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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What is the phase space for outgoing photons?

For a scattering process for which $n$ fermions are scattered, (by some conventions) the cross section acquires a phase space factor of: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ ...
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111 views

Derivation of (2.45) in Peskin and Schroeder

I'm having trouble understanding the step $$\left[\pi (\vec{x},t),\int d^{3}y ~(\frac{1}{2} \pi (\vec{y},t)^{2}+\frac{1}{2}\phi (\vec{y},t)(-\nabla^{2} +m^{2})\phi (\vec{y},t)) \right]$$ $$ =\int ...
6
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1answer
131 views

What does this question about entanglement and classical geometry mean?

Below is the question from Andy Strominger's presentation at the String 2014 conference. The question was asked by credible physicist Ashoke Sen as an important question. "What is the precise ...
3
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36 views

A question on the Bousso-Polchinski paper

In this famous paper by Bousso and Polchinski, Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant an example in M-theory compactification is given in section ...
2
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0answers
63 views

Massless $\phi^3$ theory in $d=6$ dimensions

I am asked to calculate renormalization for a massless $\phi^3$ theory in $d=6$ dimensional space using dimensional regularization. I'm having trouble finding the three-point vertex correction as one ...
6
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58 views

What is a superfluid in field theoretic terms?

I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple ...
3
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97 views

Kallen–Lehmann spectral representation for an arbitrary spin

Let's have Kallen–Lehmann spectral representation for the scalar theory: $$ \tag 1 D(p) = \int \limits_{0}^{\infty} d(\mu^{2})\frac{\rho (\mu^{2})}{p^{2} - \mu^{2} + i\varepsilon}. $$ We can represent ...
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1answer
83 views

The ridge at LHC

One of the results obtained by LHC is the following diagram for p-Pb collisions: I would like to understand what is actually depicted in the figure, what should we expect based on theoretical ...
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2answers
151 views

Functional Derivative in the Linear Sigma Model

In the linear sigma model, the Lagrangian is given by $$ \mathcal{L} = \frac{1}{2}\sum_{i=1}^{N} \left(\partial_\mu\phi^i\right)\left(\partial^\mu\phi^i\right) ...
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34 views

Another Power Counting/ mass dimension question

Are the mass dimension of the Dirac field different from those of the Klein-Gordon field, or is this just another issue of "cannonical normalization?" For instance if $\mathcal{L}_{KG}=\int ...
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53 views

Probability and the propagator

Due to the Wiki article, "...In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to ...
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236 views

O(N) sigma model at large N

I would like to better understand the main principles of large-N expansion in quantum field theory. To this end I decided to consider simple toy-model with lagrangian (from Wikipedia) $ \mathcal{L} = ...
7
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2answers
214 views

How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
2
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0answers
26 views

Theory with interaction and the birth of bound states during propagation

Suppose we want to calculate vacuum expectation $$ \tag 1 D_{lm}(x - y) = \langle \Omega | \hat {T}\left( \hat {\Psi}_{l}(x)\hat {\Psi}_{m}^{\dagger}(y)\right)| \Omega\rangle = \langle \Omega| \hat ...
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1answer
85 views

Schrödinger evolution for a Klein-Gordon equation

I have a problem with the transition from quantum relativistic wave equations (specifically Klein-Gordon equation) to QFT, since a lot of assumptions seem implicit. For example I have a problem with ...
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0answers
34 views

Renormalization of diagrams in QFT [duplicate]

Can any one suggest a good reference for studying renormalization of disjoint, nested and overlapping divergences in Feynman diagrams (for example, $\Phi^4$ theory)?
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3answers
108 views

First quantization version of quantum field theory

In quantum mechanics, we have the word second quantization for identical particles. However, when dealing with localized states, first quantization version of quantum mechanics is also very ...
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46 views

One more time about LSZ-theorem

This question is the continuation of this one. For simplicity, let's use $(1)$ from the linked question (it is called n-point Green function and in particle case coincides with internal diagram), $$ ...
4
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1answer
111 views

From Symmetry Group to Physics Equations

To the extent that I know: There are symmetry groups like the rotation groups SO(3), the Groups of Poincare Transformations,... If the physics of a system has a symmetry group G, then it can be ...
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51 views
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2answers
123 views

can gapped systems have gravitational anomalies?

The question is in the title. If it is possible, what are some examples of gapped systems--either quantum field theories or condensed matter systems--which exhibit some kind of anomaly when coupled ...
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0answers
88 views

LSZ reduction theorem derivation in Weinberg QFT

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} ...
2
votes
1answer
134 views

Lagrangian depends on second derivative of field

In case of the gauge-fixed Faddeev-Popov Lagrangian: $$ \mathcal{L}=-\frac{1}{4}F_{\mu\nu}\,^{a}F^{\mu\nu ...
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16 views

regarding vertex function and proton scattering

I am currently going through electromagnetic form factor. I came across the fact that since the proton is not an elementary particle its scattering(elastic) with electron can be modeled using general ...
4
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1answer
62 views

Expressing an adjoint representation Wilson line in terms of the fundamental representation

I'm working out some calculations with Wilson lines, defined as path-ordered exponential integrals of a gauge field: $$U = \mathcal{P}\exp\biggl(ig\int_{-\infty}^{\infty}\mathrm{d}x^\mu T^c ...
5
votes
3answers
162 views

Global vs. local gauge group in mathematical sense - physics examples?

