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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Correlation functions and connection to ward identities

I have the following definition of a general correlation function $$ \langle \Phi(x_1)\dots \Phi(x_n)\rangle = \frac{1}{Z} \int [d\Phi] \Phi(x_1)\dots\Phi(x_n)e^{-S[\Phi]} $$ I have only just ...
8
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93 views

Why does the Walecka model not include pions?

The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?
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1answer
77 views

Operator Product Expansion in Massless 2D QED

In Peskin & Schroeder chapter 19 page 656, where the axial current anomaly of massless 2D QED is discussed, the authors go from: $$ ...
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26 views

What is the current state of research about the Hayden-Preskill circuit? [duplicate]

Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a ...
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0answers
72 views

Heisenberg formalism of QFT [closed]

Has anyone tried to develop relativistic quantum theory along the lines of the Heisenberg picture and what's so difficult about promoting time to an operator??
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67 views

About the Hayden-Preskill circuit

Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a ...
2
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0answers
79 views

Spinor Commutator in Peskin and Schroeder

In (3.87, page. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + ...
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84 views

Topologically distinct Feynman diagrams

Are these two diagrams topologically distinct? I consider $\phi^4$ theory and use MS-scheme. A vertex corresponding to counterterm $-\imath \frac{m^2 \lambda}{32 \pi^2 \epsilon}$ is denoted by ...
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96 views

Fourier expansion of the Klein-Gordon field

Is there a reason(both physical and mathematical) why the Klein-Gordon field is represented as a fourier expansion in the second quantization as opposed to other mathematical expansions? Be gentle ...
6
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1answer
193 views

Free Particle Path Integral Matsubara Frequency

I am trying to calculate $$Z = \int\limits_{\phi(\beta) = \phi(0) =0} D \phi\ e^{-\frac{1}{2} \int_0^{\beta} d\tau \dot{\phi}^2}$$ without transforming it to the Matsubara frequency space, I can ...
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50 views

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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116 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
135 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 ...
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0answers
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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69 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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64 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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0answers
116 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
86 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
167 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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38 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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56 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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246 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} = ...
6
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2answers
227 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 $B$: ...
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28 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
100 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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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
115 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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48 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
120 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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2answers
140 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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100 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}} ...
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1answer
153 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
81 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
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3answers
177 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
82 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 ...
3
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1answer
125 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
126 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
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1answer
55 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
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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 ...
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0answers
57 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
134 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 ...
5
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3answers
763 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
61 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
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1answer
218 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 ...
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2answers
508 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 ...
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2answers
167 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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66 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 ...
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2answers
105 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 ...