models:toy_models:scalar_1plus1
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
models:toy_models:scalar_1plus1 [2018/03/15 13:40] jakobadmin [Layman] |
models:toy_models:scalar_1plus1 [2018/05/05 11:49] jakobadmin ↷ Page moved from models:scalar_1plus1 to models:toy_models:scalar_1plus1 |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ====== Scalar 1+1 Model ====== | ====== Scalar 1+1 Model ====== | ||
| - | <tabbox Why is it interesting?> | ||
| - | The scalar model in one spatial and one temporal dimension is the simplest type of model we can construct in field theory. | ||
| - | |||
| - | It is often used to introduce the basics of [[advanced_notions:quantum_field_theory:solitons|solitonic solutions]], since the Scalar 1+1 model contains a non-trivial kink solution. | ||
| - | <tabbox Layman> | + | <tabbox Intuitive> |
| The Scalar 1+1 Model describes how the simplest type of field interacts with __itself__. | The Scalar 1+1 Model describes how the simplest type of field interacts with __itself__. | ||
| Line 22: | Line 18: | ||
| | | ||
| | | ||
| - | <tabbox Student> | + | <tabbox Concrete> |
| {{ :models:potentialscalar.png?nolink&400|}} | {{ :models:potentialscalar.png?nolink&400|}} | ||
| Line 128: | Line 124: | ||
| We can understand the stability of the kink also by looking at the energy density of the various solutions. Between the kink and the standard vacuum solution, there is an infinite potential barrier. This barrier exists since it would take an infinite amount of energy to change the kink solution to a classical energy solution. The kink solutions would need to be transformed at every spacetime point either to $a$ or to $-a$ and since the space we are considering is infinite, this transformation would take an infinite amount of energy. | We can understand the stability of the kink also by looking at the energy density of the various solutions. Between the kink and the standard vacuum solution, there is an infinite potential barrier. This barrier exists since it would take an infinite amount of energy to change the kink solution to a classical energy solution. The kink solutions would need to be transformed at every spacetime point either to $a$ or to $-a$ and since the space we are considering is infinite, this transformation would take an infinite amount of energy. | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| The spacetime we are considering is $1+1$ dimensional. Hence the boundary of space is just two points $x_-=-\infty$ and $x_+ =\infty$. We denote this boundary of space with $S_\infty = \{ -\infty, \infty \}$. | The spacetime we are considering is $1+1$ dimensional. Hence the boundary of space is just two points $x_-=-\infty$ and $x_+ =\infty$. We denote this boundary of space with $S_\infty = \{ -\infty, \infty \}$. | ||
| Line 141: | Line 137: | ||
| + | <tabbox Why is it interesting?> | ||
| + | The scalar model in one spatial and one temporal dimension is the simplest type of model we can construct in field theory. | ||
| - | <tabbox FAQ> | + | It is often used to introduce the basics of [[advanced_notions:quantum_field_theory:solitons|solitonic solutions]], since the Scalar 1+1 model contains a non-trivial kink solution. |
| - | + | ||
| - | <tabbox History> | + | |
| </tabbox> | </tabbox> | ||
models/toy_models/scalar_1plus1.txt · Last modified: 2018/05/05 11:49 by jakobadmin
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
