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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How was this one probability amplitude derived by Mattuck?

I'm reading A Guide to Feynman Diagrams in the Many-Body Problem by Richard D. Mattuck (2nd edition). You can look at the relevant pages here. On page 45, he presents a formula for $D_t c_p(t)$. ...
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How is this possible that photons are absorbed?

From the lessons on QM, I got impression that there are some discrete orbitals that emit light when electron drops from one to another. Specific molecules emit light in very narrow bands, therefore. ...
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Plane wave solutions of Dirac equation

I'm reading chapter 3 in Peskin on the Dirac equation. First of all, they say since Dirac satisfies Klein Gordon it can be written as a linear combination of plane waves. This is fine. So a general ...
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73 views

Two creation operators acting on a state

If $a_p^\dagger$ is the creation operator for an electron with momentum $p$ and $b_q^\dagger$ is the creation operator for a positron with momentum $q$, what does $a_p^\dagger b_q^\dagger \left| 0 ...
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188 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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Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
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240 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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If the Higgs field has so few observable effects, what is its purpose in a theory? [on hold]

The Higgs boson makes absolutely no sense to me because despite the Higgs field's presence everywhere, its existence is very hard to confirm. Then why does we we posit that it exists? If it has so few ...
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What is the explicit decay width formula for a four body decay?

I'm trying to calculate the decay width for a theory with one particle having a decay mode into 4 particles. Does anyone know the explicit formula for this (not the generalized decay formula).
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83 views

Solving the Klein-Gordon equation via Fourier transform

I have been writing a personal set of notes on QFT and I'm currently writing up a section on solving the Klein-Gordon (K-G) equation. I many texts that I've read, the author starts by expressing the ...
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36 views

Lorentz-invariant phase space of a three-body decay process

I am not following the use of delta function in the 3-body decay process. In $\gamma^* \to gq\bar{q}$ process, with $\gamma^*$ being a virtual photon, we have a phase space factor $$d^9R_3 = ...
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129 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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29 views

Complex scalar theory: annihilation and creation operators give wrong commutators with Hamiltonian

The theory of a real (hermitian) scalar field can be found in many books and everywhere online. On the other hand, if we take the field non-hermitian, then I can only find notes on path integrals. I ...
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65 views

Commutation relations in second quantization

I know that for operators $a(\chi_1), a(\chi_2)$ of the same type (fermionic or bosonic) $$ [a(\chi_1), a(\chi_2)]_{-\xi} = [a^\dagger (\chi_1), a^\dagger (\chi_2)]_{-\xi} = 0 \tag{1}$$ where $$\xi ...
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315 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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79 views

One-particle scattering: LSZ vs Feynman

This question is about Klein-Gordon theory (the field is hermitian). If I calculate the amplitude for the process $\phi\to\phi$, I get two different results depending on whether I use Feynman rules ...
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345 views

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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75 views

Klein-Gordon Green's function: derivative of delta distribution?

In Peskin/Schroeder there is an explicit calculation showing that the retarded Green's function of the real Klein-Gordon field $$D_R(x-y) ~\equiv~ \theta(x^0 - y^0) \langle 0 | [\phi(x), \phi(y)] ...
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Question about the Georgi-Glashow model and the VEV of the scalar field

Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is $$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} ...
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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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Difference between Cosmologial Constant and Quantum Vacuum State

Hello I am very new to cosmology and quantum physics. I need some basic understanding (in Layman's term) of the Difference between Cosmological Constant and Quantum Vacuum. Cosmological Constant is, ...
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29 views

A functional average calculation confusion within Gaussian planar model's RG

I am trying to follow some detailed calculation in a famous paper [John, B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please ...
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34 views

Coupling an electric charge to a gauge field. How is it done in this setup?

In page 9 of Tachikawa's N=2 susy dynamics for pedestrians it says that an electric particle with charge $n$ in the first quantised setup (in what sense first quantised?), Wick rotated to Euclidean ...
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45 views

What is the defintion of a current-current diagram?

Right now I am facing some Feynman diagram calculations and in the instructions I am reading the phrase current-current diagram appears quite often so I wanted to know: What is the definition of a ...
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68 views

In QFT are fields considered a property/function of spacetime? How do they become “excited”?

I am a total layman in physics, but I've been trying to understand the various existing theories and after reading/watching lectures on QFT for months I still can't find an answer to a few very basic ...
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178 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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137 views

Momentum eigenstates in an interacting quantum field theory

Context for the following questions: two widely stated claims hinge on what appears to be an inconsistent argument. The claims are that (1) an interacting field can produce, in addition to ...
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98 views

Can you express the Feynman propagator as a limit?

