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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403 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension we'...
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13 views

Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
2
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0answers
35 views

Does Feynman parametrization commute with derivative?

Let $I = \int \frac{d^4k}{(2\pi)^4} \frac{(p+k)\cdot\gamma}{(p+k)^2-m^2+i\epsilon} \frac{1}{k^2+i\epsilon}$ I would like to do two operations on the integral, namely Feynman parametrization and $\...
6
votes
1answer
59 views

What is the mathematical motivation for complexifying momenta in BCFW?

One of the first steps in obtaining the on-shell BCFW recursion relations is complexifying the momenta of the external particles. Now complexifying things is not unprecedented (the dispersion program ...
4
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1answer
205 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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1answer
39 views

Such a huge mass for Higgs boson? And how can it, as a quantum, decay?

With a mass of 126GeV/c2 Higgs boson would have a mass slightly greater than a caesium atom. Isn't it too much? Wouldn't be in this way the ubiquitous Higgs field so dense to cause problems for the ...
4
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1answer
46 views

How to define the distance between two points in a conformal transformed space?

Consider a particular conformal transformation $x^\mu\rightarrow x'^\mu$, and the metric of a flat space transforms in the following way, $$\eta_{\mu\nu}\rightarrow g'_{\mu\nu}=\Lambda^2(x)\eta_{\mu\...
10
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1answer
274 views

Non-covariance of the higher rank propagator (from Weinberg's QFT textbook)

In chapter 6.2 of Weinberg's QFT Vol.1, he gave the general form of Wick contractions of all possible fields(scalar, spinor, vector, etc.), he showed $$\Delta_{lm}(x,y)=\theta(x-y)P^{(L)}_{lm}\left(-...
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0answers
45 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, ...
4
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1answer
179 views

Singlet neutrinos decaying to Higgs bosons during leptogenesis

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term $$f_{\alpha i}\overline{l_{L\alpha}}\hat\...
37
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9answers
6k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
2
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2answers
46 views

Does QFT modifies Quantum Mechanics? [duplicate]

The basis of Quantum Mechanics is contained in the postulates which tell us how to describe quantum systems (below I disconsider possibly degenerate spectra just for simplicity): To describe a ...
1
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1answer
101 views

A question from A. Zee's book

On page 463, it writes in eq. (3) $$4H=\Sigma_\alpha(Q_\alpha Q^\dagger_\alpha+Q^\dagger_\alpha Q_\alpha).\tag 3$$ And then it writes that this is followed by eq.(4) as $$\langle S| H|S\rangle=\frac{...
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0answers
32 views

Is it possible in this Universe to communicate a bit of information with energy that scales sub-linearly with distance?

If we look at all the ways that people do communicate information, they all seem to have a cost "at least linear in distance." For example, communicating over a wire has attenutation, so the energy ...
4
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1answer
75 views

Is the usage of the Fock space a postulate in QFT?

In this question, when I write Fock space, I mean "the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H", as it is described by Wikipedia. ...
1
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1answer
50 views

Connection between “classical” Grassmann variables and Heisenberg Equation of motion

I have been reading di Francesco et al's textbook on Conformal Field theory, and am confused by a particular statement they make on pg 22. Let $\{\psi_i\}$ be a set of Grassmann variables. Starting ...
0
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0answers
24 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 ...
2
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1answer
37 views

Experimental observation of non-perturbative effects

Many quantum field theories come with non-perturbative objects such as solitons and instantons, and non-perturbative effects such as the Schwinger effect. However, it is hard to find any review on ...
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0answers
22 views

What is a method of finding minima of the one-loop effective potential?

Say you have a theory with an arbitrary number of real scalars, and you wants to find their Vevs in the global one-loop vacuum. How is this accomplished?
4
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1answer
40 views

Polarization vectors in Quantum Electric Field

The quantum electric field is written as, \begin{equation} \mathbf{E}(\mathbf{r})=i\sum_{\mathbf{k},\lambda}\sqrt{\frac{\hbar \omega}{2 V \epsilon_0}}\left(\mathbf{e}^{(\lambda)}\hat{a}^{(\lambda)}(\...
0
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0answers
61 views

How do we compute correlation function in the Schrodinger picture?

From concreteness' sake consider $\phi^4$ theory with a real scalar (even though the choice of the theory has nothing to do in principle with what I am going to ask). Consider thefollowing ...
18
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5answers
484 views

Why Does Renormalized Perturbation Theory Work?

