advanced_notions:quantum_field_theory:qcd_vacuum
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advanced_notions:quantum_field_theory:qcd_vacuum [2017/12/17 16:33] jakobadmin |
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| ====== QCD Vacuum ====== | ====== QCD Vacuum ====== | ||
| - | <tabbox Why is it interesting?> | + | <tabbox Intuitive> |
| + | {{ :theories:quantum_theory:quantum_field_theory:pendulum-300x165.png?nolink&150|}} | ||
| + | A field in physics can be imagined as something like mattress. At every point in space we have an [[models:basic_models:harmonic_oscillator|harmonic oscillator]] and these oscillators are connected. (See the laymen explanation of [[theories:quantum_field_theory:canonical|Quantum Field Theory]]). In this picture, the vacuum state is when all these oscillators sit still. In a quantum field theory, this is never possible because there are always vacuum oscillation. Particles are then excitations of these ground state mattress. | ||
| + | This picture is quite good but misses one crucial thing. There can be tunneling processes in the vacuum. The thing is that if we study the vacuum carefully, we notice that the vacuum state is not so simple as a set of harmonic oscillators that move a little. Instead much better approximation is a set of connected pendulums. At each point in space, we have a pendulum instead of an oscillator and these pendulums are connected. | ||
| - | There is a non-zero energy density of the QCD vacuum due to non-perturbative effects (source: Eq. 1.26 [[http://inspirehep.net/record/197666||here]]) | + | This is an important distinction, because in a quantum theory a pendulum can do something in addition to the usual small vacuum oscillation around its minimum. The pendulum can tunnel such that moves once around its revelation and ends up again in its ground position. While such a process would require usually a lot of energy, in a quantum theory it can happen even at minimum energy, i.e. when the quantum pendulum is in a ground state. This is known as a tunneling process. In this specific context, the tunneling is also called an instanton process. |
| - | + | ||
| - | $$ \epsilon_{vac} \simeq -\frac{b}{128\pi^2}\langle 0|(gG_{\mu\nu}^a)^2|0\rangle \simeq 0.5 \mathrm{\ GeV/fm^3}$$ | + | |
| - | + | ||
| - | This contribution is negative, which means that non-perturbative effects lower the vacuum density we get if we only consider perturbative effects. The absolute value of $\epsilon_{vac} $ sets a scale for the energy density that is necessary to rearrange the vacuum structure. | + | |
| - | + | ||
| - | It is not known completely what is really going in the QCD vacuum, because the final solution of the QCD equations has not been found yet. The values for the vacuum energy density are inferred, for example, by fitting QCD sum rules to experimental data. | + | |
| - | + | ||
| - | <blockquote>To think is difficult. To think about nothing is more difficult than about something.<cite> Lev Okun</cite></blockquote> | + | |
| - | <tabbox Layman> | + | These processes are important, because we need to take them into account when we do calculation in [[theories:quantum_field_theory:canonical|quantum field theory]]. All particles are exictations above the ground state and describe the ground state properly, we need to take these tunneling processes into account. |
| - | <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> | + | <tabbox Concrete> |
| * A great, very pedagogical explanation of the "standard picture" of the QCD vacuum can be found in Jackiw's lecture called "Topological Investigations Of Quantized Gauge Theories ", published in the proceedings of the Les Houches Summer School on Theoretical Physics: Relativity, Groups and Topology (RELATIVITY, GROUP AND TOPOLOGY II: proceedings. Edited by Bruce S. DeWitt and Raymond Stora. Amsterdam, North-Holland, 1984. 1322p). | * A great, very pedagogical explanation of the "standard picture" of the QCD vacuum can be found in Jackiw's lecture called "Topological Investigations Of Quantized Gauge Theories ", published in the proceedings of the Les Houches Summer School on Theoretical Physics: Relativity, Groups and Topology (RELATIVITY, GROUP AND TOPOLOGY II: proceedings. Edited by Bruce S. DeWitt and Raymond Stora. Amsterdam, North-Holland, 1984. 1322p). | ||
