theories:quantum_field_theory
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| - **Theory of interacting fields**. Here we derive the correct terms in our equations that describe interactions using [[advanced_tools:gauge_symmetry|gauge symmetry]]. Unfortunately, it turns out that we can't solve these equations in closed form but only approximately. There is a powerful mathematical machinery that allows us to calculate results approximately. At the heart of this machinery are the famous [[advanced_tools:feynman_diagrams|Feynman diagrams]]. In addition, an important trick (the interaction picture) allows us to reuse most of the things we derived for free fields. | - **Theory of interacting fields**. Here we derive the correct terms in our equations that describe interactions using [[advanced_tools:gauge_symmetry|gauge symmetry]]. Unfortunately, it turns out that we can't solve these equations in closed form but only approximately. There is a powerful mathematical machinery that allows us to calculate results approximately. At the heart of this machinery are the famous [[advanced_tools:feynman_diagrams|Feynman diagrams]]. In addition, an important trick (the interaction picture) allows us to reuse most of the things we derived for free fields. | ||
| - **[[advanced_tools:renormalization|Renormalization]]**. The main problem in quantum field theory is that calulcations are technically extremely challenging. One reason for this is that when we calculate things naively we end always end up with the result "infinity". This is physically nonsensical and we need to take greater care. The mathematical machinery that allows us to tame these infinities is known as renormalization. | - **[[advanced_tools:renormalization|Renormalization]]**. The main problem in quantum field theory is that calulcations are technically extremely challenging. One reason for this is that when we calculate things naively we end always end up with the result "infinity". This is physically nonsensical and we need to take greater care. The mathematical machinery that allows us to tame these infinities is known as renormalization. | ||
| + | |||
| + | |||
| + | ---- | ||
| + | |||
| + | **Recommended Resources** | ||
| + | |||
| + | * [[https://arxiv.org/abs/hep-th/9702027|What is Quantum Field Theory, and What Did We Think It Is?]] by S. Weinberg | ||
| + | * [[https://arxiv.org/abs/hep-th/9803075|Quantum Field Theory]] by Frank Wilczek | ||
| + | |||
| <tabbox Roadmaps> | <tabbox Roadmaps> | ||
| - | -->How to get started learning QFT as an undergraduate by Flip Tanedo | + | |
| - | see https://fliptomato.wordpress.com/2006/12/30/from-griffiths-to-peskin-a-lit-review-for-beginners/ | + | |
| - | <-- | + | |
| -->Serious QFT by Tom Banks# | -->Serious QFT by Tom Banks# | ||
| Line 85: | Line 92: | ||
| <-- | <-- | ||
| - | <tabbox Lifecycle of a Quantum Field Theorist> | + | -->How to get started learning QFT as an undergraduate by Flip Tanedo |
| + | see https://fliptomato.wordpress.com/2006/12/30/from-griffiths-to-peskin-a-lit-review-for-beginners/ | ||
| + | <-- | ||
| + | |||
| + | -->Classical Solutions in Quantum Field Theory# | ||
| + | |||
| + | <diagram> | ||
| + | | AA|~@2| General overview, why should we care about classical solutions? |AA=[[advanced_notions:quantum_field_theory:solitons]] | ||
| + | | |!@4| | | | | | | ||
| + | | AA|~@2| Kink solution, stability of the kink, boundary conditions, topological charge |AA=[[models:scalar_1plus1]] | ||
| + | | |!@4| | | | | | | ||
| + | | BB|~@2| Duality |BB=[[models:sine_gordon|Sine-Gordon]] and [[models:thirring|Thirring Model]] | ||
| + | | |!@4| | | | | | | ||
| + | | BB|~@2| Vortex solution, solitons in gauge theories |BB=[[models:abelian_higgs_2plus1|Abelian 2+1 Higgs Model]] | ||
| + | | |!@4| | | | | | | ||
| + | | BB|| |BB=[[advanced_notions:quantum_field_theory:sphalerons]] | ||
| + | | |!@4| | | | | | | ||
| + | | BB|| |BB=[[advanced_notions:quantum_field_theory:instantons]] | ||
| + | | |!@4| | | | | | | ||
| + | | BB|| |BB=[[advanced_notions:quantum_field_theory:qcd_vacuum]] | ||
| + | </diagram> | ||
| + | |||
| + | <-- | ||
| + | -->Lifecycle of a Quantum Field Theorist# | ||
| <blockquote> | <blockquote> | ||
| Line 112: | Line 142: | ||
| <cite>[[https://arxiv.org/abs/math-ph/0204014|Lectures on Quantum Field Theory]] by R. E. Borcherds, A. Barnard</cite> | <cite>[[https://arxiv.org/abs/math-ph/0204014|Lectures on Quantum Field Theory]] by R. E. Borcherds, A. Barnard</cite> | ||
| </blockquote> | </blockquote> | ||
| + | |||
| + | <-- | ||
| </tabbox> | </tabbox> | ||
theories/quantum_field_theory.1525521576.txt.gz · Last modified: 2018/05/05 11:59 (external edit)
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