Unanswered Questions
3,022 questions with no upvoted or accepted answers
71
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How to apply the Faddeev-Popov method to a simple integral
Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
15
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0
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364
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Simple argument for unexpected behavior in SUSY model
Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential
$$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$
...
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14
votes
1
answer
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Trying to solve 2D Toda Lattice Equation with Lax Pair Approach
I am working on this Hamiltonian:
$$ H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3 $$
Thank you for the hint that it is a modification of the Toda Lattice Equation.
Let me sketch ...
CommunityBot
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13
votes
3
answers
836
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Magnetic scalar potential far above a magnetic film
The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that ...
CommunityBot
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11
votes
3
answers
2k
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Force problem related to adhesive and bonding
I have two PCBs (Printed Circuit Boards), and they are glued by adhesives, as shown in the pictures. The location of the adhesives is indicated in the picture (please notice that no adhesive is ...
CommunityBot
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10
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0
answers
2k
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Sphere half-submerged on a dielectric
This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
- 1,242
9
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0
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731
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)
I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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9
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0
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376
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Path Integral on Feynman Hibbs: Interaction of EM field and matter, how can we get to equation (9.68) from (9.67)?
On Feynman Hibbs "Quantum Mechanics and Path Integrals", the equation (9.67) describes the transition amplitude of the matter (for example an atom) to go from the state $M$ to the state $M$ ...
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9
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2
answers
2k
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Express Laplace transform of voltage across a capacitor in terms of charge
In Charge Tunneling Rates in Ultrasmall Junctions section 2.1, the authors consider the problem of charge relaxation in a simple circuit shown in Figure A.
The implicitly use an assumption made about ...
CommunityBot
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8
votes
0
answers
422
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Free Field Realization of Current Algebras and its Hilbert space
I have some conceptual confusion regarding the interplay between current algebras, their free field representation and the Hilbert space generated from it.
Let's sketch a simple example, $\mathfrak{...
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8
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0
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454
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LSZ Reduction Formula and Wavepackets in Peskin
In Section 7.2 of Peskin and Schroeder, the LSZ Reduction formula is discussed. I can follow the discussion leading up to the equation after (7.41) [at the bottom of Pg. 225]:
$$\sum_\lambda \int\frac{...
- 224k
7
votes
0
answers
617
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Derivation of the BCS Hamiltonian
$$
\hat{H}_{\mathrm{BCS}}=\sum_{k \sigma} \varepsilon_{k} c_{k \sigma}^{\dagger} c_{k \sigma}-\sum_{k k^{\prime}} G_{k k^{\prime}} c_{k \uparrow}^{\dagger} c_{-k \downarrow}^{\dagger} c_{-k^{\prime} \...
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7
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1
answer
2k
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Schrodinger Wave Functional (quantum fields) - Solving Functional Gaussian Integrals
Okay, So i'm doing some research that involves the Schrodinger representation in quantum field theory. The ground state wave functional for the Klein Gordon field is a generalized gaussian in position ...
CommunityBot
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7
votes
1
answer
650
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Sum of energy for 2 solids in rotation
I would like to compute the sum of energy of the following case:
Two solids are turning (disks). Yellow solid is turning at $w_1$ radians per second around its center of gravity and blue solid is ...
CommunityBot
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7
votes
0
answers
682
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Action of Parity operator on Impulse representation
Is my derivation of the action of the parity operator $\mathbb{P}$ on the $|p\rangle$ representation correct?
$$\left( \mathbb{P}\tilde\psi \right)(p)= - \tilde\psi (p).$$
Obtained from
$$\left( \...
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