ferdinandjproa @timely_pace@qoto.org
spotted typo in eqn((22.3) has been corrected and in this update, full spacetime solution (fields vary in both space and time) briefly explored
https://foxtrotpaparomeo.wordpress.com/2024/02/08/08022024rough-draftstatic-solutions-to-einsteins-field-equations-in-11-space-time/
updated from pages 53 to 58 it's clear in the construction that for the case of leptons, for example, righthanded leptons don't interact with the W^+- vector gauge bosons only their lefthanded counterparts and this is so since righthanded leptons have zero isospin however, seeing this would wait for the next updates in which we construct the covariant derivative terms for righthanded fermion singlets
https://foxtrotpaparomeo.wordpress.com/2024/01/29/29012024first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/
(additional resource material re G -- measuring G during the big bang nucleosynthesis and comparing it to its present value, results at 2sigma)
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When combining the measured abundances and the baryon density from CMB observations by Planck, we find G_BBN/G_0 = 0.99^+0.06_−0.05 at 2σ confidence level.
https://arxiv.org/abs/1910.10730
preparing outlines for a draft on refresher analysis of inductor-capacitor filter LCF with full wave rectified voltage source
additional basic resource material to my venture into 1 + 1 GR (you can refer to eqn (23) --- the vanishing of Einstein's tensor strictly in 1 + 1 dim)
https://digitalcommons.calpoly.edu/physsp/65/
i can say (with full confidence) that more than 60% of my acquired knowledge in QFT i learned from the late Prof. Pierre van Baal especially on qft perturbative calculations see pp. 51 - 56
https://library.oapen.org/viewer/web/viewer.html?file=/bitstream/handle/20.500.12657/50887/9781466594609.pdf?sequence=11&isAllowed=y
last update july 2022: there are two basic loops here arising with (22.16.6) for the 288 identical terms, while (22.16.11) for the other 432 identical terms such loops depicted in fig.2, fig.3 respectively
https://drive.google.com/file/d/1QHrsnrxS0HaDwVaG-ArOH8uNiWwId9pO/view
updated it today, you may go directly to (22.11) for the de Sitter-like solution
https://foxtrotpaparomeo.wordpress.com/2023/12/10/10122023rough-draftstatic-solutions-to-einsteins-field-equations-in-11-space-time/
in this: the equation of motion for the conformal scalar field does not solve for a particular form of this scalar, instead this equation of motion yields an identity equation... otoh, this conformal scalar is a functional of an auxiliary scalar field which itself does not have a specific form that is the only acceptable, not just one form can satisfy the identity equation
https://foxtrotpaparomeo.wordpress.com/2023/11/27/27112023rough-draftstatic-solutions-to-einsteins-field-equations-in-11-dimensions/
W^+ boson decays into an outgoing lefthanded top quark and outgoing lefthanded anti-bottom quark, seeing such interaction in the split up of involved fermions into + & - energy modes
terms that contain interactions of w^+- vector gauge bosons with members of lepton family. fermions involved expanded into + and - energy modes from such we get, for example, the term for the decay of w^+ vector bosons into an outgoing neutrino and outgoing positron, the anti-particle of electron
in this (1+1)-dimensionally reduced form of GR, the form of the conformal field is handed down by an auxiliary field not from the equation of motion for the conformal field. this auxiliary field is put in by hand and the acceptable form must satisfy a constraint resulting from the equation of motion for the conformal field.
in the static setting, it's straightforward to establish correspondence to Schwarzschild solution yet, there is also the temptation to consider a setting where the fields evolve with both lower dimensional coordinates
the forcing function is a full wave rectified voltage, we want to obtain for the forced response, which is the current i(t) but we have to perform first fourier analysis on the forcing function to get its fourier series
now, i have come to a more inclusive construction of the SU(2)XU(1) Lagrangian of the Standard Model Electro-weak theory. the other generations of the lepton family are included and as well as the three generations of the quark family.
https://foxtrotpaparomeo.wordpress.com/2023/10/15/15102023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/
of course, in my children's baseball days i was also a shortstop
https://www.youtube.com/watch?v=PJQz5-Uf-7E
