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Ever since Newton and the use of mathematics in physics, physics can be defined as a discipline where nature is modeled by mathematics. One should have clear in mind what nature means and what mathematics is. Nature we know by measurements and observations. Mathematics is a self consistent discipline with axioms, theorems and statements having absolute ...


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Consider for example, simple $\lambda \phi^3$-theory with Lagrangian $$ \mathcal{L}=-1\frac{1}{2}\left|\partial_\mu\phi\right|^2-\frac{m^2}{2}\phi^2+\frac{\lambda}{3!}\phi^3. $$ One can say that the $\lambda \phi^3$ term renormalizes the mass term, because the regularization and renormalization of the divergence of the one-loop diagram will lead to a ...


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The word "relativistic" means "compatible with principles of Special Relativity". This usually implies that we can no longer use the "classical" picture of universal stationary space and time. Instead we talk about 4-dimensional space-time. The word "quantum" means compatible with principles of quantum mechanics. You can look them up on wikipedia etc. But ...


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To understand this one shall take in quantum-mechanical approximation method namely perturbation theory into account. In perturbation theory, systems can go through intermediate virtual states which often have energies different from that of the initial and final states. This is because of time energy uncertainty principle. Consider an intermediate state ...


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The string-net condensation is a general construction to obtain gauge fields and fermions. The chiral fermion problem refers to the fact that in the Standard Model (SM), the SU(2) gauge field only couples to the left-handed fermions but not the right-handed fermions. However in the (early version of) string-net condensation, the emergent gauge field will ...


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Energy is not a Lorentz invariant quantity, it is the zero-th component of the four-vector. Only proper orthochronous Lorentz transformations preserve the sign of the zeroth component, so if the energy is positive in one frame, a non-orthochronous Lorentz transformation would yield a frame in which the energy is negative. But we usually only allow the ...


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For your first question: the physical mass is the measured mass. If $m$ is not the measured mass, don't call it the physical mass, because it isn't. If someone does, correct them. :-) For your second question, I think we should look at the physical interpretation of all those mathematical manipulations. The hierarchy problem (as I understand it) comes from ...


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I recently stumbled upon a good comment about this in Jared Kaplan's AdS/CFT notes Any quantum field theory which has hope of having an UV-completion can be viewed as as effective theory at point in the RG flow from an UV complete theory. Field theories at the UV fixed point are conformal. Hence all 'well-defined' field theories are either CFTs or points ...


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@Ihle is right. $\gamma^5\gamma^0=-\gamma^0\gamma^5$. You don't need to insert $\gamma^0\gamma^0$.


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Your second last step is incorrect: $\bar{\psi}_L = \frac{1}{2}\psi^\dagger\gamma_0\gamma^0(1+\gamma_5)\gamma_0 = \frac{1}{2}\bar{\psi}(1-\gamma_5)$, since $\{\gamma_5,\gamma_\mu\} = 0 \implies \gamma_5\gamma_0 = -\gamma_0\gamma_5$.


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The Feynman-rule for this 4-fermion-vertex is $\frac{ia}{M^2} (\sigma_{\mu\nu})_{ij} (\sigma^{\mu\nu})_{lm}$, where $i,j$ are the Spinor-indices of the neutrinos, while $l,m$ are the spinor-indices of the electrons. You see, that this vertex has no free Lorentz-indices and four free spinor-indices, as it should be. For the amplitude you find ...


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The full Green's function of an equation like the Klein-Gordon equation is the difference of the retarded and advanced Green's functions. It is only when the equation in question is an equation involving time that we often discard the advanced anti-causal part to get physically sensible solutions. In QFT, the full Green's function appears for example as the ...


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I think the confusion is due to a lack of mathematically precise definitions of what is quantum field theory? what is one trying to construct and how? etc. There are a lot of vague notions used in the physics literature: the partition function (which does not make much sense in infinite volume), the effective action,...but the bottom line is the collection ...



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