Linked Questions

3
votes
1answer
622 views

Naïve relativistic schrodinger equation [duplicate]

Possible Duplicate: Why are higher order Lagrangians called 'non-local'? Bjorken and Drell presents the equation: $$i\hbar\frac{d\psi}{dt}=H\psi=\sqrt{p^2 c^2+m^2 c^4}\psi=\sqrt{-\hbar^2 ...
86
votes
10answers
10k views

Why are differential equations for fields in physics of order two?

What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations? If someone on the street would flat out ask me ...
9
votes
4answers
2k views

Locality in Quantum Mechanics

We speak of locality or non-locality of an equation in QM, depending on whether it has no differential operators of order higher than two. My question is, how could one tell from looking at the ...
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?
11
votes
1answer
963 views

Is this field redefinition for free scalar field theory non-local?

The action of free scalar field theory is as follows: $$ S=\int d^4 x \frac{\dot{\phi}^2}{2}-\frac{\phi(m^2-\nabla^2)\phi}{2}. $$ I have been thinking to redefine field as $$\phi'(x)=\sqrt{m^2-\nabla^...
8
votes
1answer
3k views

Local versus non-local functionals

I'm new to field theory and I don't understand the difference between a "local" functional and a "non-local" functional. Explanations that I find resort to ambiguous definitions of locality and then ...
5
votes
1answer
1k views

Definition of Local Function

Now a days I am studying Srednicki's QFT book. In its third chapter it is written that Any local function of φ(x) is a Lorentz scalar, [...] . Now my question is: What is a local function?
2
votes
2answers
306 views

$\nabla$ and non-locality in simple relativistic model of quantum mechanics

In Wavefunction in quantum mechanics and locality, wavefunction is constrained by $H = \sqrt{m^2 - \hbar^2 \nabla^2} $, and taylor-expanding $H$ results in: $$ H = \dots = m\sqrt{1 - \hbar^2/m^2 \...
2
votes
1answer
477 views

Quantising the energy-momentum relation

The energy-momentum relation in special relativity states $m^2 = E^2 - ||p||^2$ (in natural units). So $$ E = \pm\sqrt{\| p \|^2 + m^2}. $$ If we want to find a theory for a relativistic free ...
7
votes
1answer
403 views

Non-Locality of Space - QFT (Srednicki's book)

I was going through Mark Srednicki's book on QFT. It says in the relativistic limit the Schrodinger equation becomes something like : $$ i\hbar\frac{\partial}{\partial t} \psi(\vec x,t) = \sqrt{-\...
4
votes
1answer
313 views

Why infinite order derivative in Lagrangian density implies non-local?

There is a homework in field theory. It says that negative order of derivative( such as $\frac{1}{\nabla^2}$), fraction order of derivative ( such as $\nabla^{2/3}$ ) and infinite order derivative in ...