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4

I'll address your issues with definition (1): $E$ is a function of $\vec p$ because $\lvert \lambda_{\vec p}\rangle\sim\lvert \lambda_0\rangle$ where by $\sim$ I mean that they are related by a Lorentz boost. That is, to "construct" these states, you actually first sort out all the states $\lvert \lambda_0\rangle,\lambda_0\in \Lambda$ ($\Lambda$ now denotes ...


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The boost generators are First of all, note that You've chosen specific representation of Lie algebra generators of Poincare group, which is vector-like matrix representation. There are many representations in general (below I'll write about them). In Your question, You've chosen the matrix representation of Poincare group algebra generators in pseudo-...


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Right now, I have no idea about what you actually mean by gauge fields, or what anyone ever means by gauge fields. According to Danu, the gauge field is the connection itself, while if I remember well, Bleecker defines gauge fields as sections of those vector bundles that are associated to principal bundles. However, I can, I think, give a definitive answer ...


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Well, the main point is that Yang-Mills theory is just one out of many gauge theories, cf. e.g. this Phys.SE post. E.g. SUGRA is a gauge theory. In fact, theoretically there are relativistic gauge theories with gauge fields transforming in virtually any possible representation of the Lorentz group. Whether they are realized in Nature is another story.


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If the graviton exists it's not a 4 vector, but a tensor.


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Comments to the post (v2): Ref. 1 is considering the $d$-dimensional real Euclidean space $(\mathbb{R}^d,|\cdot|^2)$ with the standard norm $$|x|^2~:=~\sum_{\mu=1}^d (x^{\mu})^2~=~\sum_{\mu,\nu=1}^d x^{\mu}\eta_{\mu\nu}x^{\nu}, \qquad \eta_{\mu\nu} ~=~{\rm diag}(1,\ldots, 1),\tag{A}$$ and inner product $$\langle x ,y\rangle~:=~\sum_{\mu,\nu=1}^d x^{\mu}\...


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The vacuum is defined as the state where the Higgs field (and the rest of quantum fields) have no excitations. The mass of the Higgs boson is the minimum energy that you have to supply to the Higgs field in order to create an excitation. The huge mass for the Higgs field means that it is more difficult to create excitations, so there is no problem to the ...


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Ok you say in an act of faith, and then QTF experts say that there are no virtual particles, they are just a calculation trick. The "trick" part is the assignment of the name "photon", "gluon" , "Z", "graviton", to the mathematical model that allows to predict the interactions of the four forces seen and classified as electromagnetic, strong, weak, ...


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Worldsheet supersymmetry is the fermionic symmetry of the worldsheet RNS action under the worldsheet supsresymmetry transformations that look like $$ \sqrt{\frac{2}{\alpha'}}X \mapsto \sqrt{\frac{2}{\alpha'}}X + \mathrm{i}\bar{\epsilon}\psi^\mu$$ and which I'm too lazy to type out for all fields (and which also depend on whether or not we're looking at the ...


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Mathematically, the R-matrix is an (invertible) element of a quasi-triangular Hopf algebra. The R-matrix there is what "controls" the failure of the cocommutativity of your Hopf-algebra, and the Yang-Baxter equation is a consequence of all that. You can interprete it as a "braid-like" equation. See the wiki-pages on these subjects for more precisions. In ...


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It looks like the sum appears because of the completeness relation $$\mathbf{1} = \sum_{\alpha} \left| \alpha \right> \left< \alpha \right|$$ taken over all the $\{ \alpha_j \}$ to give $$\mathbf{1} = \sum_{\{ \alpha_j \}} \left| \alpha_j \right> \left< \alpha_j \right|$$ Starting with the first expression, which I believe you corrected in ...


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A point particle is an idealization of a particle. It simplifies calculations by using a 0 dimensional object instead of a normal particle in calculations where size, shape, and structure are irrelevant. For example, in the theory of, say, electromagnetism, scientists will talk about a point charge - a particle represented by a point that has a non-zero ...


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Quantum field theory is based on quantum mechanics. The ground state which describes the fields is the free particle solution of the corresponding Dirac/KleinGordo/Maxwell equation. QFT is a theory developed to be able to calculate the many body interactions, seen even in the simplest feynman diagram. It posits fields of each type of particle described by ...


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A multisymplectic form is not a symplectic form and cannot be canonically quantized. Thus your main question doesn't make sense as made ''more precise''. (By the way, I have never seen a way to quantize a multisymplectic form. You would have to quantize the symplectic form underlying the Peierls bracket constructed from the multisymplectic framework. This ...



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