advanced_notions:chirality
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advanced_notions:chirality [2017/10/23 10:56] jakobadmin [Why is it interesting?] |
advanced_notions:chirality [2017/12/04 08:01] 127.0.0.1 external edit |
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| * [[basic_notions:spin]] | * [[basic_notions:spin]] | ||
| - | * [[advanced_notions:chirality|]] | + | * [[advanced_notions:helicity|]] |
| <tabbox Layman> | <tabbox Layman> | ||
| <blockquote>Positive and negative chirality fermions are often described as being right-handed or left-handed, respectively;if one shines a beam of positive chirality fermions (particles described math-matically as sections of S+) into a block of matter, it will begin to spin in a right-handed sense." <cite>[[http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0267.0306.ocr.pdf|from Geometry and Physics by E. Witten]]</cite></blockquote> | <blockquote>Positive and negative chirality fermions are often described as being right-handed or left-handed, respectively;if one shines a beam of positive chirality fermions (particles described math-matically as sections of S+) into a block of matter, it will begin to spin in a right-handed sense." <cite>[[http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0267.0306.ocr.pdf|from Geometry and Physics by E. Witten]]</cite></blockquote> | ||
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| <tabbox Student> | <tabbox Student> | ||
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| + | For a nice discussion see http://www.quantumfieldtheory.info/Chirality_vs_Helicity_chart.pdf and http://www.quantumfieldtheory.info/ChiralityandHelicityindepth.pdf | ||
| Chirality arises as a quantum number related to the Lorentz group. Form the [[http://notes.jakobschwichtenberg.com/doku.php?id=the_standard_model:poincare_group#representations_of_the_lorentz_group|representation theory of the Lorentz group]], we know that the corresponding Lie algebra, can be interpreted as two copies of the $SU(2)$ Lie algebra $\mathfrak{su}(2)$. Therefore, we labelled each representation by two numbers: $j_L$ and $j_R$ which indicate which $\mathfrak{su}(2)$ representations are used to construct the Lorentz algebra representations. For example, the label $(\frac{1}{2},0)$ means that we used to fundamental representation for one $\mathfrak{su}(2)$ and the trivial, one-dimensional representation for the other $\mathfrak{su}(2)$. | Chirality arises as a quantum number related to the Lorentz group. Form the [[http://notes.jakobschwichtenberg.com/doku.php?id=the_standard_model:poincare_group#representations_of_the_lorentz_group|representation theory of the Lorentz group]], we know that the corresponding Lie algebra, can be interpreted as two copies of the $SU(2)$ Lie algebra $\mathfrak{su}(2)$. Therefore, we labelled each representation by two numbers: $j_L$ and $j_R$ which indicate which $\mathfrak{su}(2)$ representations are used to construct the Lorentz algebra representations. For example, the label $(\frac{1}{2},0)$ means that we used to fundamental representation for one $\mathfrak{su}(2)$ and the trivial, one-dimensional representation for the other $\mathfrak{su}(2)$. | ||
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| - | --> Does the opposite chirality only emerge dynamically?# | ||
| - | <blockquote>"//because fundamentally all fermion particles are left-handed and all fermion antiparticles are right-handed, with the opposite handedness emerging dynamically for massive fermions. Such dynamical emergence of handed-ness is described by L. B. Okun, in his book Leptons and Quarks (North-Holland (2nd printing 1984) page 11) where he said: “… a particle with spin in the direction opposite to that of its momentum …[is]… said to possess left-handed helicity, or left-handed polarization. A particle is said to possess right-handed helicity, or polarization, if its spin is directed along its momentum. The concept of helicity is not Lorentz invariant if the particle mass is non-zero. The helicity of such a particle depends oupon the motion of the observer’s frame of reference. For example, it will change sign if we try to catch up with the particle at a speed above its velocity. Overtaking a particle is the more difficult, the higher its velocity, so that helicity becomes a better quantum number as velocity increases. It is an exact quantum number for massless particles … The above space-time structure … means … that at …[ v approaching the speed of light ]… particles have only left-handed helicity, and antparticles only right-handed helicity.//" [[http://arxiv.org/pdf/1504.03695.pdf|On the chirality of the SM and the fermion content of GUTs by Renato M. Fonseca]]</blockquote> | ||
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| - | --> Common Question 2# | ||
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| <tabbox Examples> | <tabbox Examples> | ||
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| + | <tabbox FAQ> | ||
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| + | --> Does the opposite chirality only emerge dynamically?# | ||
| + | |||
| + | <blockquote>"//because fundamentally all fermion particles are left-handed and all fermion antiparticles are right-handed, with the opposite handedness emerging dynamically for massive fermions. Such dynamical emergence of handed-ness is described by L. B. Okun, in his book Leptons and Quarks (North-Holland (2nd printing 1984) page 11) where he said: “… a particle with spin in the direction opposite to that of its momentum …[is]… said to possess left-handed helicity, or left-handed polarization. A particle is said to possess right-handed helicity, or polarization, if its spin is directed along its momentum. The concept of helicity is not Lorentz invariant if the particle mass is non-zero. The helicity of such a particle depends oupon the motion of the observer’s frame of reference. For example, it will change sign if we try to catch up with the particle at a speed above its velocity. Overtaking a particle is the more difficult, the higher its velocity, so that helicity becomes a better quantum number as velocity increases. It is an exact quantum number for massless particles … The above space-time structure … means … that at …[ v approaching the speed of light ]… particles have only left-handed helicity, and antparticles only right-handed helicity.//" [[http://arxiv.org/pdf/1504.03695.pdf|On the chirality of the SM and the fermion content of GUTs by Renato M. Fonseca]]</blockquote> | ||
advanced_notions/chirality.txt · Last modified: 2018/03/30 13:19 by jakobadmin
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