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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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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0answers
83 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 ...
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0answers
45 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 ...
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0answers
41 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 ...
6
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2answers
254 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 ...
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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 ...
2
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2answers
165 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
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1answer
85 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 ...
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2answers
94 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
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1answer
221 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 ...
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0answers
38 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
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1answer
56 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
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1answer
1k views

Gauge redundancies and global symmetries [closed]

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 ...
7
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1answer
334 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 ...
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1answer
69 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 ...
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0answers
45 views

How to go from a Higgs which transforms in the adjoint representation to a 2x2 matrix? [closed]

I have a triplet transforming in the adjoint map of the lie albegra of su(2) but I don´t know how to include it in to a Lagrangian where I have two lepton doublets. It should be a 2x2 matrix but I don´...
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1answer
46 views

Lattice QFT: Non-homogenous lattice spacing

I am interested why we fix the lattice spacing, $a$ to be homogenous in all dimensions. After a Wick rotation, $a=i \epsilon$ where $\epsilon=t_{i+1} - t_{i}$ and with euclidean time given by $\tau = ...
4
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2answers
99 views

Running coupling outside QFT

I'm reading about the running coupling in QCD. I understand the vacuum polarization and its consequences. Also I've read that you can find the same phenomenon on the strong interaction, giving us the ...
5
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1answer
78 views

Two definitions of topological terms in field theory

I've seen two distinct definitions for "topological" terms in the context of quantum field theory. Topological terms don't depend on the metric $g_{\mu\nu}$. This makes sense since topology is '...
7
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1answer
287 views

effect of a simultaneous local and a global $U(1)$ symmetry breaking

EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...
3
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1answer
89 views

Can the rate of virtual pair production from vacuum be computed?

Consider for instance the QED Lagrangian. Is it possible to compute the rate of virtual electron-positron creation from the vacuum?
4
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1answer
68 views

Questions from Srednicki's Introduction to Interacting Field Theory using the LSZ Formula

I have been reading through the chapter on the LSZ Reduction Formula from Srednicki's Quantum Field Theory, and I have a few questions about which I'm sort of confused. The questions are referenced ...
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33 views

Decay rate revisited

According to Peskin&Schroeder (pp. 107), we have $$ d\Gamma=\frac{1}{2m_A}\left(\prod_f\frac{d^3p_f}{(2\pi)^3}\frac{1}{2E_f}\right)|\mathcal{M}(m_A)\rightarrow {p_f}|^2(2\pi)^4\delta^{(4)}(p_A\...
2
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1answer
51 views

High $p_T$ and high $Q^2$ in deep inelastic hadronic collisions

When reading about high energy collisions (for example proton-proton collisions at LHC), I always find the relation $Q\sim p_T$, which, for me, is hard to demonstrate. Moreover, I found statements ...
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45 views

At most $N$ gapless charge/spin modes in a system of $N$ coupled 1D chains?

Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains) For a system of $N$ coupled 1D chains, the number of gapless charge modes ...
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59 views

Writing the Yang-Mills topological charge using differential forms

I have a very pedestrian knowledge of differential forms and I am having some trouble in a derivation. The topological charge $Q$ in Yang-Mills theories is supposed to be $$ Q=\int{}q(x)d^4x $$ where $...
8
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1answer
370 views

Casimir forces and its associated Feynman propagator

This is a continuation to my previous question, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the answers there suggest I solve the Feynman propagator ...
2
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0answers
89 views

Some questions about the Kitaev Chain Model

In the paper,'Unpaired Majorana Fermions in Quantum Wires', Kitaev shows that unpaired Majorana Modes can be found at the end of a Quantum Wire for certain conditions. The effective Hamiltonian ...
3
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1answer
42 views

Correlator of energy-momentum tensor and OPE

In http://arxiv.org/abs/hep-th/9108028 Equation (2.22), the correlation function of then energy-momentum tensor with some primary fields is We can view this as sum over the OPE of the energy-...
10
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2answers
321 views

How to count the number of cubic tree-level Feynman diagrams at $n$ points?

I'm following this paper: arXiv:0805.3993 [hep-ph] where it's said that the total number of distinct tree-level diagrams at $n$-points with cubic vertices only is $(2n-5)!!$ I want to know where this ...
2
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0answers
62 views

Field solution for spacetimes with identified regions

For a spacetime surgery wormhole, we have a manifold such that, for two connected compact sets $D_1$ and $D_2$, we remove $D_1$ and $D_2$ from the manifold and identify their boundaries. According to ...
3
votes
2answers
93 views

What kets represent on QFT?

In Quantum Mechanics kets are used to represent states of a system. This is indeed well written in the first postulate of Quantum Mechanics which states that to describe a quantum system we use a ...
2
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0answers
41 views

Can we express QFT in R^8 where the spacetime can be embedded in?

