The action principle holds by assumption. It is assumed that all equations of motion follow from this principle with the appropriate action.
By introducing an auxiliary tensor field $h_{\alpha\beta}$, one may write down the so-called Polyakov action $$S_\mathrm{Poly}=-\frac{T}{2}\int_\Sigma \m...
I want to compute the components of the Riemann curvature tensor (for a case similar to the Schwarzschild solution) in 4 + 1 dimensions, but I want to use a higher-dimensional analogue of spherical coordinates. I first want to investigate a metric for the Euclidean case, i.e. "flat" space-time wi...
SECTION A : The linearly independent elements of a Totally Symmetric Tensor $\;T_{i_{1}i_{2}\cdots i_{p-1}i_{p}}\;$(important for the interpretation of Quark Theory of Baryons in Particle Physics)
\begin{equation*}
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{\boldsymbol{3}\boldsymbol{\otimes}\boldsymbol{3}\boldsymbol...
Considering two members of an inertial system(1) (participants $P$ and $Q$ who were and remained separate and at rest to each other, in a flat region), and participant $A$ who moved from $P$ to $Q$:
Is it possible to express the average speed of $A$ wrt. $P$ and $Q$ through values of intervals?...
