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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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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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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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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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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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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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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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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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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Why do tadpoles contribute to amplitudes?

In some quantum field theories tadpoles of the form                         ...
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55 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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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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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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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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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 ...
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How to find a particular representation for the gamma matrices?

I asked this question as a subquestion in another thread, but got the answer below and thought it deserved a thread of its own. Two well-known representation of the gamma matrices are the Weyl and ...
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Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
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Loopwise expansion of effective action $\Gamma[\phi]$

My question is about the loopwise expansion of the effective action $\Gamma(\varphi)$ up to 1-loop contributions. I've understood well the results for both $Z[J]$ and $W[J]$ functionals loopwise ...
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Higgs mass and the hierarchy problem

I was wondering what is the opinion about importance of the hierarchy problem in the hep community? I'm still a student and I don't really understand, why there is so much attention around this issue. ...
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Doubts in understanding the role if quantum corrections in the Hierarchy Problem

Trying to understand the Hierarchy problem many questions come to my mind that I am unable to answer due probably to my poor understanding of renormalization. The basic set up of the hierarchy ...
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How is the hierarchy problem consistent with the decoupling theorem?

One the one hand we have the hierarchy problem in it's various forms, in my understanding in it's most serious form one could state it as the observation that if there is a heavy mass scale M in ...
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Categorizing solutions to Hierarchy problem

We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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How does the electric field operator change inside an optical cavity

In the free field, transverse electric field operator is given by the below expression; $$d^{\bot}(R)=i \sum_{p,\lambda}\Big( \frac{\hbar cq}{2V\epsilon_{0}}\Big)^{1/2} ...
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Peskin Schroeder $\phi^4$ mass renormalization

In Peskin Schroeder, section 10.2, the contributions to $M^2(p^2)$ of order $\lambda^2$ are calculated. They respective Feynman diagrams are given: why is this diagram NOT included?
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Interacting fermions on a lattice

My rough understanding about lattice simulations of bosonic quantum field theories is that the partition function can be approximated by explicitly summing over a large number of field configurations, ...
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Assumptions in the LSZ reduction formula

In Srednicki, Chapter 5, it is said that the LSZ reduction formula holds only under the assumptions $$ \langle 0|\phi(x)|0\rangle =0 \qquad\text{and} \qquad \langle k|\phi(x)|0\rangle =e^{-ikx}$$ I ...
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Amputated Green's function in the LSZ formula

From Schwartz's QFT textbook, under Ch.18, Mass renormalization, Schwartz introduces a new LSZ formula with renormalized Green's function. He states that the new LSZ formula for QED, with pole mass ...
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Argument of E. Fradkin on the mean-field theory of spin liquids

I have read the chapter 8 of Field Theory of Condensed Matter Physics (2ed.) by E. Fradkin a couple of times, but I still confused by his argument at some points. I hope you can help me with that. ...
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113 views

Counting degrees of freedom in spinor-helicity formalism

Just a couple of quick questions about the spinor-helicity formalism. We start with $p^\mu$ and $\epsilon^\mu$, so we have eight degrees of freedom. Then we have that $p^\mu p_\mu = 0$ and that ...
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116 views

Why does the photon propagator contain the metric tensor?

The Klein Gordon propagator is (Peskin p-30) $$ D_F(x-y)=\frac{i}{p^2-m^2} $$ which is actually the Green's function of the KG field. But a photon contains additionally $g_{\mu\nu}$ in the numerator. ...
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How to write magnetic dipole transition hamiltonian using ladder operator?

The magnetic dipole transition Hamiltonian is $\hat{H}=\frac{e}{2m_ec}\hat{\mathbf{B}}\cdot\hat{\mathbf{L}}$ How do I express it in terms of ladder operator $\hat{L}_+$, $\hat{L}_-$, and the ...
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What is the meaning of the dlog integrations in the on-shell/grassmannian representation of N=4 SYM scattering amplitudes?

After reading part of this paper by Nima Arkani-Hamed, http://arxiv.org/abs/1212.5605, I cannot understand what is the precise meaning of the $dlog(\alpha)$ integrations. Any on-shell diagram is ...
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Ground state symmetry breaking in Bose-Hubbard model with spin-orbit coupling

The Hamiltonian for 2D Bose-Hubbard model with spin-orbit coupling on a square lattice is written as $ H = -t\sum_{\langle ij \rangle}\Psi_i^{\dagger}\Psi_j^{\vphantom{\dagger}} + ...
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Probability of Vacuum Fluctuations near Charges

A short, simple enough question, if you know about field theory, which unfortunately I don't. Are vacuum fluctuations more probable near a charge, for example an electron with negative charge? I ...
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Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the ...
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What is primitive divergence?

As in the title, what is primitive divergence? How is it distinguished from normal divergence? As a followup, what is a primitive divergent graph in a theory? Some simple examples?
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How many particles in $\phi_0(x)^2|0\rangle$?

In Schwartz's "QFT and the standard model" on pg 22 he writes: A two or zero particle state as in $\phi_0(x)^2\left|0\right>$. I was wondering how this can be proved? I tried checking if ...
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Weinberg-Witten theorem and Landau pseudotensor, or how QFT can make prediction about GR

Weinberg-Witten theorem states that there isn't Poincare covariant stress-energy tensor for massless fields with helicity more than $1$. The only example of such higher helicity field is graviton. ...
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70 views

Understanding Fierz rearrangement identity

I'm trying to get a better grasp of the Fierz rearrangement identity for 2-component spinors (Equation 2.20 I'll be using the Van der Waerden notionation used in the given link) $$ \chi_\alpha (\xi ...
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“No-go” theorems and goldstone bosons

There are "no-go" theorems who forbid interaction through soft helicity 3 and higher massless particles and soft interaction between massless fermions with spin more than $\frac{3}{2}$. But if ...
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Why only the spin $j=\frac{1}{2}$ has relativistic wave function equation that conserves positive probability?

The Dirac wave function can be thought as a relativistic wave equation, where the solution has a positive definite norm. I know that this same equation can't be thought so seriously as a wave equation ...
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533 views

Teach me Wick's theorem the honest way

Generally speaking the average guy marginally acquainted with quantum field theory or advanced combinatorics describes Wick's theorem as some sort of correspondence between higher order differential ...
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Mass correction to a massless boson

Suppose I have a boson and a fermion: $$ \mathcal L = -\frac{1}{2}(\partial \phi)^2 -m_\phi^2\phi^2 - \bar \psi \not \partial \psi - m_\psi \bar \psi \psi + \lambda \phi \bar \psi \psi $$ In the ...
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What exactly is Weinberg's power counting theorem?

The massive gravity propagator goes like $\sim \frac{p^2}{m^4}$ at high energies and in this case we cannot apply Weinberg's standard power counting arguments. I have read something like that ...
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Higher spins elementary particles

Lorentz invariance requirement of theory imposes the absense of interactions between spin 3 and higher spins bosons and arbitrary field (like spin $\frac{1}{2}$ fermions etc) at least in infrared ...