- #106
DrDu
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Has this argumentation on anomaly freeness also been formulated in a non perturbative setting like algebraic qft or does there exist a soluble toy model?
DrDu said:Has this argumentation on anomaly freeness also been formulated in a non perturbative setting like algebraic qft or does there exist a soluble toy model?
Fujikawa's method is nonperturbative since it uses directly the path integral itself, not Feynman diagrams. However it is not rigorous for two reasons:tom.stoer said:I think that in principle it should be possible to formulate the Fujikawa method non-perturbatively.
DarMM said:Exactly, in a sense Strocchi's theorem isn't really that surprising. Even Strocchi himself in some of his books makes this point, also see the book by Steinmann "Perturbative QED and Axiomatic Field Theory".
[...] So Strocchi and others such as Nakanishi show that the Gupta-Bluer condition and ghosts arise from trying to work with a field as "Wightman-like" as we can manage.
I don't think Strocchi is really pointing anything out, more just showing where naïve assumptions from formal field theory go wrong and what is really going on behind the scenes.
kexue said:The OP droped out long ago.
and doesn't seem to have further questions.mathman said:There is a long ongoing discussion in this forum on this subject (I started it it).
tom.stoer said:Solving this consistency conditions results (besides other physical predictions) in a relation saying
q(u) = 2/3 q(e)
q(d) = -1/3 q(e)
where the 1/3 is due to the fact that each quark is counted three times b/c it exists in three different colors. That means that due to these algebraic relation q(proton) = -q(electron).
I'll put together a reply. It is taking some time because your question has a very deep answer, linking into the nonperturbative definition of the Higgs phenomena.DrDu said:As yet I got no reply to my posting #111, ...
DarMM said:I'll put together a reply. It is taking some time because your question has a very deep answer, linking into the nonperturbative definition of the Higgs phenomena.
The charge of an electron is -1.602 x 10^-19 Coulombs, while the charge of a proton is +1.602 x 10^-19 Coulombs. These charges are equal in magnitude but opposite in sign.
The charges of electrons and protons were first discovered through experiments conducted by J.J. Thomson and Robert Millikan in the late 19th and early 20th century. Thomson's cathode ray tube experiment showed that particles with a negative charge (electrons) were present in atoms, while Millikan's oil drop experiment accurately measured the charge of an electron.
The reason for the charges of electrons and protons is still a fundamental mystery in physics. Some theories suggest that these charges are a natural phenomenon, while others propose that they are a result of the interactions between particles and fields in the universe.
Yes, the charges of electrons and protons can be changed through interactions with other particles or fields. For example, when an electron and a positron (a positively charged particle) collide, they can annihilate each other and produce other particles with different charges.
The charges of electrons and protons play a crucial role in many aspects of our daily lives. For example, they are responsible for the formation of atoms, which make up all matter. They also determine the behavior of electricity and magnetism, which are essential for modern technology such as computers and smartphones.