Upon reading about the principal bundle picture of (quantum) field theory I encountered two different definitions of the gauge group: Local gauge group $G$. Corresponds to the fibers of the ...
5
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1answer
72 views

Particle/Pole correspondence in QFT Green's functions

The standard lore in relativistic QFT is that poles appearing on the real-axis in momentum-space Green's functions correspond to particles, with the position of the pole yielding the invariant mass of ...
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1answer
102 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
2
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1answer
110 views

Massless $\lambda \phi^4$ QFT

The $\lambda \phi^4$ quantum filed theory is the textbook example (which probably cannot be constructed nonperturbatively; I'm purely interested in perturbation theory). However, usually one treats ...
2
votes
1answer
52 views

Conformal compatification of Minkowski and AdS

How do I show that the compactification of Minkowski is given by the quadric $$uv-\eta_{ij}x^{i}x^{j}=0$$ with an overall scale equivalence in the coordinates.I get that for $v \neq 0$, the surface ...
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4answers
2k views

Which is more fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: I lack an adequate understanding of ...
6
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0answers
52 views

Ambiguity in Asymptotic Perturbative Series and Instantons

I know there are a number of questions about the asymptoticity of perturbative series and about instantons on StackExchange (e.g. Instantons and Non Perturbative Amplitudes in Gravity from user566, ...
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2answers
124 views

How do different fields interact with each other?

Recently I've seen a few talks and lectures about Quantum Field Theory. They explained what a "particle" means in a field, and that a large enough excitement in a certain field can excite another ...
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3answers
735 views

Why aren't all photons virtual particles even in the “vacuum” of empty space? [duplicate]

I'm thoroughly confused about the nature of electromagnetic radiation. Light is supposed to exhibit both wave and particle characteristics. But does that mean that it is both a wave and a particle or ...
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1answer
54 views

power counting and (superficial) non-renormalizability

Comment: This stuff is new to me so it doesn't entirely make sense (yet). Question: As I understand from Peskin and Schroeder chap 10 if you have a theory with interaction terms $\lambda \phi^n$ in ...
4
votes
1answer
216 views

Will we need to update Electrodynamics?

A contradiction to the Electrodynamics by the experiment. The author has said that, accordning to the experiment, photon is no more gauge invariant? Why is that? An important thing is that Although ...
16
votes
2answers
475 views

Why are only linear representations of the Lorentz group considered as fundamental quantum fields?

As described in many Q&As around here, fundamental quantum fields are expressed as irreducible representations of the Lorentz group. This argument is entirely clear - we live in a ...
5
votes
2answers
161 views

QFT's that have no action

What does it mean to have a QFT that can not be encoded by an action. What is by far the most powerful approach of study in such a case. What is the best studied physical theory that falls into this ...
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0answers
64 views

A question on spin algebra

In scattering theory, one can form a lorentz invariant quantity by $\epsilon_{\mu 1 2\nu}P^{\mu}_{1}P^{\nu}_{2}$ which is really $1\otimes 1$ 's spin 0 state. Is there such a kind of argument to show ...
2
votes
2answers
104 views

Can a fundamental particle black hole with conserved charge emit Hawking radiation?

Let's says there is a fundamental particle: That is so massive that it is a black hole by itself (Compton wavelength < Schwarzschild radius) That carries a conserved quantum number (e.g. charge ...
3
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1answer
168 views

Black hole thermodynamics in a time dependent metric

For a time dependent space time metric, to get the thermodynamics, does the standard procedure of Wick rotating the time, and then calculating the free energy, work ?
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33 views

Young Tableau Projectors: Does the order of symmetric and anti-symmetric projectors matter?

Given a Young Tableau we find the irreducible basis of an arbitrary tensor by projecting, The projectors are usually defined as first symmetrise over the row entries and then anti-symmetrise over the ...
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votes
1answer
88 views

Would a high energy bottom quark 'decay' to a top quark?

The reason for the long life time of $B$-hadrons is that the CKM element $|V_{tb}| > 0.999$, meaning that the preferred decay of the $b$-quark is to a $t$-quark (and vice versa). However because ...
4
votes
1answer
109 views

Why is string theory a two dimensional quantum (conformal) field theory on its worldsheet?

In string theory, we quantize the two dimensional field theory on the string's worldsheet. I have a question about this kind of quantization of string theory: did we have similar theory for point-like ...
3
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0answers
60 views

Supersymmetric cancellation of loop contributions in a SUSY gauge theory

It is known that in SUSY models, loop contributions are automatically zero leading to a technically natural solution of the Higgs mass hierarchy problem. In many SUSY books/notes, it is often shown ...
5
votes
2answers
94 views

Protection of the electron mass by chiral symmetry

In many textbooks it is said that mass renormalization of the electron mass is only logarithmic $\delta m \sim m\, log(\Lambda/m)$ because it is protected by the chiral symmetry. I understand that in ...
3
votes
1answer
54 views

If non-zero cosmological constant interpreted as a repulsive field, what would be the properties of this field's quanta?

If non-zero cosmological constant interpreted as a repulsive field, what would be the properties of the excitation of such field, i.e. the particle which serves as the field's quantum? What would be ...
2
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1answer
57 views

How exactly to show that s-matrix elements diverges because time-ordering is not well determined?

Let's have s-matrix: $$ S_{\alpha \beta} = \langle \alpha | \hat {S} | \beta \rangle , $$ $$\hat{S} = \hat{T}e^{-i\int \hat{L}(x)d^{4}x}, \quad \hat{T} \left( \hat{\Psi}(t) \hat{\Psi}(t') \right) = ...
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1answer
74 views

Naive unification of scalar QFT and GR is possible?

I am thinking on the Klein-Gordon equation with curved (non-diagonal) metrics. Is it possible? Doesn't have it some inherent contradiction? If yes, what? If no, what is this combined formula?
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1answer
143 views

Rigorous QFT on a Torus

The problem description for the Yang-Mills Existence and Mass Gap problem (http://www.claymath.org/sites/default/files/yangmills.pdf) says in its "Mathematical Perspective" section that Some ...