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 is cut-off regularization is not Lorentz invariant?

Why is it said that the cut-off regularization is not a Lorentz invariant regularization method?
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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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117 views

Why can't quantum field theory be quaternion instead of complex?

So, the definition of QFT in terms of path integrals is that the partition function is: $$Z[J] \propto \int e^{iS[\phi]+J.\phi} D[\phi]$$ But does it have any meaning if instead of this $U(1)$ ...
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Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
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Why is the introduction of a quantization volume necessary for quantization of the EM field

I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit ...
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225 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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Wick's Theorem: Why is the vacuum expectation value of uncontracted operators zero?

I'm am right now reading Chapter 4.3 (Wick's Theorem) in Peskin & Schroeder. It is said that In the vacuum expectation value, any term in which there remain uncontracted operators gives zero ...
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302 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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42 views

Classical vacuum and quantum vacuum

How to determine the ground state of a classical field, for example an electromagnetic field? What is the difference between the the ground state of a classical field and that of a quantum field?
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71 views

Why is the chiral symmetry only $SU(3) \times SU(3)$ and not $SU(6)$?

In the limit where the masses vanish, low energy QCD has a well known chiral symmetry (see http://arxiv.org/abs/hep-ph/0505265 for a very extensive review, and pg 19 for the section relevant for my ...
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218 views

What's the heuristic reasoning for Chiral Symmetry breaking

In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not ...
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78 views

Field theory in four dimensions

I was reading Schwartz's book on QFT. In chapter 14.5 at p.267, while speaking about path integral he says: [...] the path integral (and field theories more generally) is only known to exist (i.e. ...
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112 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
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What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
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Shape of the Higgs branching ratio to ZZ

I've been looking at the, now very popular, graph of the SM Higgs decay branching ratios: You see that the ZZ branching ratio has a funny dip around the $170\, GeV$, very different from the WW ...
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167 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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Why can we set mass to zero in Yukawa RGE derivation?

In problem 12.1 from Peskin&Schroeder's book I have to derive the beta functions in massless Yukawa theory. What's the justification for setting mass to zero and what's the difference between ...
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389 views

The problem in Sredniki's textbook: How do I calculate loop corrections for $\phi\phi\to\phi\phi$ with this Lagrangian?

The problem in Sredniki's textbook 10.5 : For a free scalar field $\psi$, the Lagrangian is $$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$ Here we use the metric ...
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Goldstone's theorem massless states

I'm currently trying to wrap my head around Goldstone's theorem proof as given by Itzykson & Zuber. The reasoning is pretty straightforward, but there's a result that's bothering me from a ...
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47 views

How is polarization vector in QFT related to polarization in classical electrodynamics?

As i know in classical electrodynamics polarization shows the orientation of the electric vector in a plane perpendicular to the direction of propagation of light. But in quantum field theory ...
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51 views

Compton Scattering Feynman diagram integral expression

I'm trying to write down the integral expression according to the feynman-rules for this Diagram of an electron with compton scattering and a one-loop correction: ![Compton Scattering][1] ...
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A classically charged point particle interacting with electromagnetism and gravity

Consider a classically charged point particle interacting with electromagnetism and gravity. The relevant dynamical variables are $\chi^\mu (\tau)$ of the particle, the electromangetic potential ...
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A No-Nonsense Introduction to Quantum Field Theory

I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump ...
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Virtual photons, what makes them virtual?

The wikipedia page "Force Carrier" says: The electromagnetic force can be described by the exchange of virtual photons. The virtual photon thing baffles me a little. I get that virtual particles ...
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157 views

Can the Higgs condensate be described in terms of creation operators?

In superconductivity, the BCS condensate can be described in terms of 2 creation operators (the 2 electrons of the pair) acting on the vacuum. I'm wondering whether a similar description can be given ...
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Pseudoscalar particle decay

Suppose I want to calculate amplitude of pseudoscalar particle decay into electron + positron. Interaction Hamiltonian is given by (ignoring the positive and real constants) $\mathcal{H} = \bar{\psi} ...
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104 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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191 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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Creating an arbitrary state of the quantum simple harmonic oscillator [duplicate]

Suppose $\mathcal{B}=\{\lvert 0\rangle, \lvert 1\rangle, \lvert 2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} ...
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81 views

Does the Unruh effect really describe a thermal bath?

If we consider a free (massless scalar) field $\phi$ in Minkowski space and look at it in Rindler coordinates (which correspond to what an accelerated observer sees), we find that the action of the ...
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161 views

Zumino's consistent and covariant anomalies - applied to quantum hall?

What is the `physical' meaning of consistent anomalies and covariant anomalies? Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. ...
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28 views

Current density defined by the scattering operator

I have a problem with the definition of the current density. In most literature it is defined as $j^\mu=\frac{i}{2}(S^*\frac{\partial S(A)}{\partial A_\mu(x)})$. I understand that normally we use ...
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30 views

Analogy between a classical discrete system and non classical continous system

Most introduction textbooks about quantum fieldtheory start with a discrete classical harmonic oscillator and then looks at it in the continuous quantized case (quantized field). This leads to the ...
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342 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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Does spontaneous emission actually emit in a random direction, or is it measured in a random direction?

When an excited state couples to the vacuum, it has an infinite number of directions of the quantized electromagnetic field to couple to. Does it evolve into a superposition of all those directions at ...
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61 views

Why do tadpoles contribute to amplitudes?

In some quantum field theories tadpoles of the form                         ...
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321 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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54 views

Is there a theoretic temperature where single quarks might become individually stable?

This question is what lead me to ask this. Strong force between quarks that are out of causal contact and my understanding of the standard model is that the answer is no - but the standard model ...
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What is the physical interpretation of second quantization?

One way that second quantization is motivated in an introductory text (QFT, Schwartz) is: The general solution to a Lorentz-invariant field equation is an integral over plane waves (Fourier ...
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1answer
290 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
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398 views

Is electric charge truly conserved for bosonic matter?

Even before quantization, charged bosonic fields exhibit a certain "self-interaction". The body of this post demonstrates this fact, and the last paragraph asks the question. Notation/ Lagrangians ...
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How does a photon mediate both electric attraction and repulsion?

The answer to this question probably lies in QFT, which I know just enough about to appreciate my current lack of understanding of the subject, if you follow me. About a year ago I asked our ...
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151 views

Has a phonon, a formal quasi-particle, ever been observed as a point particle?

Phonons are a nice tool to simplify the quantum-mechanical description of lattice vibrations by identifying the ladder operator of normal modes as creation operators of a certain quasi-particle. In ...
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52 views

Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
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33 views

Are the pion fields in chiral perturbation theory complex or real fields?

The chiral perturbation theory Lagrangian is written $$\mathcal{L}_2=\frac{f_{\pi}^2}{4}Tr(D_{\mu}U^{\dagger}D^{\mu}U)$$ shouldn't we complex conjugate the first covariant derivative? what triggers ...
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149 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
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266 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
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For a particle to have physical mass, is it always necessary to have a mass term in the lagrangian?

Since the self-energy adds to the bare mass defined in the Lagrangian, is it possible to create a physical particle mass from the self-energy alone, with no mass terms occuring in the Lagrangian? On ...