Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

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Why multiply by volume when integrating over final momenta in scattering amplitude calculations?

I am learning about calculating decay rates from quantum field theory amplitudes from David Tong's lecture notes (page 74 in the notes, 24 in document). However, I have some doubts: When he says the ...
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233 views

What is a “reggized gluon”?

I'm reading a paper in which the author used these words many times assuming that the reader knows what he is talking about. Can someone please explain what it is? What is the difference between a ...
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1answer
297 views

How to derive the form of the parity operator acting on Lorentz spinors?

I'm reading Berestetskii (Volume 4 of Landau & Lifshitz) section 19 on inversion of spinors. Berestetskii says parity $P$ maps undotted spinors into dotted spinors and vice-versa as ...
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125 views

How to show that higher derivative theories (mostly) breaks unitarity

How to show that higher derivative theories (mostly) breaks unitarity? Spinor field $\psi_{a_{1}...a_{n}\dot {b}_{1}..\dot {b}_{m}} $, which refer to the $\left( \frac{n}{2}, \frac{m}{2} \right)$ ...
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472 views

What forbids the existence of a $\lambda (A^\mu A_\mu)^2$ term in the Stueckelberg action?

In QFT, the Stueckelberg "trick" is often used to show how one can write a fully gauge invariant Lagrangian out of one that is not. For example, if we have $\mathcal{L} = ...
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950 views

Occupation Number Representation in Second Quantization Formalism — What do the entries mean?

I'm reading about the second quantization formalism. I can see the advantages of using number states to represent multiparticle states. Here's my question: Let's say we're given a single-particle ...
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161 views

Quantum Field Theory phenomenology

Suppose you know everything about Quantum Field Theory, but nothing about the very specific interactions and particles which exist in our real word. Which physical or mathematical principles could ...
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151 views

Commutator problem

I am trying to calculate the following commutator $$[\mathcal{H}_0(r',t'),\psi(r,t)]_-$$ where $\mathcal{H}_0 = (\frac{1}{2m}\nabla^2 + e\mathbf{A}(r',t'))^2 + e\phi(r',t') - \mu$, and $\mu$ is the ...
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1k views

Is the firewall paradox really a paradox?

The firewall paradox is a very hot topic at the moment (1207.3123v4). Everyone who is anybody in theoretical physics seems to be jumping into the action (Maldacena, Polchinski, Susskind to name a ...
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1answer
231 views

Why there is the requirement for derivatives no higher than second order in free quantum field equations? [duplicate]

Why there is the requirement for derivatives no higher than second order in free quantum fields equations? We can get the equations for the free fields of an arbitrary spin by using the requirements ...
4
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1answer
646 views

Representations of the Conformal Group in terms of the Poincare Group Reps

The Conformal group contains the Poincare group. Typically, if you take a representation of a group and then look at it as a representation of a subgroup, the representation will be reducible. I often ...
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385 views

Is a QFT in a classical curved spacetime background a self-consistent theory?

EDIT: Better rewording by Chris White: Is it possible to have a theory that treats both GR and QFT (e.g. QFT on a curved spacetime dynamically influenced by the standard QFT fields)? Is such a theory ...
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2answers
650 views

Why are there no particles in conformal theories?

In Matt Strassler's recent post (here) he makes the statement that scale invariant (I assume he means conformally invariant, more generally) theories have no particles in them. What's the reason for ...
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0answers
112 views

Sharp cut-off, quadratic corrections and naturalness

When introducing the fine-tuning problem, a sharp cut-off as a regulator in the calculation of the Higgs mass corrections is used. Since this regulator breaks translational and gauge invariance, up to ...
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1answer
1k 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 ...
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776 views

What is precisely a Yangian symmetry?

