# Explaining Rank 0, 1 and 2 Field Theory in Simple Terms

• actionintegral
In summary, this quote seems to be discussing the difficulty of describing the gravitational field using different types of equations.
actionintegral
"Between the simplest rank 0 field theory and the simplest rank 2 field theory is the simplest rank 1 field theory."

I found this quote buried in a huge thread. It seems to be the central point of that thread but I don't know what it means.

Can someone explain what it means using really small words that will fit into my little brain?

I think that these are references to ways to describe the gravitational field. A "rank 0" theory is a "scalar" theory, like ordinary Newtonian gravitation with the gravitational potential (a scalar field) $$\phi$$ [which satisfies the Poisson Equation $$\nabla^2\phi=\rho$$]. A "rank 2" theory is a "tensor" theory, like the Einstein's General Relativity with a "rank 2" object, the metric tensor field $$g_{ab}$$, which must satisfy the Einstein Field Equations. A "rank 1" theory is a "vector" theory, like Maxwell's Electrodynamics with a vector potential $$A_a$$.

From Quantum Field Theory, these ranks are associated with the "spin" of the [massless] quanta of that theory.

I vaguely recall an argument from a Quantum Field Theory class that somehow rejects odd-spin theories for gravitation. (Does it have to do with the attractive property of gravity?)

The only time I have heard the "rank 0, rank 1.." terminology is wrt to Tensors, with a rank 0 tensor being a scalar, rank 1 being a vector and rank 2 being a matrix.

I guess the statement is saying that vector field theory is harder than scalar field theory but easier than matrix field theory...which doesn't make a great deal of sense. Tensor fields of different ranks are all linked via their derivatives, i.e. the derivative of a scalar field is a vector field and so on.

Perhaps whoever posted it meant that vector calculus lies in between scalar calculus and tensor calculus in difficulty...

Without any context, I can't really add any more insight.

Claude.

## What is field theory?

Field theory is a branch of physics that studies the behavior of particles and their interactions through the concept of "fields." These fields are regions of space that have certain properties and can affect the behavior of particles within them.

## What is rank 0, 1, and 2 in field theory?

Rank 0, 1, and 2 refer to the dimensions of a field. Rank 0 fields have no dimensions and can be thought of as a single point. Rank 1 fields have one dimension and can be represented as a line. Rank 2 fields have two dimensions and can be represented as a plane.

## How can rank 0, 1, and 2 fields be explained in simple terms?

Rank 0, 1, and 2 fields can be thought of as different layers of a cake. Rank 0 fields are like the center of the cake, with no dimensions. Rank 1 fields are like the first layer of the cake, with one dimension. Rank 2 fields are like the second layer of the cake, with two dimensions.

## What is the significance of rank 0, 1, and 2 in field theory?

The significance of rank 0, 1, and 2 in field theory is that it helps us understand the behavior of particles in different dimensions. For example, particles interacting with a rank 0 field will behave differently than those interacting with a rank 2 field.

## How does field theory relate to other branches of physics?

Field theory is a fundamental concept in many branches of physics, including quantum mechanics, electromagnetism, and general relativity. It helps us understand the interactions between particles and how they behave in different environments.

Replies
8
Views
518
Replies
5
Views
1K
Replies
8
Views
2K
Replies
6
Views
1K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
4
Views
2K
Replies
5
Views
942
Replies
2
Views
1K
Replies
12
Views
2K