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3
votes
2answers
79 views

Why scalar function of vector can only depend on norm of vector?

In Field Quantization by Greiner and Reinhardt as well as The Qunatum Theory of Fields by Weinberg, concerning the spectral function, the authors say a scalar function of the four-vector $p^\mu$ can ...
1
vote
1answer
50 views

Is metric tensor invariant under rotation?

It is said that metric tensor depend on the local coordinate system and therefore are not intrinsic to the surface of an 3d-object? How is it possible, kindly provide any proof or discussion. Also is ...
3
votes
2answers
80 views

Scalar operators In Quantum Field Theory

I am trying to learn Quantum Field Theory and I am stuck in a basic point. What is the definition of a scalar operator in QFT? That is, how does it transform under a Poincare transformation? Why do ...
7
votes
1answer
160 views

Invariance of action $\Rightarrow$ covariance of field equations?

Invariance of action $\Rightarrow$ covariance of field equations? Is this statement true? I have only seen examples of this, like the invariance of Electromagnetic action under Lorentz ...
0
votes
1answer
61 views

Calculate minimum energy of incident neutrino using Mandelstam variables

I am studying the following nuclear reaction: $v + \tilde{v}\rightarrow Z^0$ where the antineutrino is motionless and has a given mass. The $Z^0$ boson has also a known mass. I'm trying to calculate ...
11
votes
4answers
632 views

A common definition of a scalar

Some dictionaries define a scalar as follows: A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction. -- The Free Dictionary However, it ...
2
votes
4answers
90 views

Is relative velocity invariant under special relativity?

If a metre stick passes an observer at speed $v$, would all observers in any inertial frame of reference say the speed of the meter stick relative to the observer is exactly $v$? If so what is it ...
0
votes
1answer
36 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 ...
1
vote
0answers
29 views

Heat energy in special theory of relativity [duplicate]

Is heat energy invariant under Lorentz transformation? If so then how?
2
votes
1answer
111 views

All possible electromagnetic Lorentz invariants that can be built into the electromagnetic Lagrangian?

Given the electromagnetic Lagrangian density $$ \mathcal{L}~=~-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}~=~\frac{1}{2}(E^2-B^2) $$ is a Lorentz invariant, how many other electromagnetic invariants exists that ...
4
votes
2answers
284 views

Reason why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant

I'm trying to think of an intuitive reasoning for why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant. By this I mean that I don't simply want to show that they remain ...
2
votes
1answer
180 views

Is Lagrangian a scalar?

I may be wrong: Lagrangian are scalars. They are NOT invariant under coordinate transformations. The simplest example is when you have a gravitational potential ($V=mgz$) and you translate $z$ by $a$ ...
2
votes
2answers
148 views

Showing the Poincare invariance of a term

I know that this is a simple question! But I would like to know the details. How we can show that the term $$A_\mu(x)\dot{x}^\mu$$ is global and local Poincare invariant? Where $A_\mu(x)$ is ...
0
votes
1answer
195 views

Modular invariance of CFT

I am looking at the Cardy formula for entropy in CFT, and in the article 'Kerr/CFT correspondence and its Extensions' there is a sentence: In any unitary and modular invariant CFT, the asymptotic ...
12
votes
4answers
882 views

Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
5
votes
1answer
153 views

Lorentz covariance of the Noether charge

The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int ...
4
votes
0answers
112 views

Principle of relativity - a second, equivalent form, using invariants

Most people state the principle of relativity like this: "The rules of physics must take the same form in all inertial frames." Question: is this an equivalent way of saying the same thing: ...
2
votes
1answer
132 views

Does a constant of motion always imply a Hamiltonian formulation?

If a continuous dynamical system has a constant of motion that is a function of all its variables, and is not already evidently Hamiltonian, is it always possible to use a change of variables and ...
1
vote
1answer
308 views

Calculating electromagnetic invariant in matrix form

I'm kind of confused. I want to calculate the electromagnetic invariant $I := F^{\mu\nu}F_{\mu\nu} $, but I'm not sure what is the easiest way to do so. So, I was trying to do it in matrix form, i.e. ...
13
votes
4answers
1k views

To which extent is general relativity a gauge theory?

In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
-1
votes
3answers
2k views

Is kinetic energy a scalar? [closed]

Is it correct to say that kinetic energy is a scalar?