| * Another great introduction is Section 4.7 "The Structure of the Gauge Theory Vacuum" in the book An Invitation to Quantum Field Theory”, by Alvarez-Gaume et. al. | * Another great introduction is Section 4.7 "The Structure of the Gauge Theory Vacuum" in the book An Invitation to Quantum Field Theory”, by Alvarez-Gaume et. al. | ||
| + | * See also [[http://jakobschwichtenberg.com/demystifying-the-qcd-vacuum-part-1/|Demystifying the QCD vacuum]] by Jakob Schwichtenberg, [[http://jakobschwichtenberg.com/demystifying-the-qcd-vacuum-part-2/|part 2]],[[http://jakobschwichtenberg.com/demystifying-the-qcd-vacuum-part-3-the-untold-story/| part 3]], [[http://jakobschwichtenberg.com/demystifying-the-qcd-vacuum-part-4-physical-implications-of-theta/|part 4]], [[http://jakobschwichtenberg.com/demystifying-the-qcd-vacuum-part-5-anomalies-and-the-strong-cp-problem/|part 5]] | ||
| + | * [[http://inspirehep.net/record/197666|Theory and phenomenology of the QCD vacuum]] by Edward V Shuryak | ||
| + | * http://muellergroup.lassp.cornell.edu/Basic_Training_Spring_2011/Semiclassics_files/semiclassical3.pdf | ||
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| <-- | <-- | ||
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| **Interpretations of the QCD Vacuum** | **Interpretations of the QCD Vacuum** | ||
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| - | <tabbox Researcher> | + | |
| + | |||
| + | <tabbox Abstract> | ||
| The interpretation of the QCD vacuum is highly gauge dependent. | The interpretation of the QCD vacuum is highly gauge dependent. | ||
| Line 261: | Line 256: | ||
| Claude W. Bernard, Erick J. Weinberg. | Claude W. Bernard, Erick J. Weinberg. | ||
| + | <tabbox Why is it interesting?> | ||
| + | There is a non-zero energy density of the [[models:standard_model:qcd|QCD]] vacuum due to [[advanced_tools:non-perturbative_qft|non-perturbative effects]] (source: Eq. 1.26 [[http://inspirehep.net/record/197666||here]]) | ||
| + | $$ \epsilon_{vac} \simeq -\frac{b}{128\pi^2}\langle 0|(gG_{\mu\nu}^a)^2|0\rangle \simeq 0.5 \mathrm{\ GeV/fm^3}$$ | ||
| + | This contribution is negative, which means that non-perturbative effects lower the vacuum density we get if we only consider perturbative effects. The absolute value of $\epsilon_{vac} $ sets a scale for the energy density that is necessary to rearrange the vacuum structure. | ||
| + | It is not known completely what is really going in the QCD vacuum, because the final solution of the QCD equations has not been found yet. The values for the vacuum energy density are inferred, for example, by fitting QCD sum rules to experimental data. | ||
| - | <tabbox Examples> | + | <blockquote>To think is difficult. To think about nothing is more difficult than about something.<cite> Lev Okun</cite></blockquote> |
| - | --> Example1# | ||
| - | + | <blockquote> | |
| - | <-- | + | Consider the theory of instantons and remember that standard QCD theory says that the vacuum which we inhabit is an instanton sea with about one instanton per femtometer. This means that the physical reality which we inhabit, if you remove everything and just consider the plain vacuum, is already densely filled with, if you wish, physical incarnation of identity types. |
| - | --> Example2:# | + | <cite>https://plus.google.com/+UrsSchreiber/posts/jXEF2UTE8tA</cite> |
| - | + | </blockquote> | |
| - | + | ||
| - | <-- | + | |
| <tabbox FAQ> | <tabbox FAQ> | ||
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