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2
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1answer
73 views

Functional Derivative of action

Consider the action of free Klein-Gordon theory $S[\phi]=\frac{1}{2}\displaystyle\int d^4y(\partial_\mu\phi(y)\partial^\mu\phi(y)-m^2\phi^2(y))$ Integrating by parts in the first term gives me $S[\...
2
votes
0answers
366 views

Vacuum to vacuum transition amplitude

I have two questions about Vacuum to vacuum transition amplitude. Can any particle stay in $|0\rangle$? I was studying this topic from Srednicki's QFT book. He writes in eq.$(6.22)$ $$\langle0|0 \...
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0answers
53 views

How to calculate the second functional derivative of the action of a one-particle system?

Given the Lagrangian $$L(q,\dot{q})=m\dot{q}^2/2-V(q)$$ and the corresponding action $$S[q]\equiv\int_0^t dt' (m\dot{q}^2/2-V(q)),$$ I need to be able to evaluate the second functional derivative $\...
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0answers
66 views

Eigenfrequencies of a truss

I want to calculate the eigenfrequencies of a 3D truss using the finite element method. The beams should be modelled as Timoshenko beams and I want to use arbitrary shape functions. I know how to ...
1
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0answers
32 views

Commutativity Variation and derivative

When in general is true that $\nabla_{\mu}\delta=\delta\nabla_{\mu}$ where $\nabla_{\mu}$ is covariant derivative? I was thinking this when one has to find the equations of motion for example in ...
1
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0answers
70 views

Variation in Entropy in Einstein's Brownian Motion Paper

In Einstein's Brownian motion paper, he derives a formula for the diffusion coefficient of suspended particles by assuming the system is in dynamic equilibrium and thus, for a variation $\delta x$ (...
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0answers
46 views

Functional Differetiation of a complex functional

Suppose I have a simple functional $$F=\int{dx\;\phi^{*}(x)\phi(x)}\tag{1}.$$ Assuming $\phi(x)$ and $\phi^{*}(x)$ are independent and I take a functional differential with respect to $\phi(x)$ and $\...
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0answers
43 views

What to do when the fields are arranged in a matrix?

I am dealing with a Lagrangian in which the fields are arranged in an $N\times N$ matrix and i have to find the minima of the potential. Usually i would write the Lagrangian in components and then ...
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0answers
46 views

Force of Leaky Bucket over time

Indie Lab Procedure: I attached a cylindrical can to a force sensor. On the bottom of the can I drilled holes of various diameters. I then added a volume of water while collecting data from the force ...
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0answers
69 views

Doubts taking the second functional derivative of the Klein Gordon action

I have very little background with functional derivatives and I would like to clarify some issues. I am trying to compute the second functional derivative of the Klein Gordon action expressed in real ...