Tagged Questions

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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90 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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61 views

1-particle momentum eigenfunction in terms of field operator for real Klein-Gordon field

Suppose $\phi(x)$ is a real Klein-Gordon field, then the single-particle wave function $\psi(x)$ corresponding to a momentum $p$ is given by (QFT, Ryder) $$\psi_p(x)=\langle0|\phi(x)|p\rangle.$$ The ...
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2answers
55 views

Is there any difference between massless Dirac fermions and Weyl fermions?

In graphene we call the low energy excitations around the Dirac point Dirac fermions, which are massless. Is this just by convention or is there any further differences between massless Dirac ...
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68 views

Can you gauge a $U(1)_L$ symmetry?

I recently calculating the one loop correction for the propagator of a gauge boson, $\hspace{5cm}$ I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop ...
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1answer
165 views

Understanding the Charge Conjugation Operator

I am trying to understand the charge conjugation operator. http://en.wikipedia.org/wiki/C_parity Because the operator is Hermitian, this seems to imply that there is a (possibly spontaneous?) ...
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3answers
165 views

The need for a 'particle description' of electrons

Is there any phenomenon where the 'wave description' of the electron's motion is not applicable? The reason for this question is to find out if there are any situations were quantum wave theories ...
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1answer
63 views

What are the quantum numbers of an exchange particle in the t channel?

i know that for an s channel reaction, the quantum numbers of the intermediate particle have to be the same as those of the particles coming in, for example in the reaction $\gamma \pi \rightarrow a_2 ...
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2answers
885 views

Is the Standard Model consistent (UV complete)?

This is a question about the self-consistency of the Standard Model - which I believe is the same as asking whether it is UV complete - in other words, can it be used to predict experimental results ...
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2answers
94 views

Dashed lines in Feynman diagram

In this article, in e.g. figure 2, what does these dashed lines across the Feynman diagram mean?
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1answer
141 views

About solitons, what is the difference between kinks and vortices?

I am reading papers about solitons for my small reports, and i could not understand its physical meaning in detail. I know soliton is solitary wave which behaves like particle. And many text they ...
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1answer
77 views

The Thermodynamic Limit of Quantum Statistical Mechanics & Interpretation of Quantum Field Theory [closed]

The philosopher of physics Laura Reutsche argues in her book Interpreting Quantum Theories (review/summary here: http://philsci-archive.pitt.edu/9493/1/ruetsche-review.pdf ) that a "pristine" ...
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67 views

Getting Slavnov-Taylor identity

Let's have generating functional in path integral form for gauge $SU(n)$ theory with interaction: $$ \tag 1 Z[J] = \int DB D\bar{\Psi}D\Psi D\bar{c}Dc e^{iS}. $$ Here $$ S = S_{YM}(B, \partial B) + ...
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351 views

Question about infinite sum in quantum field

I read from some books of number theory that $$\sum_{n=1}^{\infty}\frac{1}{n^s} = -\frac{1}{12}\text{,when } s=-1.$$ Now is there such a result $$\sum_{n=1}^{\infty}\frac{1}{n^s} = \pi \text{,when } ...
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121 views

Effective Field Theory (EFT) decoupling top

The decoupling theorem of Appelquist-Carazzone says that if you want to decouple a particle, the low energy resulting theory need to be renormalizable. You can't do that for the top, because you break ...
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27 views

diff-invariant, regulator, cutoff integral on string theory

The diff-invariant distance between $z'$ and $z$ is (for short distances) $e^{w(z)}|z'-z|$, so a diff-invaraint cutoff would be at $|z'-z|=\epsilon e^{-w(z)}$. Then $$ \int ...
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38 views

What is the mechanism for equilibration?

I read on page 5 of Matthew Schwartz' book QFT & the SM that if you heat a box with monochromatic light, then (later) all the frequencies will get excited. The author says that particles have to ...
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1answer
106 views

Is gauge connection unique?

In QFT, given a gauge group and matter field, is the form of the gauge field unique? In other words, given a principal G-bundle and its associated vector bundle, is the construction of the principle ...
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2answers
72 views

How is the integrand concluded to be identically zero?

In expanding the classical Klein-Gordon field in Fourier space to write it in terms of $\phi(\mathbf{p})$ instead of $\phi(\mathbf{x})$, I reached the following result. $$\int ...
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1answer
101 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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1answer
106 views

Is there a method which quantizes non-abelian gauge theories without path integrals formalism?

In the most QFT books there is a method of quantization of non-abelian theories through path integral methods. But I want to learn also the other methods without using of this formalism. Does anyone ...
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1answer
77 views

Instantons as a -1 dimensional object

I don't know much about Instantons, and looking through the Wiki page it seems like one must have a lot of knowledge about QFT to understand them. However recently I've encountered a statement (which ...
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2answers
185 views

Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory

In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this. Now ...
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1answer
140 views

Spontaneous symmetry breaking and time-reversal symmetry

In most textbooks on field theory you read that "spontaneous symmetry breaking implies degeneracy of the ground state". (Like for example in ...
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1answer
233 views

Gauge Field Tensor from Wilson Loop

It is possible to introduce the gauge field in a QFT purely on geometric arguments. For simplicity, consider QED, only starting with fermions, and seeing how the gauge field naturally emerges. The ...
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61 views

What is the derivation of the speed of light $c$ that is not based on electromagnetism? [duplicate]

The "speed of light" is not just the speed of electromagnetic radiation, but of any massless particle. Therefore must not there be an expression for $c$ that is not in terms of $\mu_0$ and ...
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2answers
42 views

Logarithmic discretization in Anderson´s model

Is there some motivation for the construction of Ladder operator that compound the recursive halmitonian of the Anderson model for numerical renormalization contained is this paper?
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56 views

General relativity from helicity 2 massless field theory by using Deser's arguments

Recently I have discovered the method of constructing of GR from massless field with helicity 2 theory. It is considered here, in an article "Self-Interaction and Gauge Invariance" written by Deser S. ...
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81 views

Can we introduce the mass of a quantum field as an interaction?

