) the Minkowski...
Homework Statement
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Question:
(With the following definitions here: )
- Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}##
- Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0##
- where ##d## is the dimension of the space ##d=\eta^{uv}\eta_{uv}##
For the L1 operator I am...
Just when I thought I had finally wrapped my brain around relativity, Quantum theory took off. Then the Higgs Boson was discovered. How does the Higgs field under-pin relativity, namely space-time?
How is the Higgs field distributed? Does it have curvature like space time, or is omnipresent...
I been studying quantum field theory and standard model lately. I not see how a unified theory could fit between quantum field and special or general relativity. One being for big objects and the other for microscopic one. In fact, standard model not seem to be all proven. Many particles are not...
What are the branches that we can say are categorized under [Quantum Theory](http://en.wikipedia.org/wiki/Quantum_theory)? [Broken] I am thinking they are QFT, Standard Model and Quantum Mechanics. How about atomic physics and Solid state physics? Also how about Quantum Gravity and Quantum...
Homework Statement
A sub-atomic particle is near the event horizon of a black hole. Due to the nearby gravitational field, the Ricci Curvature Tensor is changing rapidly. The particle then performs quantum tunneling.
Homework Equations
Which version of spacetime does the tunneling particle...
Hi all,
I have an undergraduate degree in Physics, but I've since specialized in more environmental applications of Physics. I've taken a few quantum Physics courses as part of my degree, but, if I'm being honest, what I took from those courses was more of a mathematical view of the field, such...
If a ball is held at rest on a slope and then released what is it's next velocity? How can it's velocity change from nothing to something ?If the change from zero is infinitesimally small would this contradict the Quantum Theory as it's change of energy would be continuous.