The terms Yangian and Yangian symmetry appear in a list of physical problems (spin chains, Hubbard model, ABJM theory, $\mathcal{N}= 4$ super Yang-Mills in $d=4$, $\mathcal{N}= 8$ SUGRA in $d=4$), ...
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1answer
898 views

Why does Quantum Field Theory use Lagrangians rather than Hamiltonains? [duplicate]

Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains? I heard many reasons, but I'm not sure which is true. Some say it's just a matter of beauty, so Lagrangians are more ...
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1answer
482 views

What is the definition of a “UV-complete” theory?

I would like to know (1) what exactly is a UV-complete theory and (2) what is a confirmatory test of that? Is asymptotic freedom enough to conclude that a theory is UV-complete? Does it become ...
6
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1answer
294 views

Has non-conservation of baryon number been observed?

CP violation (as I understand it) allows for non-conservation of baryon number, and thus can contribute (at least a little) to the baryon asymmetry in the universe today (far more matter than ...
12
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2answers
465 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 ...
3
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0answers
110 views

S-matrix and it's exponential form

By using Dyson series for the representation of the $S$-matrix, it's expression can be written in a form $$ \hat {S}(\infty , -\infty) = \sum_{n = 0}^{\infty}\frac{(-i)^{n}}{n!}\int ...
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1answer
114 views

Spinor and Scalar Bose-Einstein condensate

I read about an order paramater that describes a Bose-Einstein condensate. But I don't understand, the classification into "scalar" condensate and "spinor" one. Is it linked with spin of atoms that ...
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1answer
1k views

How does one actually compute the amplituhedron?

I was watching Nima's very popular talk (download if you're using chrome) (also mirrored at youtube here) about the "Amplituhedron", which has suddenly become very popular recently. He talks all ...
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1answer
533 views

Naive quantum gravity

My question involves an analogy I have to point out. Consider the Lagrangian density for the a complex scalar field: \begin{equation} ...
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1answer
388 views

Is integrability necessary for the Amplituhedron?

It is well known that there exist mappings between operators in N = 4 Super Yang–Mills and spin chain states making the theory Bethe Ansatz integrable. Is integrability a necessity for the ...
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75 views

An Equality in The Calculus of Many Instantons

I am reading the review on instantons. When I tried to derive formula (2.27) on page 17, I always get the different coefficient of $gF_{mn}$ term. My calculation is just directly expanding the first ...
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416 views

Scale invariance plus unitarity implies conformal invariance?

What has the reaction been towards the recent paper claiming to have a proof that scale invariance plus unitarity implies conformal invariance in 4d?
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2answers
293 views

Unitarity in QFT and measuring unitarity

I am trying to make sense of statements about unitarity in this popular science article about Nima and Jaroslav's new idea. My first query is that it is claimed that unitarity is a pillar of quantum ...
3
votes
1answer
273 views

Ambiguity in Beta Functions (2-loop)

Beyond one-loop, the beta function of a QFT is scheme dependent. I would like to understand better this ambiguity. The easiest thing to say is that you haven't calculated something physical, so of ...
2
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1answer
500 views

Vectors of polarizations from vector boson field solution

Let's have the solution for vector boson Lagrangian in form of 4-vector field: $$ A_{\mu } (x) = \int \sum_{n = 1}^{3} e^{n}_{\mu}(\mathbf p) \left( a_{n}(\mathbf {p})e^{-ipx} + b_{n}^{+} (\mathbf p ...
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2answers
315 views

Motivation to introduce von Neumann algebras in addition to $C^*$algebras?

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be ...
3
votes
1answer
396 views

Delta functional in path integral

I've recently encountered a path integral of the form $$\int \delta[a\phi+b\phi']\,L(\phi,\phi')\;\mathcal D\phi\mathcal D\phi'$$ (where $a$, $b$ are integers) and would like to eliminate one of the ...
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5answers
27k views

What is the actual significance of the amplituhedron?

The news that physicists have discovered a geometrical object that simplifies a lot our models of quantum physics has recently became viral. For an outsider like me, it is difficult to actually ...
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691 views

In what sense is the path integral an independent formulation of Quantum Mechanics/Field Theory?

