7
votes
1answer
103 views

Assumptions of the Coleman-Mandula Theorem

In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of Poincaré symmetry. The ...
1
vote
0answers
60 views

Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
4
votes
2answers
104 views

Picture of supports

This questions stems from Axiomatic Quantum Field Theory and is mathematical in nature. However, I feel that an answer from physicists is more in line with what I will be asking. Let $\phi$ be a ...
1
vote
3answers
157 views

Non-locality and quanta

Quantum mechanics is non-local in that long distance correlations are present, though there is no signalling possible. But QFT is Lorentz invariant and contains quantum mechanics as a special case. I ...
3
votes
1answer
545 views

What is known on violations of unitarity or locality?

Recently the amplituhedron become a hot topic. I realized that two of the central pillars that QFT is based on, unitarity and locality, are no longer playing an important part (due to gravitational ...
10
votes
2answers
255 views

Locality in the scattering amplitude

Early in this talk by Nima Arkani-Hamed, he describes what locality means for scattering amplitudes. "Locality tells you that the only poles in the scattering amplitude occur when the sum of a subset ...
1
vote
0answers
118 views

QFT basics for Klein-Gordon fields

I am teaching myself QFT from Peskin for next years maths course and I have two questions: What is a c-number? Is it a complex number, and if so why does it mean, ...
9
votes
2answers
384 views

Algebraic/Axiomatic QFT vs Topological QFT

Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
8
votes
1answer
242 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 ...
3
votes
1answer
112 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?
6
votes
2answers
263 views

How does locality decouple the UV and IR behaviour of a QFT?

I came a comment in this paper: Scattering Amplitudes and the positive grassmannian in the last paragraph of page 104 which says: "One of the most fundamental consequences of space-time locality is ...
7
votes
1answer
232 views

Theories with non-vanishing commutators outside the lightcone

I'm reading Weinberg's new book on Quantum Mechanics, and in Chapter 8.7 "Time-Dependent Perturbation Theory" he derives the usual Dyson series for the $S$ matrix when the interaction Hamiltonian ...
2
votes
1answer
256 views

How to tell local and unlocal 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 unlocal.
3
votes
2answers
158 views

Could we get rid of explicit fields derivatives in Quantum Field Theories?

For instance, if we choose the following scalar field Lagrangian, which is (I hope) Lorentz-invariant, where $l$ is a a length scale, and with a $(-1,1,1,1)$ metric: $$ \mathfrak{L}(x) \sim ...
7
votes
1answer
301 views

How is the 'cluster decomposition principle' implemented in holographic theories?

Since holographic theories are non-local by definition, how is this principle implemented? Naively, it seems to me it is not, at least, in some sense. I would appreciate an explanation as simple ...
2
votes
1answer
472 views

How are fundamental forces transmitted?

How are the fundamental forces transmitted? In particular I wonder, are all "processes" local, i.e. without superluminal distant interactions? But if they are local, then particles would have to ...
4
votes
3answers
457 views

Special conformal transformations and locality

In the conformal symmetry, used in some QFT theories, the infinitesimal generators, applying to space-time, are all linear (translations, rotations, boosts, dilatation), except the special conformal ...
13
votes
3answers
2k views

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

And in what sense are they 'non-local'?
6
votes
2answers
1k views

Why is lagrangian density correct?

The textbooks I have available explain that due to the infinite degrees of freedom of a field, the relevant object in QFT is the lagrangian density. A lagrangian is then obtained for the field by ...