# Questions tagged [invariants]

This tag is for questions relating to invariant, a property of a system which remains unchanged under some transformation. In physics, invariance is related to conservation laws.

173 questions
Filter by
Sorted by
Tagged with
59 views

### Curvature and Symmetries of spacetime

Is there any relation between symmetries of spacetime and the curvature invariants? For example is spherical symmetric spacetimes, necessarily have positive curvature? Could we define any spherical ...
203 views

### What is the difference between invariance and covariance? [duplicate]

In relativistic physics, paricularly in General Relativity and Quantum Field Theory, we often find the use of the two terms 'invariance' and 'covariance'. But I couldn't find any mention of the ...
164 views

### Chern-Simons action as a topological invariant

It is stated that the Chern-Simons action is a topological invariant that is proportional to the Chern-Simons form. But the latter is just a conformal invariant. How do we reconcile these views? Both ...
42 views

### What are the analogues of momentum, inertia and angular momentum for energy?

If Energy and mass are the same thing, then is it logical to look for analogous (duals) of properties of one in another? or there is there any conceptual framework that such questions make any sense? ...
207 views

### Is every Lorentz invariant a Lorentz scalar?

All examples of lorentz invariant quantities that I have come across seem to be scalars: rest mass, proper time, spacetime interval,dot product of two 4 vectors etc. Another thing is that these are ...
33 views

### Classifying all symmetries of a mechanical system [duplicate]

Given a newtonian mechincal system with $n$ objects, we may think of it as living in $\mathbb{R}^{6n+1}$ ; one dimension is time, $3n$ dimensions for velocities, and $3n$ for positions. We then have ...
78 views

### Geometrical interpretation of curvature invariants

Consider a Riemannian manifold. It is possible to describe it by curvature invariants. Now, is there any geometrical description (intuition) for simple invariants such as scalar curvature, Ricci ...
127 views

### Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

What's the physical reason that all (inertial) observers agree on the value of the spacetime interval $$ds^2 = (c dt)^2 - dx^2 - dy^2 -dz^2 \, ?$$ What would be the physical implications if different ...
230 views

### How could 'rest mass' and 'invariant mass' be the same?

The terms rest mass and invariant mass are often interchanged, however i cannot reconcile these concepts: Consider a photon ...
53 views

### time invariance for “Translations” versus “Galilean transformations”

Why would the time coordinate (t) be NOT invariant under translations, but invariant under Galilean transformations? I thought it should be invariant under both Here is what I'm tying to understand:
104 views

185 views

### Can GR be reformulated in terms of invariant observables?

Question So recently I was thinking about this: How many scalars are available in $4$ dimensions in General Relativity (without being redundant)? For example, with metric we can construct the ...
436 views

### Physical meaning of the Casimir operators of Poincarè algebra

If one considers the algebra $su(2)$, it is well known that the Casimir Operator is $$C=L_1^2+L_2^2+L_3^2.$$ It corresponds to the total angular momentum and correctly is a conserved quantity. ...
104 views

### Value of the invariant $R_{\mu \nu}F^{\mu \nu}$

Is there a simple way to find the value of $R_{\mu \nu}F^{\mu \nu}$ (where $R_{\mu \nu}$ is the Ricci tensor and $F^{\mu \nu}$ is the electromagnetic tensor), knowing that it is an invariant? ...
298 views

### Can anyone provide a simple, inuitive explanation for Noether's Theorem? [duplicate]

I recently came across this theorem for the first time. As I understand it, what she showed was that conservation 'laws' are often simply an artifact of symmetry or invariance. For example, the ...
112 views

### How is Einstein's postulate about the invariance of the laws of physics justified? [duplicate]

According to one of Einstein's postulates related to special relativity, > "the laws of physics remain invariant in their form and nature in all inertial frames". But global inertial frames don't ...
111 views

### Restrictions on the form of a scalar-valued function imposed by Lorentz invariance

Let $f(p,q)$ be a smooth Lorentz-invariant function of 4-vectors $p$ and $q$. Should $f$ necessarily be of the form $f(p,q) = g(p^2, q^2, p_\mu q^\mu)$, where $g(x,y,z)$ is some scalar-valued ...
115 views

### Scalar versus invariant in Newtonian mechanics

I looking up coriolis transport theorem for rotating refrence frames and while reading through this derivation he wrote: In Newtonian mechanics, scalar quantities must be invariant for any given ...
487 views

### Gauge invariant scalar which is not Lorentz-invariant

I'm looking for examples of the following descriptions: A gauge invariant scalar which is not Lorentz-invariant A Lorentz covariant scalar For 1. I was thinking about the scalar potential $A$ (for ...
502 views

### What is the physical meaning of the third invariant of the strain deviatoric?

In continuum mechanics of materials with zero volumetric change, the material condition can be expressed by the strain deviatoric tensor instead of the strain tensor itself. To express the plasticity ...
256 views

### Are there Galilean scalars?

In special relativity there are scalar quantities which are invariant under any Lorentz transformation, called Lorentz scalars. For example, the magnitude of the four-velocity is a Lorentz scalar. If ...
78 views

### Formal Term for an invariant constant to all observers

I was thinking of the speed of light and realized I don't know how to quickly name the concept of "physical quantity that is measured to be the same in all reference frames". Are there examples of ...
148 views

### Using the energy-momentum invariant for a decay process

For a decay process in which particle A ----> particle B + a photon in which particle A has mass $m_A$, particle of mass $m_B$ and energy and momentum are conserved. Show that in the frame in ...