advanced_tools:gauge_symmetry
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advanced_tools:gauge_symmetry [2018/07/24 10:21] jakobadmin [FAQ] |
advanced_tools:gauge_symmetry [2020/04/02 20:12] 95.90.205.199 |
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| ====== Gauge Symmetry ====== | ====== Gauge Symmetry ====== | ||
| - | //see also [[theories:gauge_theory]] // | + | //see also [[models:gauge_theory]] // |
| <tabbox Intuitive> | <tabbox Intuitive> | ||
| A gauge symmetry is analogous to how we can describe something //within// one language through different words (synonyms). A description of the same thing in different languages is called a [[advanced_notions:duality|Duality]]. | A gauge symmetry is analogous to how we can describe something //within// one language through different words (synonyms). A description of the same thing in different languages is called a [[advanced_notions:duality|Duality]]. | ||
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| When we describe things in physics, we have always some freedom in our description. For example, it doesn't matter what coordinate system we choose. It makes no difference where we choose the origin of the coordinate system or how it is oriented. | When we describe things in physics, we have always some freedom in our description. For example, it doesn't matter what coordinate system we choose. It makes no difference where we choose the origin of the coordinate system or how it is oriented. | ||
| - | The computations can be different in different coordinate systems and usually, one picks a coordinate system where the computation is especially simple. However, the physics that we are describing, of course, doesn't care about how we describe it. It stays the same, now matter how we choose our coordinate system. | + | The computations can be different in different coordinate systems and usually, one picks a coordinate system where the computation is especially simple. However, the physics that we are describing, of course, doesn't care about how we describe it. It stays the same, no matter how we choose our coordinate system. |
| In modern physics, we no longer describe what is happening merely through the position of objects at a given time, as we do it in classical mechanics. Instead, we use abstract objects called fields. The best theory of what is happening in nature at the most fundamental level is [[theories:quantum_field_theory:canonical|quantum field theory]]. Like the electromagnetic field, these fields can get excited (think: we can produce a wave or ripple of the field). For example, when we excite the electron field we "produce" an electron. | In modern physics, we no longer describe what is happening merely through the position of objects at a given time, as we do it in classical mechanics. Instead, we use abstract objects called fields. The best theory of what is happening in nature at the most fundamental level is [[theories:quantum_field_theory:canonical|quantum field theory]]. Like the electromagnetic field, these fields can get excited (think: we can produce a wave or ripple of the field). For example, when we excite the electron field we "produce" an electron. | ||
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| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| - | Gauge symmetries are at the heart of the best theory of fundamental interactions, the [[models:standard_model|standard model]] of particle physics. Theories that make use of gauge symmetry are commonly called [[theories:gauge_theory|gauge theories]]. | + | Gauge symmetries are at the heart of the best theory of fundamental interactions, the [[models:standard_model|standard model]] of particle physics. Theories that make use of gauge symmetry are commonly called [[models:gauge_theory|gauge theories]]. |
| In addition to this application, gauge symmetry can also be useful to understand finance. This is shown, for example, in | In addition to this application, gauge symmetry can also be useful to understand finance. This is shown, for example, in | ||
advanced_tools/gauge_symmetry.txt · Last modified: 2020/04/02 20:12 by 95.90.205.199
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