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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Upper bound to annihilation cross section into heavy particles

For a process in which two relativistic particles annihilate to produce two or more heavy(er) particles of mass $M$: Is it true that the cross section $\sigma_{ann}$ cannot be larger than ...
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Are relative phases observable for identical particles but not for non-identical ones?

In quantum mechanics, amplitudes are represented by complex numbers $e^{i\phi}$, which have phase angles $\phi$. These phase angles are clearly not observable in absolute terms. If I have two ...
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67 views

Are Matsubara states pure states?

Generally in a non-interacting QFT one can solve the Klein-Gordon equation to get a (complete) set of states $\frac{e^{i\omega_k t-ikx}}{\sqrt{2\omega_k}}$. It is not clear to me how to construct the ...
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Justification of not quantizing small extra dimensions

When dealing with extra dimensions ($ x ^\mu $ represents $ 4D $ spacetime and $ y $ the extra dimension) we use what's known as Kaluza-Klein decomposition (basically a Fourier transform), ...
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74 views

Do physicists use agent based models?

I am hoping that this is a simple and specific question. I just wanted to know whether physicists from any branch of physics use agent based models as a tool in their research? If so, then in which ...
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Are terms with spinors analogous to $ ( \partial_\mu \Phi )(\partial^\mu \Phi)$ forbidden in the Lagrangian?

For scalar particles, the Lagrangian involves terms of the form $ ( \partial_\mu \Phi )(\partial^\mu \Phi)$, which is equivalent through integration by parts to $ ( \partial_\mu \partial^\mu \Phi ...
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1answer
107 views

Second derivative of dirac delta expression

I have come across the expression $$ \int f(x) \delta(x-a) \delta''(x-a) \mathrm dx$$ where the prime represents the derivative. Usually with derivatives of the delta distribution I'd partially ...
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What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
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One loop correction to $F^2$ in massless QED, question from Peskin & Schroeder

In Peskin & Schroeder chapter 19, about trace anomaly in massless QED, the trace of $\Theta^{\mu\nu}$ is given by $$ {\Theta^\mu} _\mu =-\frac{4-d}{4} (F_{\lambda\sigma})^2 + (1-d) \bar{\psi} i ...
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Are vacuum fluctuations really happening all the time?

In popular physics articles and even some physics classes I've been to, the vacuum of space is described as being constantly full of quantum fluctuations. Supposedly, all sorts of ...
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80 views

Scalar operators In Quantum Field Theory

I am trying to learn Quantum Field Theory and I am stuck in a basic point. What is the definition of a scalar operator in QFT? That is, how does it transform under a Poincare transformation? Why do ...
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2answers
66 views

What makes a one particle state?

I'm trying to understand free particle states in quantum field theory but I'm having trouble with one thing: what exactly defines a one particle state? For example, we can define a 'plane wave' as a ...
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Is everything made of space? [closed]

I had been studying quantum field theory for a while now, and how there had been many efforts in physics to finally create a "Theory of Everything" (TOE). But while I was learning about all this, I ...
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classical and quantum correlation functions

Quantum Field, quantum fluctuation even with no temperature In QFT, the correlation function $<0|\hat{\phi} (x)\hat{\phi} (y)|0>$ describes the fluctuation correlations of vacuum state ...
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1answer
43 views

Leptogenesis with singlet neutrinos

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term $$f_{\alpha ...
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50 views

Incoherent assumption of the parton model

Consider the scattering process $ep\rightarrow eX$, in the frame of an ultra-relativistic electron, the partons inside the proton are "frozen," and since the time scale of strong interaction is much ...
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Can quantum fields be simulated on a computer?