At first I thought that the Feynman propagator was the limit of: $$ G(x) = \frac{1}{x^2 + i \varepsilon} $$ But if you apply the wave equation to this you get: $$ \Box G(x) = ...
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Problems 2.3 in Peskin's book [migrated]

It's about how to evaluate the integral below, $$ D(x-y)=\int \frac{d^3 p}{(2\pi)^3}\frac{1}{2\sqrt{p^2+m^2}}e^{-i\vec p\cdot (\vec x-\vec y)} $$ it describes the amplitude for a scalar particle in ...
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134 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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29 views

Are the mass matrices the same if Higgs corresponding to different Cartan generators get a vev?

I'm trying to understand what happens when a Higgs field in the adjoint representation of a given gauge group gets a vacuum expecation value (vev). Normally, the fermions do not couple to adjoint ...
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The bounds of axion domain walls are axion strings?

There are two phase transitions which are important for the axion physics. The first one is Peccei-Quinn phase transition, during which axions arise. The second one is QCD phase transition, at which ...
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1answer
56 views

How to choose the proper loop correction?

I review my QFT lecture notes and I am having hard times to figure out the significance of Ward identity in vacuum polarization. In class, we calculated one loop correction stated as $$ ...
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101 views

How unique are the quantum numbers we commonly use?

We use the eigenvalues of the Cartan generators (=diagonal generators) of a given gauge group as quantum numbers in physics. Are these numbers somehow fixed and if not, what transformations are ...
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Charged CFT observables and AdS/CFT

I have a simple question regarding the holographic dictionary when mapping operators on the CFT side to those in AdS. One piece of the dictionary is that a global symmetry maps onto a gauge symmetry ...
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311 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
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1answer
177 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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Target Space Lorentz Invariance vs. World Sheet Weyl Invariance

The Polyakov action, $S\sim \int d^2\sigma\sqrt{\gamma}\, \gamma_{ab}\partial^a X^\mu \partial ^b X_\mu$, has the well known classical symmetries of world sheet diffeomorphism invariance, world ...
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Problem getting a product of traces out of a single trace in a chiral perturbation theory computation

I am stuck at a computation and I would appreciate any help. $U$ is the pion matrix in chiral perturbation theory $$U=e^{i\sigma_a\phi_a/f}$$ where $\sigma_a$ are Pauli matrices, $\phi_a$ are three ...
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402 views

Energy-Momentum Tensor in QFT vs. GR

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
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35 views

Representation theory and the Nekrasov partition function

Is there any review or lecture notes on the Nekrasov partition function which particularly thinks of this from a representation theorist's point of view? Some possibly related references I know of ...
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354 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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Time-independence of Hamiltonian of atomic chain

In the first chapter of Atland and Simons book he gives the Hamiltonian of the atomic chain $$ H[\pi,\phi] = \int dx \Bigg(\frac{\pi^2}{2m} + \frac{k_sa^2}{2}(\partial_x\phi)^2\Bigg) $$ After ...
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How to find the remaining subgroup after some linear combination of Higgs fields gets a VEV?

This is a follow-up question to this question. How can I compute which generators remain unbroken when a linear combination of Higgs fields $a \Phi_1+ b\Phi_2$ get a vev? If I compute the unbroken ...
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74 views

Consequences of local and global anomaly

Are the physical consequences of anomalies associated with a local symmetry is different from that of a global symmetry? If yes, why? We have global anomaly in the standard model but not local ...
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46 views

Books on superconductivity and its relation to spontaneous symmetry breaking

I wish to understand more about the relationship between superconductivity and spontaneous symmetry breaking. I would also appreciate sources for learning about symmetry breaking and particles in more ...
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39 views

Unruh radiation and conservation of energy

Consider the Minkowski spacetime filled by some fields in their Minkowskian vaccum state. Now consider a Rindler observer carrying with him, say, one liter of water. According to Unruh formula, the ...
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QED and anomaly

I've just started to learn anomalies in quantum field theories. I have a question. How to show that QED is free from vector current anomaly and what would happen if it were not? In other words, how ...
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1answer
178 views

Relationship between plasma physics and quark gluon plasma

To what extent do the ideas common in modern plasma physics, such as magnetohydrodynamics, cold plasma models, common types of plasma waves, Maxwell's Equations, etc, relate to the study of quark ...
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Does QFT prevent preparation of an entangled particle pair as in EPR experiment?

This is the claim Tommasini makes in Reality, Measurement and Locality in Quantum Field Theory:"Two spin $1/2$ particles, A and B, are created in coincidence in a spin-singlet state, and are detected ...