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<blockquote data-quote="sjastro" data-source="post: 77079227" data-attributes="member: 352921"><p>In your very quotation the “….<strong>supersymmetric</strong> Yang-Mills theory…..” is an explicit statement for the requirement of supersymmetry in the study of amplituhedrons.</p><p>I suggest you watch this video I referred to in an earlier thread on symmetry paying particular attention to the UA(1) rotation and its application to conserved quantities such as the Dirac Lagrangian.</p><p></p><p style="text-align: center">[MEDIA=youtube]paQLJKtiAEE[/MEDIA]</p><p></p><p>Yang-Mills theory is a generalization of this example where a SU(N) transformation is applied to a <a href="https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory" target="_blank">Yang-Mills Lagrangian</a>.</p><p>For the Lagrangian to be conserved or symmetrical the resulting gauge fields are composed of massless bosons.</p><p>The theory is incomplete as W and Z bosons do have mass and is explained using spontaneous symmetry breaking and the Higgs field.</p><p></p><p>Where as in the Yang Mills theory the gauge fields are boson fields, in supersymmetric Yang-Mills theory there are both boson and fermion fields which are linked by the quantum mechanical supercharge operator Q which transforms fermions IF> into bosons |B> and vice versa according to the equations.</p><p></p><p>Q|F>= |B> and Q|B>= |F>.</p><p></p><p>As an example the fermion electron defined by the wavefunction |Ψₑ> has a corresponding bosonic superpartner the <strong>s</strong>electron |Ψₛₑ> and is defined by the transformation equation Q|Ψₑ> = |Ψₛₑ>.</p><p>There are four different types of supercharges Q hence N= 4 in four dimensional space D = 4 which defines the N = 4 D = 4 supersymmetric Yang–Mills theory.</p><p>Supersymmetry is very much a requirement for amplituhedrons.</p></blockquote><p></p>
[QUOTE="sjastro, post: 77079227, member: 352921"] In your very quotation the “….[B]supersymmetric[/B] Yang-Mills theory…..” is an explicit statement for the requirement of supersymmetry in the study of amplituhedrons. I suggest you watch this video I referred to in an earlier thread on symmetry paying particular attention to the UA(1) rotation and its application to conserved quantities such as the Dirac Lagrangian. [CENTER][MEDIA=youtube]paQLJKtiAEE[/MEDIA][/CENTER] Yang-Mills theory is a generalization of this example where a SU(N) transformation is applied to a [URL='https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory']Yang-Mills Lagrangian[/URL]. For the Lagrangian to be conserved or symmetrical the resulting gauge fields are composed of massless bosons. The theory is incomplete as W and Z bosons do have mass and is explained using spontaneous symmetry breaking and the Higgs field. Where as in the Yang Mills theory the gauge fields are boson fields, in supersymmetric Yang-Mills theory there are both boson and fermion fields which are linked by the quantum mechanical supercharge operator Q which transforms fermions IF> into bosons |B> and vice versa according to the equations. Q|F>= |B> and Q|B>= |F>. As an example the fermion electron defined by the wavefunction |Ψₑ> has a corresponding bosonic superpartner the [B]s[/B]electron |Ψₛₑ> and is defined by the transformation equation Q|Ψₑ> = |Ψₛₑ>. There are four different types of supercharges Q hence N= 4 in four dimensional space D = 4 which defines the N = 4 D = 4 supersymmetric Yang–Mills theory. Supersymmetry is very much a requirement for amplituhedrons. [/QUOTE]
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