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Is Dirac viewpoint still correct under the current modern physics view (in the 2021, in the 21 century)? No, it's old-fashioned. A significant percentage of physicists (I can't give you a number) have a new paradigm based on the string theory landscape and eternal inflation. In string theory there are a vast number of possible vacuum states: $10^{272,000}$, ...


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In the comments, OP clarifies that the issue is with equation (13.2.3). I was confused about this part as well when I first learnt it. The proper way to perform the calculation is as follows. First, do the $q^0$ integral by contour integration. We assume that the numerator of the integrand (which involves the lower point amplitude, the numerator of ...


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The hierarchy problem has to be framed in the context of beyond standard model physics. You have to distinguish between 5 mass scales, namely $m$: the mass of the particle in concern, e.g. Higgs mass $m_H$. $\Lambda$: the UV cutoff scale of the regularization scheme (in dimensional regularization (DR), $\frac{1}{\epsilon}$ plays the role of $\Lambda$, ...


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It seems that the current does mix with $A^\mu$, or $\partial_\nu F^{\nu\mu}$ more precisely, as discussed in this paper written by J. C. Collins et al. (I fount it from another question in PSE). I quote from the abstract: It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that ...


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I've seen references specifically to the "Callan-Symanzik beta function", so I don't think it was much later. (Curt Callan and Kurt Symanzik independently discovered their equation in 1970.) Although the notation of Callan (1970) is unclear to me, Symanzik (1970) implicitly defined $\beta(g)$ [Eq. (I.13)] Then, Symanzik (1971) clearly defined $\...


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The answer is either yes, or else physicists have essentially pulled the greatest heist of the century. The key to why the particular scheme you choose doesn't matter really comes down to the idea of a renormalization point, that is, the point in momentum space at which we fix the values of the correlators and compute the necessary counter terms. It's also ...


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Let me take the point of view of Wilsonian renormalization. Then we do not allow momenta larger than some cutoff $\Lambda$ in the theory, and in particular momenta larger than $\Lambda$ do not appear in loop diagrams. The Wilson coefficients (the coefficients of operators in the Lagrangian) depend on $\Lambda$, in such a way that physical observables do not ...


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Before going to dangerous irrelevance, it helps to briefly recapitulate what irrelevance under RG means in itself. When thinking of an RG fixed point, the scaling behaviour at low energies/long wavelengths is typically controlled only by a handful of relevant operators which dominate the physics, while all irrelevant terms progressively get smaller and ...


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A couple points to add onto the other answer: it is important to consider order parameters depending on $\vec{x}$ , so we can study nonhomogeneous systems too. It's important to stress that the spatial dependence of the order parameter is not (necessarily) used to model nonhomogeneous systems. The Ising model is a perfect example: it's completely ...


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One does not talk about dangerously irrelevant fixed point but of a dangerously irrelevant coupling (or operator). The gaussian fixed point of a $\phi^4$ theory (describing phase transitions in dimension $d\geq 4$) has one relevant coupling (corresponding to the mass/correlation length) and an infinity of irrelevant couplings (one marginally so in $d=4$). ...


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Let's consider the mass of the electron. We can write a Hamiltonian (let's just do non-relativistic quantum mechanics for 1 electron, and let's just pretend the spin is zero for simplicity): \begin{equation} H = \frac{1}{2 m_e^{(b)} }(\vec{p}- e \vec{A})^2 + e \phi(x,t) \end{equation} where $\vec{A}$ is the vector potential and $\phi$ is the scalar potential....


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Agreeing well with experiment is an understatement: the theoretical value matches the experimental value to 10 significant figures, making it the most accurate prediction in all of science. The $g$-factor for elementary spin-$1/2$ particles is $g=2a+2$, where $a$ is (essentially defined as) the anomalous magnetic moment - the constant $2$ is the classical, ...


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