I am not experienced with quantum physics or QFT. I wanted to know if it is possible that a computer simulate a quantum field according to a quantum field theory. I know that making simulations based ...
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47 views

Is many-body Hamiltonian valid in strong-correlated system

Condensed-matter textbook often states that there is a many-body Hamiltonian $$ H= \sum_i \frac{ p_i^2}{2m_i} + \sum_{i>j} V_{ij} \tag{1} $$ where $V_{ij} = Z_i Z_j/r_{ij}$. This Hamiltonian ...
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What is the physical meaning of $a_{\vec{p}} \! \mid \! 0 \rangle$

$a^\dagger_{\vec{p}} \! \mid \! 0 \rangle = \mid \! p \rangle$ is interpreted as a creation of a particle with momentum $p$ from the vacuum. $a_{\vec{p}} \! \mid \! p \rangle = \mid \! 0 \rangle$ is ...
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1answer
69 views

Spin statistics

I have a very intrinsic question about quantum field theory and even more general, why in 3+1-dimensional spacetime, we have only two statistics for particles to obey? Therefore why we have only two ...
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Regularization ambiguity for leading singularity in dimensional regularization

I have a question with a perhaps well-known answer. Consider a two-loop sunset (log divergent) integral in two dimensions: $$ I_S = \int \frac{d^2k d^2l}{(2\pi)^4} \frac{ ...
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34 views

Polarization sum rule for Rarita-Schwinger field

There are Rarita-Schwinger equations: $$ \tag 1 (p\!\!\!/ - m)\psi_{\mu} = 0, \quad \gamma_{\mu}\psi^{\mu} = 0, \quad i\partial_{\mu}\psi^{\mu} = 0. $$ So the polarization sum $D_{\mu \nu}(p) = ...
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masslessness of Goldstone boson, Effective action, and functional-integral measure

I have difficulty in understanding the path-integral formalism of SSB, and that of Effective Action. Let's say a complex scalar field theory has the global $U(1)$ SSB, $$L(\phi)=(\partial^\mu ...
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54 views

Non-abelian bosonization

Reading this review about non-abelian bosonization, Non-abelian bosonization by I.Karmazin, I stumbled about two questions Below equation 6, I don't get the final point in the statement about the ...
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Infrared divergences in QCD

As we know, we can remove infrared divergences by summing over all final states with arbitrary number of soft photons. But in QCD this does not work, since gluons are not "neutral" because they carry ...
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67 views

Yukawa potential, which is correct?

Sometimes I see Yukawa interaction term written as $$-g\bar{\psi} i \gamma^5 \phi \psi$$ and other times as $$-g \bar{ \psi} \gamma_5 \psi \phi $$ Which is the correct form?
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Help to understand vertex function

In Weinberg's book (the quantum theory of fields, volume 1, pag 446, equation (10.4.19) ) is stated that $\int \ dx \ dy \ dz \ exp(-i p x - ik y + i lz) \langle\Psi_0,T\{J^{\mu}(x)\Psi_n(y)\bar ...
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2answers
103 views

Can we regard field operator $\Psi (x)$ as $a_{x}^{\dagger }$ ,$a_{x}$?

In real scalar CG-field, do we have $a_{x}^{\dagger }$ and $a_{x}$ operators? Because we have $a_{p}^{\dagger }$ and $a_{p}$ , also the relation $\Psi (x)=\int dp\, \, a^{\dagger }e^{-ipx-i\omega ...
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1answer
78 views

Are there QFTs in which a field cannot produce a real particle?

The usual mantra of a quantum field theory is that real particles (as opposed to virtual ones) are excitations of a field. Is this a necessary property of all (operator-valued) quantum field ...
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1answer
38 views

SU(2) kinetic term as a trace

Is there a easy way to rewrite the SU(2) kinetic term as a trace? As in $$\mathcal{L} = -\frac{1}{4}\vec{F}_{\mu\nu}\vec{F}^{\mu\nu}\\[1cm] = -\frac{1}{2}\mathrm{tr}\Bigg[\bigg(\vec{F}_{\mu\nu}\cdot ...
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Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
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1answer
70 views

Guidance needed in finding scattering amplitude

If I have the Lagrangian $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How to find the scattering amplitude for $$ ...
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37 views

What's the importance of background field gauge?