I've read about renormalization of $\phi^4$ theory, ie. $\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-m^2\phi^2-\frac{\lambda}{4!}\phi^4\,,$ particularly from Ryder's book. But I am ...
0
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0answers
23 views

A few questions concerning one loop corrections to the action

When we perform a Legendre transform on the connected generate functional $W[J]$ we get the quantum action (or 1PI action) $ \Gamma[\phi] = W[J(\phi)] - \int\mathrm{d}^4x\,\phi J,\quad\phi(J)=\frac{\...
7
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1answer
198 views

Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
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0answers
21 views

Gaussian Model scaling fields

last week one of my lectures mentioned the "scaling fields" for the 2D Gaussian Model, $\Phi = e^{\pm ip\phi}$ but did not give any further explanation what that means or where that comes from. ...
0
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1answer
55 views

Solving a step in the derivation of the anomalous magnetic moment of the electron

In the book An Introduction to Quantum Field Theory by Peskin and Schroeder there is a derivation of the anomalous magnetic moment of the electron. The Feynman diagram to be solved is this one: and ...
21
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7answers
3k views
+100

Reading list in topological QFT

I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
0
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0answers
25 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)^...
7
votes
2answers
917 views

History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Edit: Use this PO.org question instead. Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, ...
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votes
1answer
53 views

Reading a Paper on the Cosmological Constant Problem [on hold]

My professor wants to give me (and another kid) a problem in quantum cosmology. To that end, he asked me to read through his recent paper that appeared in the Physical Review Letters. He said that I ...
2
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0answers
74 views

Wilsonian Renormalisation — Peskin & Schroder Sect. 12.1

I'm working my way through Peskin & Schroeder, but some of the details of the calculations done in their introduction to the renormalisation group are slipping past me. For concreteness, the ...
0
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0answers
41 views

Fine Structure and Fine Structure Constant - intuitive relation?

How does the fine structure and fine structure constant relate to each other, intuitively? I've seen $\alpha$ extrapolated as a term in energy calculations for fine structure, but is there a ...
0
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0answers
38 views

Doubts about the theta angle and the ground state energy density in Euclidean Yang-Mills theory

I am reading the following notes https://munsal.files.wordpress.com/2014/10/marino-lectures2014.pdf. On section 4.3 the euclidean Yang-Mills theory is considered. It is said that renormalizability and ...
0
votes
0answers
45 views

Equal amplitude for the processes P1: u g->W+ d and P2: d g->W- u? [on hold]

My question is the following: We have two processes P1: ug->W+d and P2: dg->W-u. At tree level and in the limit of vanishing quark masses, which is the ratio between the averaged square amplitudes? ...
5
votes
2answers
238 views

From Quantum Mechanics to Quantum field theory to String theory?

Today during a very "unique" study session, I might have internalized why Quantum mechanics was not enough, and Quantum field theory makes sense. It seems the reasons are that When a potential is ...
0
votes
1answer
113 views

What happens to Goldstone bosons in the Higgs potential after symmetry breaking?

When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), ...
0
votes
1answer
62 views

About the non-locality of gravitational energy 2

Gravitational energy is non-local which is essentially because of the equivalence principle. The equivalence principle says that you can always transform your frame so that you feel like in a ...
0
votes
1answer
105 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 ...
2
votes
2answers
157 views

Quantum Operators: An Identity

I came across the following neat property: For an operator $\hat{A}$ which is a linear combination of creation and annihilation operators, we have: $$ \langle e^{\hat{A}} \rangle = e^{\langle \...
1
vote
1answer
73 views

Wick renormalization

I'm trying to understand the Wick renormalization in the framework of the Ito integral. I saw the Wick theorem as presented on Wikipedia in a QFT course and I would like to understand how that is ...
0
votes
2answers
91 views

The “harmonic paradigm” in physics

Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one. On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of ...
2
votes
1answer
215 views

One-Loop Yukawa RGEs

I'm currently trying to understand how one can write the one-loop RGEs for the Yukawa couplings using the general formula: One example I'm interested in is how the author derives, using this ...
0
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0answers
29 views

OPE coefficents and commutation relations, and OPE with stress tensor

Basic question about conformal field theory: In a conformal field theory in $d\geq 3$ dimensions, what is the relation between commutation relations and OPE coefficients? In particular, because ...
2
votes
1answer
51 views

Is there scale invariance in the region of QCD aymptotic freedom?

It is said that in the deep inelastic scattering, scale invariance emerges. In the scattering of electrons off protons, this reflects the asymptotic freedom. Now I got a question. Normally, a system ...
18
votes
1answer
1k views

Gauge redundancies and global symmetries [on hold]

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
3
votes
1answer
582 views

Gradient involved commutator in $\phi^4$ theory

In a phi fourth theory, the Hamiltonian density is: $$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$ Now I impose the usual equal time ...
7
votes
1answer
282 views

Why is there no fundamental force following from the $SU(4)$ symmetry?

I've understood that the three fundamental interactions described by the Standard Model (the electromagnetic, the weak and the strong force) are thought to correspond (roughly) to gauge invariances ...
1
vote
1answer
66 views

Question on Step in Lancaster's “Quantum Field Theory for the Gifted Amateur”

I'm having trouble understanding a single step in Lancaster's book. In Chapter 16, the propagator is derived and proved to be the Green's function of the Schrodinger equation. The derivation is pretty ...