Linked Questions

33
votes
5answers
6k views

Why are infinite order Lagrangians called 'non-local'?

And in what sense are they 'non-local'?
32
votes
3answers
17k views

Deriving the Lagrangian for a free particle

I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away. Proving that a free ...
21
votes
5answers
5k views

Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
15
votes
1answer
13k views

How to understand locality and non-locality in Quantum Mechanics?

What actually is the definition of locality and non-locality? Does non-locality in Quantum Mechanics mean however far you separate 2 entangled atoms in space, the 2 atoms can still influence each ...
4
votes
1answer
2k views

What is meant by a local Lagrangian density?

What is meant by a local Lagrangian density? How will a non-local Lagrangian look like? What is the problem that we do not consider such Lagrangian densities?
4
votes
1answer
3k views

How to tell local and non-local in QFT?

I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?
9
votes
3answers
686 views

How does the functional measure transform under a field redefinition?

My question is: how does the path integral functional measure transform under the following field redefinitions (where $c$ is an arbitrary constant and $\phi$ is a scalar field): \begin{align} \phi(x)&...
4
votes
1answer
400 views

Is the change in the Lagrangian always a total derivative for symmetry transformations of the action?

Let $\Omega\subset\mathbb R^n$ and consider an arbitrary functional $$ S\colon C^k(\Omega)\to\mathbb R $$ that is local, $$ \phi\overset S\mapsto \int_\Omega L(\phi,D\phi,\dots,D^k\phi) $$ for $L$ ...
1
vote
1answer
128 views

Converse of the Lagrangian form-invariance

The form-invariance of the Lagrange equations implies the existence of a function $\ A( q_k, t)$ so that $\ \begin{equation} L' (q_k, v_k, t) -L(q_k, v_k, t) = \frac d {dt} A( q_k, t) \end{equation}...
4
votes
2answers
86 views

What is locality?

In QFT and statistical mechanics, one is usually interested in studying integrals of the form: $$Z(\phi) =\int d\mu_{C}(\phi')e^{-V(\phi+\phi')}$$ where $\mu_{C}$ is Gaussian measure with mean zero ...
1
vote
1answer
109 views

QFTs without Lagrangian

I have been reading other questions in this site, but I have not found answers to all my questions about theories without Lagrangians. What do we mean exactly when we say that they do not have a ...