# Tagged Questions

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### effect of a simultaneous local and a global $U(1)$ symmetry breaking

EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...
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### Noether currents in QFT

I am trying to organize my knowledge of Noether's theorem in QFT. There are several questions I would like to have an answer to. In classical field theory, Noether's theorem states that for each ...
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### Cut-off Regularisation and Renormalisation in Scalar Field Theory, Deriving the Cutoff Independent Physical Mass

I'm having trouble reproducing Equation 42: $$\tag{1} m^{2}_{\text{phys}}= m^{2}_{r} + m^{2}_{r} \tilde{\lambda} \text{log} \left( \dfrac{m^{2}_{r}}{\mu^{2}} \right)$$ ...
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### Is there a field for which neutral particle and antiparticle, can be considered as positive and negative charge?

I apologize, but QFT is not my domain. What I ask is connected with the question Do the fields exist without charges? . By analogy with the electron and proton, that carry the electric charges of the ...
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### Space orientation of light waves

Recently I've started to be really intrigued with the electromagnetic spectrum and bumped into this problem: According to the wave theory of light (or any electromagnetic wave, really), the magnetic ...
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### Question about global internal $SO(n)$ symmetry

I have the following Lagrangian (density) for bosons $$L = \partial_{\mu} \phi^i \partial^{\mu}\phi^i+ m^2\phi^i \phi^i$$ and I am trying to understand why this Lagrangian is invariant under ...
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### Why Do Stark Manifold Graphs All Have Negative Energy?

I have been studying Rydberg-Stark State Atoms and their Stark Manifolds (like the one on Wikipedia: http://en.wikipedia.org/wiki/File:Hfspec1.jpg) and I was wondering, Why does the y-axis (of Energy ...
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### Maxwell's Inspiration to think about fields

I was looking at a Wikipedia article which had the following statement Atomists, notably James Clerk Maxwell and Ludwig Boltzmann, applied [...]. In modern literature Maxwell is often thought ...
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### Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
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### Relation between $f(R)$ gravity and Tensor–vector–scalar (TeVeS) gravity

We know that there is a relation between f(R) gravity and scalar-tensor gravity. By applying the Legendre-Weyl transform, we can receive brans-dicke gravity from $f(R)$ gravity. If we start with the ...
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### Scalar field in a Schwarzschild metric

I have found this article recently published in Classical and Quantum Gravity giving the exact solution of a scalar field in the Kerr-Newman metric. These authors also derived Hawking radiation for ...
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### Relationship between the on-shell and BPHZ renormalization schemes

In his book Quantum Field Theory - A Tourist Guide for Mathematicians, Gerald Folland introduces the on-shell renormalization scheme for the $\phi^{4}$-scalar field theory. According to my ...
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If we have a Lagrangian $\mathcal L$ that depends on some scalar field $\phi$, we define the momentum as $\pi \doteqdot {\partial \mathcal L \over \partial \dot \phi}$. The Hamiltonian then is $\... 1answer 146 views ### Complex scalar field In his book on Quantum Field Theory, Ryder mentioned in p. 91 under the title Complex Scalar Fields and Electromagnetism, the following: He said that under a global phase transformation $$\phi \... 1answer 172 views ### Rigorous version of field Lagrangian In Classical Mechanics the configuration of a system can be characterized by some point s\in \mathbb{R}^n for some n. In particular, if it's a system of k particles then n = 3k and if there ... 1answer 653 views ### Difference between a “source dipole” and a “force dipole” I know quite well what a dipole is and in general what multipole moments are (in the context of, for instance, electrodynamics). What I find myself confused by is something called a "force dipole" in ... 2answers 349 views ### Is internal symmetry the same as gauge symmetry? This is more a terminology question. I have seen that some people differentiate between the two types of symmetry: internal symmetry and gauge symmetry (of a field theory). Is there a difference (in ... 0answers 113 views ### In SUSY, why do fermions and gauge bosons in the same multiplet both transform in the adjoint representation of the gauge group? I'm trying to understand a certain point about supersymmetry. We are dealing with a N=1 (i.e, one supersymmetric flavour), massless, four dimensional theory. Then the vector multiplet consists of a ... 0answers 94 views ### Mixed two-point vertex in QFT I am considering a theory with two fields, say \phi and \psi. The Lagrangian contains quadratic terms, i.e., propagators for both fields and a quartic interaction term for one of the fields. ... 1answer 315 views ### Which transformations *aren't* symmetries of a Lagrangian? As far as I understand, Noether's theorem for fields works, as explained in David Tong's QFT lecture notes (page 14) for example, by saying that a transformation \phi(x) \mapsto \phi(x) + \delta \phi ... 1answer 240 views ### How to find the Hamiltonian density for electromagnetic field? And, how to solve the stress tensor for electromagnetic field? [closed] How to find the Hamiltonian density for electromagnetic field? And, how to solve the stress tensor for electromagnetic field? 0answers 100 views ### What's the conserved stress energy tensor? [closed] I've worked on this problem for forever and still don't really see the solution. Any help appreciated. Say we have the Lagrangian for a scalar field that's U(1) charged,$$\mathcal{L} ={1\over4}(F_{\... 0answers 137 views ### Electric charges on compact four-manifolds Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form$\mathbb{R} \times M_3\$ where the first factor ...
This is a homework problem for a field theory class dealing with an axion model. Originally, we are given that $$S[a]=\int_Md^4x \frac{1}{2}(\partial_{\mu}a(x))^2$$ has a continuous global ...