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advanced_notions:chirality [2017/10/23 10:56] jakobadmin [Why is it interesting?] |
advanced_notions:chirality [2018/03/30 13:19] (current) jakobadmin |
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====== Chirality ====== | ====== Chirality ====== | ||
+ | //see also [[basic_notions:spin]] and [[advanced_notions:helicity|]]// | ||
- | <tabbox Why is it interesting?> | + | <tabbox Intuitive> |
- | Chirality is one of the fundamental labels we use to identify [[advanced_notions:elementary_particles|elementary particles]]. (Other labels are the mass or the electric charge.) | + | |
- | **Important Related Concepts:** | + | <blockquote>One of the things we observe in everyday life is that things have a distinct left and right. The simplest case is just the hands of a human: Obviously, the left hand and the right hand are different from each other. That is a very general thing in nature that things can be 'like a left hand' or 'like a right hand'. Of course, they do not need to be so. A ball has obviously no distinct left or right. But things can have. This fact is known in science as chirality, originating from a Greek word for hand. |
+ | <cite>http://axelmaas.blogspot.de/2011/11/chiral-or-why-left-and-right-is-not.html</cite></blockquote> | ||
- | * [[basic_notions:spin]] | ||
- | * [[advanced_notions:chirality|]] | ||
- | <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> | ||
- | <tabbox Student> | + | <tabbox Concrete> |
+ | |||
+ | 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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<cite>Quantum Field Theory and Standard Model by M. Schwartz</cite></blockquote> | <cite>Quantum Field Theory and Standard Model by M. Schwartz</cite></blockquote> | ||
- | <tabbox Researcher> | + | <tabbox Abstract> |
<note tip> | <note tip> | ||
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</note> | </note> | ||
- | --> 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> | ||
- | + | <tabbox Why is it interesting?> | |
- | <-- | + | Chirality is one of the fundamental labels we use to identify [[advanced_notions:elementary_particles|elementary particles]]. (Other labels are the mass or the electric charge.) |
- | --> Common Question 2# | ||
- | + | <tabbox FAQ> | |
- | <-- | + | |
- | + | ||
- | <tabbox Examples> | + | |
- | --> Example1# | + | --> 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> | |
- | <-- | + | |
- | + | ||
- | --> Example2:# | + | |
<-- | <-- | ||
| | ||
- | <tabbox History> | ||
</tabbox> | </tabbox> | ||