✎ Boundary Conditions [The Physics Travel Guide]

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====== Boundary Conditions ======

<blockquote>
The [[:equations|field equations]] and the boundary
conditions are inextricably connected and the latter can in no way be considered less important
than the former<cite>V. Fock, The theory of space, time and gravitation</cite></blockquote>

<blockquote>Now, Nature is described by fields, and this elegant and powerful formulation of classical
and quantum mechanics based on the action needs to be supplemented with a careful treatment
of boundary conditions at infinity. The issue of boundary conditions is particularly important
and interesting in the case of [[advanced_tools:gauge_symmetry|gauge theories]] where the assumption ‘all fields decay sufficiently
rapidly at infinity’ is not justified. <cite>https://arxiv.org/pdf/1601.03616.pdf</cite>
</blockquote>

<blockquote>[I]t is natural to regulate infinite sized systems by imposing boundary
conditions at finite distance, often described as placing the system in a box. This idea
has a long history in the gravitational context (see e.g. [15–27]) where it is common to
impose a Dirichlet boundary condition, fixing the induced metric at the walls of the box1
.<cite>https://arxiv.org/abs/1508.02515</cite></blockquote>

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student>

* For boundary conditions for waves, see chapter 9 in Georgi's "[[http://www.people.fas.harvard.edu/~hgeorgi/onenew.pdf|THE PHYSICS OF WAVES]]"
  * For boundary conditions in gauge field theory, see section 4.5 "Cauchy problem and gauge conditions" in Rubakov's "Classical Theory of Gauge Fields". 
 
<tabbox Researcher>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

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<tabbox History>

</tabbox>

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