0
votes
1answer
25 views

Action of the Poincare Group on a Scalar Function

Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific ...
2
votes
1answer
124 views

Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...
4
votes
1answer
137 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: ...
2
votes
1answer
109 views

Noether Charge For Scalar Fields Under Lorentz Transformations

The conserved charge associated with the Lorentz transfomation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is ...
1
vote
2answers
206 views

Can a scalar field model gravity? How accurate would be the results? Are there any difficulties with such a model?

Newtonian gravity can be described by the equation: $$ \nabla^2 \phi = 4 \pi \rho G $$ where $\rho$ is the mass density, $\phi$ is the gravitational potential, and G is the universal gravitational ...
2
votes
0answers
337 views

The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
1
vote
1answer
261 views

Lorentz Invariant Equation of Motion for Scalar Field

I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
8
votes
1answer
3k views

The Euler-Lagrange equation in special relativity

How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.