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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Position of indices in QFT

I have recently started studying quantum field theory from the book Quantum Field Theory and the Standard Model by Schwartz. In chapter 2 it is said that, contrary to GR, one can ignore the index ...
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Distinguishing Insulator, Metal, Superconductor by a flux insertion argument

I have the following argument to distinguish Insulator, Metal and Superconductor. For simplicity let's consider electrons on a circle and thread one quantum of flux (e$\Phi_0 = 2\pi$) through it (or ...
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Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
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Instantaneous transfer of information?

If suppose there is some charge which is not under influence of any other thing. Let us for observation surround this charge with circles of pointers pointing in the direction of its field. If I move ...
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47 views

Feynman diagram elementary vertex with 4 lines?

Are there processes that require vertices with 4 lines in a Feynman diagram? (And cannot be written as composition of 3-line vertices?) If not, is it matter of models we use (where there are no ...
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37 views

Photon as a gauge boson for static fields

Excuse me if my question is naive, but I have never taken a proper QFT. I used to think of a photon as a quantum of EM field, quantum of light. But form QFT and particle physics prospective, photon ...
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Feynmann Propagtor and the Green's Function for a Free Field

I'm going through Mark Srednicki's Quantum Field Theory. Chapter 8 on The Path Integral for the Free Field Theory includes the following: In the presence of a classical source, $J$, the ground state-...
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268 views

Coupling of matter field with gauge boson and Goldstone boson:

What's the fundamental difference between the way a gauge boson gets coupled to a matter field, preferably a Fermionic field and the way a Goldstone boson gets coupled to the matter field ? In ...
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944 views

Noether current for the Yang-Mills-Higgs Lagrangian

I am trying to calculate the Noether current, more specifically, the energy density of the Yang-Mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
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Closed form expression for the partial decay widths of Higgs boson in massive vector bosons

Can anybody help me obtain a closed form expression for the Higgs partial decay width into massive vector bosons (off shell decays)? I am writing code for the partial decay widths of the Higgs and ...
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852 views

What sort of experiment would directly test time reversal invariance?

I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to ...
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49 views

An Integral involving solid angle in Peskin and Schroeder

I cannot figure out an integral in the textbook Quantum Field Theory by Peskin and Schroeder. On P.201 the integral above Eq.(6.70), the relevant part in question reads $$\int\frac{\mathrm d\Omega_k}...
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449 views

Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
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An integral in mass renormalization in Peskin and Schroeder

I cannot figure out an integral (which involves certain approximations) in the textbook Quantum Field Theory by Peskin and Schroeder. On P.220 Eq.(7.28-29), it is mentioned that the integral (7.28) ...
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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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How can tree level amplitudes have poles? And how can amplitudes have dimensions?

Consider the $\phi^{3}$ theory, whose lagrangian is $\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{3!}\phi^{3}$ The amplitude for tree level (2->1) process is simply ...
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149 views

What exactly is NASA's proposed mechanism for “propellantless” “EM Drive” propulsion? [duplicate]

Of course, this question runs perilously close to this site's prohibition against discussing non-mainstream physics. However, the accepted answer in meta about what is acceptable and what is not ...
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505 views

Calculating $\mathrm{Tr}[\log \Delta_F]$

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = \frac{1}{(p^0)^2-\left(\left(n\pi/...
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irrational conformal dimension

I know examples of Conformal Field Theories in which the scaling dimension of certain operators is an integer number or a fractional number. However I do not know any example in which the scaling ...
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130 views

Which are some best sources to learn Algebraic Quantum Field Theory (AQFT)?

Which are some best sources to learn Algebraic Quantum Field Theory (AQFT)? I am a beginner and I am currently following Haag's Local Quantum Physics and feel like I need some more notes or some ...
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Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
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What's the difference between helicity and chirality?

When a particle spins in the same direction as its momentum, it has right helicity, and left helicity otherwise. Neutrinos, however, have some kind of inherent helicity called chirality. But they can ...
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What is the matrix representation of the momentum operator (generator of translations) that is used in the commutators of the Poincaré Group?

So the commutators of the Poincareé group are given by \begin{eqnarray} [J_{i},P_{j}]=i\epsilon_{ijk}P_{k}, \quad [J_{i},J_{j}]=i\epsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\epsilon_{ijk}K_{k}, \quad [...
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222 views

How are bound states handled in QFT?

QFT seems very well suited to handle scattering amplitudes between particles represented by the fields in the Lagrangian. But what if you want to know something about a bound state without including ...
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124 views

How can fields interaction give rise to particles?

