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But fields aren't inherently relativistic, you can easily construct non-relativistic QFTs, a relativistic QFT is one with a Lorentz invariant Lagrangian. … Those would be expected in a non-relativistic theory, just like the gravitation of the Sun on the Earth is spooky action at a distance in Newtonian gravity. …

I'm doing some field theory, on linearized gravity backgrounds by treating $h_{\mu\nu}$ as a massless spin-2 field. I can't seem to find the ${\cal O}(h^3)$ terms in the Lagrangian anywhere. … Are there any known references that just lists the next to leading order terms in the above Lagrangian? …

The following question comes from this observation, that there are totally different (mirroring) options with which Calabi-Yau you can start (considered in the Lagrangian) if you go in the quantization … But I suspect different metrics in the non-linear sigma model Lagrangian will also affect the classical picture in some essential way, directly or not. …

-1, -1, -1). $$ I have the question about lagrangian of fields in this case: in the book it is written in a form $$ L_{f} = -\frac{1}{32 \pi G}\left( \frac{1}{2}(\partial_{\alpha}h_{\nu \beta}) \partial … alpha} \bar {h}_{\mu \alpha })\partial_{\beta}\bar {h}^{\mu \beta}\right), \qquad (1) $$ where $$ \bar {h}^{\mu \nu} = h^{\mu \nu} - \frac{1}{2}\eta^{\mu \nu}h^{\alpha}_{\alpha} $$ It is argued that this lagrangian …

I consider gravity as a pure scalar field in Minkowski spacetime. … these equations couldn't be found from an action, and this could be raised as an objection (even in a classical field context), since it would be hard to find the scalar field energy-momentum without the lagrangian …

Quantum electrodynamics based upon Euler-Heisenberg or Born-Infeld Lagrangians predict photons to move according to an effective metric which is dependent on the background electromagnetic field. … In other words, photon trajectories are curved in presence of electromagnetic fields, meaning that an effective gravity is acting upon. …

For example, when discussing the precession of Mercury's perihelion we: Derive a Lagrangian associated with a test particle in Schwarzschild geometry which follows a geodesic. … Such methods have been described as unreasonably effective in discussing gravity and it is a well deserved accolade. …

I am trying to find the Lagrangian this gauge produces, and the other discussions stop just short of providing that. … Is there a prescription to construct a Lagrangian from 1,2 and 3? …

I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling? …

He mentions that a straightforward generalization will work for any real, bosonic, linear field provided that it has a well-posed initial value problem; it is derivable from a Lagrangian. … What I find particularly surprising in these remarks is that linearized gravity is described by a spin $s = 2$ field. …

Expressing the metric as $g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}$, assuming $h_{\mu \nu} \ll 1$ we can write the Einstein Hilbert action to leading order in $h_{\mu \nu}$ and quantize the linearized … (This should be especially true if we take the action to be the Kretschmann scalar, which seems to be equivalent to the Yang Mills Lagrangian. $$ \mathrm{Tr}(F_{\mu \nu} F^{\mu \nu}) \leftrightarrow R^ …

Let's say we consider Einstein's Lagrangian from GR. In linearized gravity, we would expand the Ricci scalar to quadratic order in the perturbation parameter to find the propagator. …

To do this, I modeled the Lagrangian density by a scalar field in spacetime with a particle introduced at event ($x_0$, $t_0$), which is: \begin{equation}\mathcal{L} = \frac{1}{2}\partial_\mu\phi^\mu-g … When I plug the field into the Euler-Lagrange equation, I get this: \begin{equation}\frac{\partial^2\phi}{\partial t^2}-c^2\Delta\phi = -g\delta(x-x_0)H(t-t_0). …

From Euler-Lagrange equations, and choosing a parameter $u$ which is linearly related to the interval $s$, the equation for a metric geodesic becomes $$\frac{d^2x^a}{ds^2}+\frac 12 g^{ad}\left(\partial_cg … In my lessons I was told that non-zero torsion has to be taken into account in quantum gravity theories . …

THE PARADOX In Special Relativity, assuming for simplicity a point-like, massive, free body moving along a single coordinate x (thus no quadri-potentials, no gravity, etc.), I have this equation for relativistic … Funny trivia: the linked source corrects the definition of momentum precisely to fix a similar "paradox" with the Lagrange formalism. …