Recently I've read that background field gauge is very convenient for gauge theories, because it fixes the connection between normalization constants of gauge field and gauge coupling constant one. I ...
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1answer
102 views

How to know if the pseudoscalar Yukawa Lagrangian is invariant under chiral transformation?

The pseudo-scalar Yukawa theory Lagrangian is $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How can I show it is ...
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Charge conjugation matrix in baryon current

In his paper Calculation of baryon masses in quantum chromodynamics (ScienceDirect), B.L. Ioffe considers currents describing baryons. In equation (13) he gives an interpolating current for the isobar ...
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2answers
70 views

Vacuum to vacuum transition amplitude using functional integral

The vacuum to vacuum transition amplitude for a free particle with source $J$ is given by $$Z_0[J]=\int D\phi \mathrm{exp}\{-i\int [\frac{1}{2}\phi(\square +m^2-i\epsilon)\phi-\phi J]d^4x\}$$ Let ...
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2answers
58 views

Off-shell external line

In some QFT textbooks, an external line which is off mass shell also concerns us. But according to the motion equation, shouldn't the single external line be on the mass shell? Especially when we ...
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1answer
59 views

Can we calculate L-S coupling without Dirac equation?

It is known that there exists an orbital and spin angular momentum coupling for an electron moving in the atom. And the Hamiltonian can be directly derived using Dirac equation. I want to use a ...
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30 views

Quantization conditions/ Real Scalar field

It is often written in books, the quantization conditions for classical field theory leading to Lagrangian of a real scalar field and thus to Klein Gordon equation. And these are introduced by ...
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1answer
89 views

How does conservation of energy manifest itself quantum mechanically?

We know that classically, if we have some theory $\mathcal{L}$ such that the action $\int d^4 x \mathcal{L}$ is invariant under time translation, then we can use Noether's theorem to find that (the ...
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1answer
83 views

Apparent spacetime dependence of creation and annihilation operators

I'm currently going through An Introduction to Quantum Field Theory by Hartmut Wittig I've stumbled upon. Having trouble with equation (2.29), I'm asking the question: Do creation and annihilation ...
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2answers
131 views

Renormalization, integrating out high momenta Wilson way

In equation $(12.5)$ in Peskin and Schroeder, they write out the generating function but leave out all quadratic terms of the form $\phi\hat{\phi}$ arguing that they vanish since Fourier ...
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particle and antiparticle notation

This may be a very simple question but I'm really confused. If $\psi$ represents a particle (a Dirac fermion). What is an anti-particle represented by? Is it $\bar\psi=\psi^\dagger\gamma^0$ or ...
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1answer
66 views

Can the strings in string theory be thought of as troughs in a field?

I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module, however my question is that since elementary ...
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1answer
91 views

What does an excitation in a field mean?

The term "field excitation" is used a lot especially when I hear about the Higgs boson. However, I cannot find an explanation of what precisely that means. I have a few questions relating to this. ...
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Pair production and initial separation

I was looking at the wiki article on electron-positron pair production (http://en.wikipedia.org/wiki/Pair_production) and have a question. The article states that the photon energy needs to exceed ...
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2answers
160 views

Electron's self-energy in QED in arbitrary gauge

Recently I've tried to evaluate electron's self-energy in QED in the second order of perturbation theory by using dimensional regularization. Corresponding 1PI-diagram leads to $$ \Sigma_{1loop} = ...
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3answers
93 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. Suppose we ...
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1answer
78 views

Weinberg QFT Chapter 5: gamma matrices consistency

Currently reading through Weinberg's QFT book (Vol. 1) [readable in parts here]. In his derivation of the causal Dirac field in Ch. 5, he chooses his gamma matrices as (5.4.17) \begin{align} ...
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1answer
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What is the four-dimensional representation of the $SU(2)$ generators?

Recently, I have been learning about non-Abelian gauge field theory by myself. Thanks @ACuriousMind very much, as with his help, I have made some progress. I am trying to extend the Dirac field ...