We are all familiar with the version of Quantum Mechanics based on state space, operators, Schrodinger equation etc. This allows us to successfully compute relevant physical quantities such as ...
5
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1answer
205 views

Quantization surface in QFT

What does the Quantization Surface mean here? Reference: H. Latal W. Schweiger (Eds.) - Methods of Quantization
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1answer
377 views

Are there two types of D-term and two types of F-term in SUSY?

I've noticed that one can obtain D-terms either by integrating a vector superfield (the vector multiplet) over superspace or by integrating a Kahler potential over superspace. In both cases we get ...
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3answers
2k views

Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com:
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2answers
436 views

How do we know we've unified two interactions?

What is the precise definition of unification of fields (in classical and quantum mechanics)? In general, does unification of a field mean that we can write both of them at both sides of an equation ...
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0answers
49 views

Book to read before “introduction to gauge field theory” by Bailin and Love [duplicate]

A teacher has recommended me to read this book in order to prepare for a project I am doing. Anyway, I feel that I should need a book in order to prepare for this one. Any suggestions?
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1answer
392 views

How to understand the Lagrangian of the standard model, effective or “fundamental”

I have a question about understanding the Lagrangian of standard model, should we view it as a "fundamental" or effective theory? The "fundamental" theory here means the theory with physical cutoff ...
3
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1answer
292 views

Does effective theory have the same meaning in particle and condensed matter physics

I have a naive question about the meaning of effective theory in particle physics and condensed matter physics. In particle physics, from what I know, the effective theory comes from the Wilsonian ...
2
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1answer
78 views

If an Electrical Field can jump over a point on its stright path of propagation?

Consider point B between points A and C on a stright line in vaccum(or any other environment). If the electrical fild $\vec E$ (or an EM wave) should necessarily pass through B to affect C and appear ...
4
votes
3answers
2k views

Fermionic anti-commutation relations

For Pauli's exclusion principle to be followed by fermions, we need these anti-commutators $$[a_{\lambda},a_{\lambda}]_+=0 $$ and $$[a_{\lambda}^{\dagger},a_{\lambda}^{\dagger}]_+=0 $$ Then ...
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votes
2answers
369 views

Do I need to study the “Standard Model” before studying String Theory?

After this semester, I'll have a background up to a first course in QFT (first 5 or 6 chapters of Peskin and Schroeder). The next step in QFT will be something specific to the Standard Model ...
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2answers
788 views

Why are only logarithmic divergence relevant for the Callan-Symanzik equation? Intuitive understanding?

I may be wrong, but it seems that only logarithmic divergences need to be retained when using the Callan-Symanzik equation, finding running couplings, etc. Why is this the case? Is there some simple ...
3
votes
2answers
932 views

Global phase symmetry for complex scalar field theory

I have started to study QFT. And I have some difficulties in such classical situation. Suppose i want to calculate $\frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\phi$ for lagrangian ...
2
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1answer
120 views

UV-IR cancellation of the open string cylinder diagram and the field theory limit

In string theory, the ultraviolet divergences of open string loop diagrams are reintepreted as closed string infrared divergences, by seeing that an annulus with a small loop is also a long tube. In ...
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1answer
542 views

Non-relativistic limit of complex scalar field

In page 42 of David Tong's lectures on Quantum Field Theory, he says that one can also derive the Schrödinger Lagrangian by taking the non-relativistic limit of the (complex?) scalar field Lagrangian. ...
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1answer
343 views

How do non-transverse photon polarizations cancel in Euclidean QED?

First, recall how to write scattering amplitudes in covariant fashion in Minkowskian QED. One starts by considering some process with an external photon whose momentum is chosen to be ...
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1answer
301 views

Some questions about the paper, “AdS description of induced higher spin gauge theory”

I am referring to this paper. I guess that in this paper one is trying to relate the massless spin $s$ gauge fields in $AdS_4$ to conformal spin $s$ theory on $S^3$. So am I right that the ...