Questions tagged [field-theory]

For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.

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Can we use discrete symmetry in order to generate neutrino mass in two higgs doublet model?

It is seen that an u(1) symmetry is generally used to explain the seesaw mechanism for neutrino mass in 2HDM.it is used because the theory then naturally predicts the existence of a right handed ...
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Help with an specific example of a higher derivative Lagrangian

I want to find the equation of motion that comes from the following Lagrangian density $$\mathscr{L}=\mathbf{E}\cdot\left(\nabla^{2}\mathbf{E}\right)$$ where $E_{i}=\partial_{i}\phi\;(i=x,y,z)$ . In ...
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Why are fields which do not transform in a certain way not fundamental?

When I was first exposed to Math physics textbooks and textbooks on vector calculus, I found: Temperature distribution in a room $T(x,y,z,t)$ or the density variation in a fluid $\rho(x,y,z,t)$ etc ...
118 views

Does it make sense to speak in a total derivative of a functional? Part III

In this third part of the series, I will continue the deduction of Noether's theorem initiated in the previous post - Does it make sense to speak in a total derivative of a functional? Part II. ...
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Computation in QFT

I'm always a mess with the upstairs and downstairs notation. To be specific, say I want to calculate the Euler-Lagrange equations of \mathcal{L} = \frac{1}{2}\partial^\mu\phi \...
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Does it make sense to speak in a total derivative of a functional? Part II

I am trying to derive the Noether theorem from the following integral action: S=\int_{\mathbb{\Omega}}d^{D}x~\mathcal{L}\left( \phi_{r},\partial_{\nu}% \phi_{r},x\right) , \tag{II.1}\...
316 views

Does it make sense to speak in a total derivative of a functional? Part I

I would like to consider the problem of the total derivative of a given functional \mathcal{L}\bigg[\phi\big(x,y,z,t\big),\frac{\partial{\phi}}{\partial{x}}\big(x,y,z,t\big),\frac{\...
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Sum over real photon polarizations. The minus sign

Ok for real photons there is the formula when summing over the polarizations: $$\sum_{\lambda=\pm}\epsilon^{*\mu}_\lambda\epsilon^\nu_\lambda = -\eta^{\mu\nu}$$ But if I have a matrix element of ...
127 views

Non-existence of double time-derivative of fields in the Lagrangian and violation of equal footing of space and time

In classical field theory, we consider the Lagrangians with single time-derivative of fields whereas double derivative of the field w.r.t. space is allowed sometimes. I understand that the reason of ...
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Origin of $\sqrt{-g}$ in the integral of action $S$

I have a question that might (and probably will) be stupid: I do not understand where does the factor $\sqrt{-g}$ (i.e. $\sqrt{-\det\left(g_{\mu\nu}\right)}$) come from in the action integral S when ...
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Is there any experiment going on to test the TWO HIGGS DOUBLET MODEL?

We know that the two higgs doublet model which is a beyond standard model theory predicts five higgs bosons.Is there any experiment that is going on to test this theory and if so have they found any ...
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Conserved currents in quantum electrodynamics

A general Noether theorem in fields theory says that an infinitesimal symmetry of the action leads to a conserved current $j^\mu$, i.e. $\partial_\mu j^\mu=0$. Below I would like to consider a minor ...
130 views

Why is gravity the weakest force if, theoretically, it is made up of all the other forces' fields?

I'm quite new to the physics world and want to get an idea as to how physicists have been able to sum all fields/forces (higgs boson, electromagnetic, weak force, strong force etc) in a said object, ...
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Covariant derivative of a composite field and the chain rule

I have a gauge theory with some rather strange covariant derivatives and I am wondering how they act on a composite field like $\psi= \phi\psi'$. In my setup, the covariant derivative acting on a ...
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Showing the form of the covariant derivative of $\phi$, if $\phi$ transforms as the adjoint representation of $SU(n)$

I want to show that if $\phi$ transforms as the adjoint representation of SU(n), its covariant derivative is given by $\textbf{D}_\mu \phi = \partial_\mu \phi + i [\textbf{A}_\mu, \phi]$. (Exercise in ...
108 views

Non-relativistic E&M Lagrangian: number of dynamical variables greater than 6

There is an argument I do not understand given in "Introduction to quantum electrodynamics" by Cohen-Tannoudji (page 111 for the French version of the book). We are dealing with the non-relativistic ...
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Are electromagnetic waves a substance? [duplicate]

I would generally consider fields to not be substances, since substances are generally associated with matter. I know that energy is not a substance. Are electromagnetic waves a substance?
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Field degrees of freedom from equations of motion and higher spin

It is my understanding that we compute the number of degrees of freedom of a quantum field as the number of its components minus the number of non trivial equations we get by taking the divergence of ...
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Derivation of Coulomb's law from classical field theory

In the section on Coulomb's law in QFT by Schwartz, he expands $-\frac{1}{4}F_{\mu\nu}^{2}$ to get $-\frac{1}{2}(\partial_{\mu}A_{\nu})^{2} + \frac{1}{2}(\partial_{\mu}A_{\mu})^{2}$, can someone ...
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$\phi^3$ 2D 1-loop diagram disambiguation

I would like to calculate the 1-loop 1-PI correction to the propagator for $\phi^3$ scalar theory in 2 dimensions, where the integral is finite. Performing the usual procedure (Feynman trick, Wick ...