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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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/...
1
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0answers
34 views

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 ...
5
votes
1answer
125 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 ...
2
votes
2answers
101 views

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, ...
20
votes
4answers
6k views

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 ...
4
votes
1answer
115 views

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 [...
6
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1answer
216 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 ...
2
votes
4answers
122 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 ...
2
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0answers
43 views

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 $b$. ...
1
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1answer
52 views

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 ...
10
votes
1answer
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 ...
1
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2answers
268 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 ...
12
votes
1answer
218 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 ...
0
votes
0answers
48 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 (...
4
votes
2answers
160 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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0answers
66 views

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 ...
2
votes
1answer
778 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 ...
0
votes
1answer
26 views

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 ...
1
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1answer
39 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 ...
-4
votes
1answer
78 views

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?
4
votes
1answer
82 views

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 ...
1
vote
1answer
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 ...
1
vote
2answers
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 ...
5
votes
1answer
69 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 ...
3
votes
1answer
167 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 ...
0
votes
1answer
132 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 ...
1
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2answers
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 ...
9
votes
3answers
111 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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votes
0answers
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?
1
vote
1answer
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 ...
1
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0answers
41 views

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 (...
5
votes
1answer
183 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 ...
1
vote
2answers
80 views

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, ...
0
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0answers
45 views

Examples of other hierarchy problems

The commonly quoted version of the hierarchy problem (at least, the one that I have heard), is concerned with the surprisingly low mass of the Higgs. We would expect the Higgs mass squared to have ...
1
vote
1answer
37 views

Why can precomputed sets of lattice QFT field configurations be used to measure arbitrary observables?

My knowledge of quantum mechanics is rusty and my understanding of (lattice) quantum field theory on a very novice level at best, so it is likely my whole question is based on completely wrong ...
0
votes
0answers
40 views

Complex field with a chemical potential

This is probably a very basic question. I'm looking at the following Lagrangian with a single complex field $\phi$, $$\mathscr{L} = D_{\mu}\phi^*D^{\mu}\phi - m^2 \phi^* \phi - \lambda (\phi^* \phi)^...
3
votes
1answer
266 views

Understanding CP-violation from a toy model of two fermions and a scalar boson

Consider a field theory given by the following Lagrangian $$\mathcal{L}_{int}=y\overline{\psi_1}\psi_2\phi+y^*\overline{\psi}_2\psi_1\phi^\dagger$$ where $\phi$ is a complex scalar field, and $\psi_1,\...
10
votes
1answer
636 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 ...
0
votes
1answer
32 views

constraints on quartic interaction coefficients in double scalar field Lagrangian

Consider the 4-dimensional Lagrangian density with two real scalar fields $\phi_1$ and $\phi_2$: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi_1 \partial^{\mu}\phi_1 + \frac{1}{2}\partial_{\mu}\phi_2 \...
1
vote
2answers
2k views

Is it possible that the Big Bang was caused by virtual particle creation?

As far as I understand, it is understood that throughout the universe there exists, what is known as, a quantum field from which, due to its fluctuations, temporary (pairs of) virtual particles ...
1
vote
1answer
739 views

Conservation of Energy and Quantum Fluctuations

Regarding conservation of mass-energy Wikipedia says: "this is an exact law, or more precisely, has never been shown to be violated." However, regarding quantum fluctuations, Wikipedia says here: "...
2
votes
0answers
40 views

Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
3
votes
2answers
78 views

Does the Flavor symmetry forbid $uu\rightarrow cc,ss$?

This question comes from the reading of this paper. They suppose a flavor symmetry group $G_F = U(3)_q\times U(3)_{d} \times U(2)_{d}$ which acts on the three LH quarks $q_L$, three RH quarks $u_R$ ...
0
votes
0answers
48 views

Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
4
votes
3answers
313 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
6
votes
1answer
519 views

How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?

I'm trying to compute the angular momentum $$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$ where ${T^\mu}_\nu=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\partial_\nu\phi-{\delta^\mu}_\...
7
votes
1answer
152 views

Canonical second quantization vs canonical quantization with multisymplectic form in AQFT

First of all, I'm a mathematician that knows less than the basics of QFT, so forgive me if this question is trivial. Please, keep in my mind that my background in physics is very poor. 1) The usual ...
0
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0answers
39 views

Why must the Vacuum Manifold contain the quotient group?

For a symmetry breaking pattern $G \rightarrow H$, the vacuum manifold must contain the quotient space $G/H$. In most cases, we take the vacuum manifold to be the quotient space. My question is, Is ...
14
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2answers
2k views

Why do some anomalies (only) lead to inconsistent quantum field theories

In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard ...
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0answers
30 views

Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...