At a free massless Lagrangian \begin{equation} L_0 = \frac 1 2 ( \partial \psi)^2 ,\end{equation} add an interaction term \begin{equation} L_I = \frac 1 2 m^2 \psi^2\end{equation} where m is small ...
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68 views

Normal ordering

If I understood correctly there are two terms called normal ordering: $:c c^\dagger: = c^\dagger c \hspace{.5cm}$so shifting all creation operators to the left and all annihilation operators to the ...
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14 views

Non Zero correlation function (for large separations) in one particle state?

So i computed the following equal time correlation function for a one particle state. The vacuum correlations give the function $$\langle \phi(\vec x)\phi(\vec y)\rangle_0=D(\vec x-\vec y)\\ ...
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36 views

Why only fully connected diagrams contribute to T matrix

In Peskin's introduction to QFT, he wrote: only fully connected diagrams, in which all external lines are connected to each other, contribute to the T matrix. I don't understand this ...
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0answers
39 views

Spin-dependence of the directionality of dipole radiation

I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the ...
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0answers
87 views

Variations of S-matrix functional and Feynman diagrams in Weinberg QFT

Weinberg on p. 287 of his QFT vol. 1 introduces the extended interaction operator: $$ \tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x). $$ ...
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42 views

How can one diagonalize the second variation of action?

Suppose we have action $S[q]$ and its stationary path $q_s$, I want to find the orthonormal paths $\psi_n$ that can diagonalize the second variation of the action $S[q]$. How to do that? Thanks
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35 views

Electron photon interaction potential in old fashioned perturbation theory (OFPT)

In this PDF on old fashioned perturbation theory (OFPT) we find from equation (14) the potential describing the interaction between the electron and photon: $$ V = \frac{1}{2}e \int \mathrm{d}^3x\, ...
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2answers
61 views

Toy models of asymptotic safety?

Are there some toy model QFTs where the asymptotic safety scenario is realized?
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2answers
76 views

What's the difference between energy and temperature in field theory?

I'm familiar with the formalisms for both zero temperature and finite temperature field theory, but (somewhat embarrassingly) I don't actually have a good physical intuition for when physical ...
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2answers
296 views

(Un)countability in QFT

I am a mathematician self-studying physics, and a currently working on QFT with Srednicki's book. One thing that bothers me is that for a scalar field (in the Hamiltonian version) there is a ...
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1answer
83 views

Expansion in Quantum Fluctuations of the Path Integral

In this post: Dimensionless Constants in Physics there is a discussion about dimensionful vs. dimensionless constants in physics. In the context of this discussion, I'm wondering about the ...
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1answer
71 views

The particle content of a given state

In Carroll's we read ...The Unruh effect teaches us the most important lesson of Quantum Field Theory (QFT) in curved spacetime, the idea that "vacuum" and "particles" are observer-dependent ...
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Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. ...
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1answer
44 views

Properties of the Scalar Field in Scalar-Tensor Theories

I've been reading about scalar-tensor theories of gravity, such as Brans-Dicke theory, and I started thinking about the scalar field. Now, I know that the Higgs field is a scalar field, and of course ...
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0answers
39 views

What are differences between Spin(3,1), SL(2,C), SO(3,1) and SU(2) representations? Which one is correct exact representation for spinor fields? [duplicate]

I want to understand which group transformations exactly represent spinor fields. That is, do spinor fields transform under the Lorentz group $\mathrm{SO}(3,1)$ or under $\mathrm{Spin}(3,1)$? What ...
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2answers
83 views

What is the axial transformation of a group, i.e. $SU(3)$?

The Gell-Mann matrices $\lambda^\alpha$ are the generators of $SU(3)$. Applying an SU(3) - transformation on the triple $q = ( u , d, s )$ of 4-spinors looks like this: $$ q \rightarrow q' = e^{i ...
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1answer
68 views

A question about the asymptotic series in perturbative expansion in QFT

Related post I heard about the argument that the perturbative expansion in QFT must be asymptotic, such as http://ncatlab.org/nlab/show/perturbation+theory#DivergenceConvergence Roughly this can ...
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1answer
130 views

Understanding the four fundamental forces of the standard model - are they magic [closed]

Don't misunderstand the question, my purpose is exploration and understanding of what defines "mainstream physics". It is not asked idly, or with ill purpose.... My understanding of current ...
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1answer
114 views

Lagrangian and grassmann numbers

Why sometimes we remember that "classical" lagrangians of fermions are constructed from grassmann numbers, while sometimes don't? For example, for Majorana's field in terms of 2-component spinors ...
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40 views

U(1) local gauge transformation for Dirac spinor field

How can we define U(1) local gauge transformation for Dirac spinor field?, like scalar fields?
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33 views

Wick theorem applying to partly ordered operator

I symbolize $T$ as the time-ordered operator and $::$ as normal order symbol. I know that in quantum field theory generally we have: $$T\phi_1(x_1)\dots\phi_n(x_n)=:\phi_1(x_1)\dots\phi_n(x_n):+A$$ ...
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1answer
74 views

The n-point Green functions and Heisenberg picture

Let's have the S-matrix: $$ S_{\beta \alpha} = \langle \beta | \hat{S} | \alpha\rangle . $$ Here $|\alpha \rangle , | \beta \rangle$ are $t \to \mp \infty$ limit of the free states, $\hat {S} = ...