Mordred Posted December 3, 2022 Share Posted December 3, 2022 7 hours ago, Mordred said: Feymann Integrals set c=ℏ =1, (D-1), momentum o particle p as D dimensional vector D(00) =E/c with D-1 remainder spatial components Minkowskii scalar product of pa,pb pa⋅pb=pμagμνpμb set propogator of a scalar particle momentum p and mass m 1p2+m2 consider graph G with Next external edges, Nint internal edges and L=loop number for connected graphs page 16 forwards on Feymann graph rules Feymann Integrals by Stefan Weinzierl https://arxiv.org/abs/2201.03593 project goal examination of the gauge group langrangians with above reference and applying the QFT creation and annihilation operators and QFT propogators Electroweak Lanqrangian L−14WαμνWμνα−14Wμνμν+Ψ¯¯¯¯iγμDμΨ W1,2,3μ[ and Bμ are the 4 spin 1 fields Covariant derivative D2=∂μ+igWτ2−ig´2Bμ W+ andW− bosons are expressed as W±μ=12−−√W1μ∓iW2μ) γ and Z as Aμ=Bμ cosθw+W3μ sinθW Zμ=−Bμ sinθw+W3μ cosθW The Cabibbo-Kobayashi-Maskawa matrix Why did all the math symbols and structures dissappear? Will have to redo this from scratch Link to comment Share on other sites More sharing options...
studiot Posted December 3, 2022 Share Posted December 3, 2022 2 hours ago, Mordred said: Why did all the math symbols and structures dissappear? Will have to redo this from scratch Hey Mordred, it's good to see you back. Hope you made your fortune during you long(ish) abscence. I can still see you maths, they haven't disappeared. But the forum layout has been updated so rolls up a longer post with "expand" at the bottom. Link to comment Share on other sites More sharing options...
Mordred Posted December 3, 2022 Share Posted December 3, 2022 Unfortunately it dropped the math structure in the fractions and dropped the superscript to subscripts etc. I will simply redo it. At least the Electroweak section and just reference the statements for the Feymann Integrals I want to explore. Maybe a few days though. The reference is one I just recently found and is extremely informative. Link to comment Share on other sites More sharing options...
Mordred Posted December 3, 2022 Share Posted December 3, 2022 (edited) Electroweak Langrangian L=−14WαμνWμνα−14BμνBμν+Ψ¯¯¯¯iγμDμΨ W1,2,3μ and Bμ Covariant Derivative Dμ=∂μ+igWμτ2−ig´2Bμ mass eigenstates observed in experiments are linear combinations of the electroweak eigenstates. Hence W− and W+ W±μ=12−−√(W1μW2μ) γ and Z are\ Aμ=BmucosθW+W3μsinθW Zμ=BmusinθW+W3μcosθW Cabibbo-Kobayashi-Maskawa matrix ⎛⎝⎜⎜d´s´b´⎞⎠⎟⎟⎛⎝⎜VudVcdVtdVusVcsVtsVubVcbVtb⎞⎠⎟⎛⎝⎜dsb⎞⎠⎟ symmtric massless SU(2)L⊗U(1)γ −LW=g2√UIL¯¯¯¯¯¯γμ1DiLW+μ+hc UIL and DIL is a vector in generation space of the up/down quark interaction-eigenstates. while 1 is a unit-matrix in generation space. Symmetry break (weak) LY−UIL¯¯¯¯¯¯FUIRH0∗+DILGDIRH0+hc VeV 〈H0〉=v/2–√ F and G are Yukawa matrices. quark mass terms MU=Fν2–√::MD=Gν2–√ Gauge Interaction LW=gsqrt2UL¯¯¯¯¯¯γV†LDLW+μ+hc where V†L is the mixing matrix for quarks giving n generations (n*n unitary matrix) with n2 parameters, in which n(n-1)/2 can be chosen as real angles and n(n+1)/2 are phases subsequent transformation v=PUV†LP∗D v=⎛⎝⎜VudVcdVtdVusVcsVtsVubVcbVtb⎞⎠⎟ for 3 generations of quarks THE CKM QUARK-MIXING MATRIX 1) https://escholarship.org/content/qt1jt6c151/qt1jt6c151_noSplash_4cb0f722c2c328730fbac6c5d0971db9.pdf Feymann Integrals by Stefan Weinzierl 2) https://arxiv.org/abs/2201.03593 PMNS mixing matrix https://pdg.lbl.gov/2020/reviews/rpp2020-rev-neutrino-mixing.pdf Edited December 5, 2022 by Mordred Link to comment Share on other sites More sharing options...
Mordred Posted December 5, 2022 Share Posted December 5, 2022 I give up this is the 4th time this got screwed up the last time was when i tried inserting the url for an image Link to comment Share on other sites More sharing options...
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