We say light a matter-wave, meaning along with its wave property it shows particle nature. But how can fields interaction (electric and magnetic) give rise to particles (photon)? I wish someone could ...
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dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b,$ then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
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Spinors in 2+1 dimensions

I am trying to understand representations of the Poincare/Lorentz group, and in particular spinors, in 2+1 dimensions. I know some of the math, but I'm not sure about the physical interpretation of it ...
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189 views

What are the remaining obstacles to low-energy quantum gravity?

In a 2003 review Burgess outlined how the QFT perturbative methodology is being extended to gravity, and described some effective quantum gravity expansions that reproduce general relativity in the ...
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270 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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219 views

Monopoles and the magnetic Higgs mechanism

In a paper of 't Hooft about the rôle of magnetic monopoles for a model of quark confinement, I don't understand the following sentence (end at paragraph 14) [...] in order for monopoles to ...
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52 views

Superfields in 2D SUSY

Many textbooks present expressions for superfields in $4$ dimensions. For my current project, I have to find out how things work in $2$ dimensions. Let me summarise in short what we know about $4$d (...
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164 views

A question about Fierz identities in Peskin's Quantum field theory

In Peskin's "quantum field theory", there is a identity of Pauli matrix which is connected to Fierz identity,(equation 3.77) $$(\sigma^{\mu})_{\alpha\beta}(\sigma_\mu)_{\gamma\delta}=2\epsilon_{\alpha\...
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why exactly do we use regulators for infinite sums? [duplicate]

Disclaimer: I really apologize for not being educated in QFT a priori. Im trying to learn. I really really am. I am a doctor of physics but i sadly never took QFT in my program and so im now ...
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779 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
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Can CP-violation arise due to interference between two tree-level diagrams in a QFT?

In Leptogenesis, CP-asymetry arises due to the interference of the tree-level amplitude $N\rightarrow l_\alpha\phi$ (where $N$ is heavy sterile neutrino, $l_\alpha$ is a lepton flavour, and $\phi$ is ...
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41 views

Is the reduction of tensor loop integrals to scalar integrals using Passarino Veltman Functions, theory dependent?

While reducing the tensor integrals to scalar integrals all that we use are Lorentz covariance and the physical interpretation of the result. Thus I think that the Pa Ve Reduction of Tensor integrals ...
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Where do people go (online) to present big ideas they have discovered? [closed]

I can't realistically travel, but is there somewhere online where I can present some ideas? Or do I just put it on arXiv and hope someone important reads it?
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Lie Algebra for fermion fields

A key identity (e.g. when deriving BRST symmetry for gauge fields) is that: $$[c,d]_a =f_{abc}c_b d_c$$ where $c$ and $d$ are both Fermion Fields. How do I derive this from the lie algebra ...
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109 views

Does massive particle really move at speed of light? [closed]

According to this answer I understood that particles with mass also move at speed of light but interaction with higgs field make this movement zigzag. So average speed is below speed of light. Is ...
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243 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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70 views

Shifting integration variable and taking derivative seemingly giving problem

I am doing loop integral in quantum field theory, and an issue in shifting integration variable is giving me a problem. Let me illustrate with an example. I have an integral that looks approximately ...
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1answer
170 views

How are Clifford algebras related to Dirac Equation

Given a vector space $V$ and a quadratic form $q$ for the vector space. The tensor algebra is defined as $\mathcal{T}(V)=\sum_{i=1}^{\infty} V^{\otimes i}$. The set $\mathcal{I}=\{x\otimes x-q(x)\cdot ...
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134 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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65 views

Interpretation of the mass of the field

Before QFT I had never thought if a field should or should not have any mass. Now it turns out that either case is possible. It might be naive to think this way, but I picture the mass of the field in ...
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112 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
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62 views

Does string theory predict QFT? [duplicate]

Does string theory predict QFT? Or is it only consistent with it? Or is it build-in from the start?
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74 views

Euler-Lagrange Equation in Quantum Field Theory

The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a ...
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Vertex renormalization and the probability to produce $n$ soft photons

On P. 208 of the book An Introduction of Quantum Field Theory by Peskin and Schroeder, the probability of production $n$ soft photos all with with energies between $E_- < E < E_+$ is discussed (...
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184 views

BRST quantization and norm

States with definite ghost number have zero norm (since ghost number is anti-hermitian and has real eigenvalues). E.G. when quantizing relativistic point particle, physical spectrum turns out to ...
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De Broglie- Bohm Quantum Theory

From what I have read the Standard Model of Particle Physics uses quantum mechanics,special relativity, along with other assorted mathematics to make predictions and provide a framework for QED, QCD, ...