A smooth, 4-dimensional manifold can be embedded in $R^8$. Isn't it a natural selection of space for QFT when we try to extend QFT with gravity?
5
votes
1answer
127 views

axion couplings

As I understand it, the axion $a$ originates from the spontaenous symmetry breaking of $U(1)_{PQ}$. This symmetry being anomalous, and because of the QCD vacuum structure, a non vanishing term like $\...
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0answers
62 views

Definition of anomalous symmetry in Hamiltonian formalism

In the Lagrangian path-integral formulation of QFT, an anomalous symmetry is defined to be a symmetry of the action which is not a symmetry of the measure of the path integral, and therefore not a ...
11
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3answers
672 views

What areas of physics should a mathematician study to understand TQFT?

I am studying topological quantum field theory from the view point of mathematics (axiomatic treatise). So it has no explanation about physics. I would like to know physic background of TQFT. But I ...
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0answers
56 views

Physical side of TQFT

How would one go about understanding the physical side of TQFTs? What are the best introductory resources? I know Atiyah axioms but I don't know any QFT.
2
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0answers
102 views

How to arrive at the Dirac Equation from Poincare Algebra?

For the case of Galilean group, the time translation is given by the generator $H$. Hence, $$\mid\psi(t)\rangle\to \mid\psi(t+s)\rangle =e^{-iHs}\mid\psi(t)\rangle$$ Which immediately is the ...
5
votes
3answers
298 views

Weinberg QFT (2.5.5)

I'm slightly confused about something in volume 1 of Weinberg. He says $U(\Lambda)\Psi_{p,\sigma}=\sum_{\sigma'}C_{\sigma'\sigma}(\Lambda,p)\Psi_{\Lambda p,\sigma'}$. Then, "In general, it may be ...
6
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0answers
97 views

In QED/Yang Mills, why do fermions contribute 4 times as much as scalars to vacuum polarization?

Consider a Yang-Mills theory in $4D$ over a gauge group $G$ $$ \mathcal{L} = - \frac{1}{4} F^{a\mu\nu}F_{\mu\nu}^a + \bar \psi i D_\mu \gamma^\mu \psi + (D_\mu \phi)^\dagger D^\mu \phi $$ where $\...
1
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2answers
107 views

Concepts regarding BCS Theory of superconductivity and Cooper pairs

I have a little conceptual doubt about the BCS theory of superconductivity. A visual model of the Cooper pair attraction has a passing electron which attracts the lattice, causing a slight ripple ...
5
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0answers
78 views

The relation between anomalous dimensions and renormalization constants

I am trying to understand the general strategy and technical details of calculating $\beta$-function at higher orders. $\beta$-function is the anomalous dimension of the coupling constant and there is ...
4
votes
2answers
106 views

Partition function and coherent state path integral

I have been working through the derivation of the partition function expressed as a path integral in terms of coherent states, following the many-body condensed-matter field theory books of Altland &...
1
vote
3answers
63 views

Time dependence of canonical variables

As far as I understand it, at least in scalar QFT, the canonical variables are the field operator $\hat{\phi}(x)$ and its conjugate momentum $\hat{\pi}_{\phi}(x)=\frac{\partial\mathcal{L}}{\partial\...
4
votes
1answer
72 views

Non-abelian current commutators

There many articles, in which non-abelian current commutators are computed. The general result is that quantum corrections lead to additional term in commutator $$[J^a_\mu (x), J^b_\nu (y)] \delta (x^...
2
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0answers
48 views

Noether charge in light-cone coordinates (1+1D)

I have read in this article http://arxiv.org/abs/1107.2917 that the noether charge (in 1+1 D) $$ Q= \int dx \; q_t$$ could be written in terms of lightcone coordinates $x^\pm = t\pm x$ as $$Q=\int dx^...
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1answer
49 views

Reason behind choosing the invariant states for an operator which commutes with an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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1answer
61 views

Central charges in 2D CFT and Virasoro algebra

Suppose we quantize some classical CFT algebra given by generators which satisfy $$[l_n,l_m]=(n-m)l_{n+m},$$ $$[\overline{l}_n,\overline{l}_m]=(n-m)\overline{l}_{n+m},$$ $$[l_n,\overline{l}_m]=0.$$ ...
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1answer
93 views

Virtual particles in EM interaction and Weak interaction

I know that a real electron has a probability (which depends on the intensity of the EM force) of emitting a photon, changing his 4-momentum. The photon should be virtual. Now, my teacher says that ...
0
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1answer
63 views

Renormalization group invariant objects of a quantum field theory

Consider an arbitrary QFT with $g_b$ as the bare coupling constant. After dimensional regularization, is $g_b \mu^\epsilon$ a renormalization group invariant object of the theory? In other words, is ...