Timeline for Boundary conditions for Klein-Gordon equation
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Jul 1, 2016 at 20:19 | answer | added | Willie Wong | timeline score: 5 | |
| Jul 1, 2016 at 19:34 | history | reopened |
Charles Rezk asv Willie Wong Andrés E. Caicedo Carlo Beenakker |
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| Jul 1, 2016 at 18:18 | comment | added | asv | @WillieWong: Done. | |
| Jul 1, 2016 at 18:17 | history | edited | asv | CC BY-SA 3.0 |
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| Jul 1, 2016 at 13:32 | comment | added | Willie Wong | @sva: please edit that in to the question statement proper. Your question can be concisely formulated as "Under what decay assumptions are solutions to $(\Box +m^2) u = 0$ necessarily trivial?" with the clarification that decay means "decay toward space/time infinity". // That question is partially answerable and is topic of current research. I've cast a vote to re-open and will provide an answer after the question is re-opened. | |
| Jul 1, 2016 at 4:54 | comment | added | asv | @WillieWong: The domain is the whole space-time. By the boundary conditions I mean any extra assumptions on the decay of a function. | |
| Jun 30, 2016 at 20:28 | comment | added | Willie Wong | Boundary conditions... where? Can you specify the (space-time) domain and boundary that you are interested in? | |
| Jun 25, 2016 at 13:28 | review | Reopen votes | |||
| Jun 26, 2016 at 9:39 | |||||
| Jun 25, 2016 at 13:11 | history | edited | asv | CC BY-SA 3.0 |
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| Jun 24, 2016 at 18:40 | history | closed |
Michael Renardy Willie Wong Igor Khavkine Stefan Waldmann Wolfgang |
Needs details or clarity | |
| Jun 24, 2016 at 18:35 | comment | added | asv | @IgorKhavkine: I have updated the post and added yet another example of a situation of interest which is more elementary and mathematically rigorous. | |
| Jun 24, 2016 at 18:34 | history | edited | asv | CC BY-SA 3.0 |
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| Jun 24, 2016 at 10:29 | review | Close votes | |||
| Jun 24, 2016 at 18:40 | |||||
| Jun 24, 2016 at 9:57 | comment | added | Igor Khavkine | Unfortunately, since you have not actually formulated a concrete mathematical question, your post is not really appropriate for MO. From the context, I can tell that a better forum for your question would be physics.SE. But, just to guide your thinking: the heuristic that you mentioned comes from thinking of a mechanical system with generalized position $q(t)$ on an interval $[t_0,t_1]$, where fixing the values of $q(t_i)$ usually uniquely fixes $q(t)$ (which could be $q(t)=0$). | |
| Jun 24, 2016 at 9:46 | comment | added | asv | @IgorKhavkine: As far as I understand, when one computes amplitudes of various scattering processes the boundary conditions may depend on the choice of In and Out states. | |
| Jun 24, 2016 at 9:42 | comment | added | asv | @IgorKhavkine: Let us consider the case $m=0$. Let $A_\nu$ be an EM field (it does not have to be free). When one computes various path integrals over $A_\nu$ it is necessary to fix a gauge. Let's fix the Lorentz gauge $\partial^\nu A_\nu=0$. One integrates over such fields satisfying some boundary conditions I would like to understand. One can still make a gauge transformation $A_\nu\mapsto A_\nu+\partial_\nu f$ where $\Box f=0$. One would like to have that the boundary conditions implied that $f=0$, i.e. there is no non-trivial gauge transformations. | |
| Jun 24, 2016 at 9:32 | comment | added | Igor Khavkine | That's rather strange statement and it's hard to clearly understand what it means out of context. Can you provide a source where such a statement actually appears? One possible interpretation is that $u(x_0,x_i) = 0$ when $u(0,x_i) = 0$ and $\frac{\partial}{\partial x_0} u(0,x_i) = 0$, by the well-posedness of the initial value problem for the Klein-Gordon equation. | |
| Jun 24, 2016 at 9:01 | comment | added | Slereah | In QFT it is usually either compact support funtions or Schwartz functions. | |
| Jun 24, 2016 at 8:44 | history | asked | asv | CC BY-SA 3.0 |