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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177 views

Recovering QM from QFT

Reading through David Tong lecture notes on QFT. On pages 43-44, he recovers QM from QFT. See below link: QFT notes by Tong First the momentum and position operators are defined in terms of "...
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66 views

How do I decide when to use raised/lowered indices when calculating the amplitude of a Feynman diagram?

I am learning the Feynman rules for QCD. The book I am reading tells me that gluon propagators contribute a factor of $$\frac{-ig_{\mu\nu}\delta^{\alpha\beta}}{q^2}$$ However, in one of the ...
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3answers
95 views

Why is this proof that all $\overline{\psi}\psi\overline{\psi}\psi$ interactions are trivial incorrect?

This is a homework question for my quantum field theory class. I haven't been able to figure out the answer, and neither has anybody I asked. The homework was due two days ago. Consider a spinor ...
6
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181 views

Intuition for parameter $\mu$ in dimensional regularization

In dimensional regularization, a dimensionless coupling $g$ is replaced by $\mu^{4-d}g$ so that it can remain dimensionless. $\mu$ is unphysical, though its choice affects the values of counterterms. ...
3
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184 views

How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
4
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83 views

Baryons annihilation

I was wondering if there is a way of calculate the annihilation cross section for two baryons, say $p\bar p\to\pi\pi$ or $p\bar p\to\gamma\gamma$. The problem here is that we cannot use the usual ...
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1answer
171 views

can a gapless system be a topological state?

For a gapless system without boundary (i.e. in the bulk there is gapless excitation while no clear meaning of boundary excitations like QFT), can it be a topological state? What is the property of EE ...
3
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92 views

Renormalization confusion

I'm starting to read about renormalization in the case of scalar field theory. I have some confusions. I will consider momentum renormalization. First, consider a theory with a coupling constant $g$....
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45 views

Hamiltonian of KG free scalar field

Reading through David Tong lecture notes on QFT. On page 24 we compute Hamiltonian operator for the KG free scalar field in terms of raising and lowering operators. See below link: QFT notes by Tong ...
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55 views

Different Signs in Yang Mills Gauge Transformations

I have seen the Yang-Mills Gauge Theory be constructed in many books and papers, however I have seen pretty much equal disparage of + and minus signs in the following equations, the definition of the ...
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2answers
91 views

Fermion Lagrangian with linear momentum versus quadratic momentum

$$ L = \bar{\psi} (\gamma^\mu (p_\mu -A_\mu)- m)\psi \tag{1} $$ $$ L = \bar{\psi} ((\gamma^\mu( p_\mu-A_\mu))^2 - m^2)\psi \tag{2} $$ Is there a difference between the two Lagragians in equations 1 ...
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63 views

Electro magnetic duality, Strong weak duality and N=4 super Yangmils

How we can interpret this self-dual, or duality in terms of generalized version of electro magneitc duality, or Strong weak duality. Let me address some basic information. First, electro magnetic ...
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1answer
70 views

How is the perturbative expansion justified in QED if we make $A_{\mu}\to{}\frac{A_{\mu}}{e}$?

Consider the QED Lagrangian $$\mathcal{L}=\bar{\Psi}(i\gamma^{\mu}D_{\mu}-m)\Psi-\frac{1}{4}F_{\mu\nu}^2$$ where $D_{\mu}\Psi=\partial_{\mu}\Psi-ieQA_{\mu}$ where $e$ is positive. For concreteness' ...
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2answers
488 views

Why are correlation functions so important in QFT?

Apparently correlation functions capture all the important information about a quantum field theory. Nonetheless, I have never been given a reason of why this should be the case. So, does anybody have ...
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53 views

Momentum of 1-D real scalar Klein-Gordon quantum field on segment

I'm trying to get into QFT and as such I try to quantize a real scalar field with Klein-Gordon field equation (Lagrangian density) on a segment of lenght L and with fixed ends. I get orthonormal basis ...
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76 views

What is the meaning of thermal spectral function and thermal decay width in thermal field theory?

In Kallen-Lehmann spectral representation of 2-point correlation function \begin{equation} \langle 0|T\phi(x)\phi(0)|0\rangle=\int_0^\infty \frac{dM^2}{2\pi}\rho(M^2)D_F(x-y;M^2),\quad (a) \end{...
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597 views

Hawking Radiation: how does a particle ever cross the event horizon?

The heuristic argument for Hawking Radiation is, that a virtual pair-production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation. ...
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30 views

Feynman rules complex field in polar form

I am trying to derive the Feynman rules for this field: $$L=-\partial \phi^*\partial \phi - \frac{\lambda}4 (|\phi|^2-v^2)^2 $$ With this coordinates $\phi = \frac 1 {\sqrt2}\rho \exp(i \theta)$, $\...
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1answer
62 views

Interpretation of 4-vector quantum field operator

Peskin and Schroeder, on page 24, quotes the following expression for a generic (scalar) field operator: $$ \phi(\mathbf{x})|0\rangle = \int \frac{d^3\,p}{(2\pi)^2}\frac{1}{2E_{\mathbf{p}}}e^{-i\...
3
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0answers
60 views

Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...
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51 views

Are SUSY transformations free from anomalies?

Although I've studied supersymmetic field theories for several years, there is a fundamental problem annoying me: Do SUSY transformations (including both the ordinary ones in various dimensions and ...
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40 views

Expansion of comparator

Currently I am working on Pesking Schroeder Section 15.1 and trying to understand the expansion given in (15.5), which is $$ U(x+\epsilon n, x) = 1 - i\,e\,\epsilon\,n^{\mu}\,A_{\mu}(x)+O(\epsilon^2) $...
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1answer
65 views

Definition of leading log terms in one loop corrections for gravity

One loop corrections for gravity usually includes non-local terms in the action such as $R\log(\frac{-\Box}{\mu^2})R$, where $\Box=g^{\mu\nu}\nabla_\mu\nabla_\nu$ is the D'Alembert operator, $R$ is ...
3
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1answer
148 views

Boundary conditions in holomorphic path integral

Consider the holomorphic representation of the path integral (for a single degree of freedom): $$ U(a^{*}, a, t'', t') = \int e^{\alpha^{*}(t'') \alpha(t'')} \exp\left\{\intop_{t'}^{t''} dt \left( -a^...
3
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1answer
106 views

Grassmann numbers in the dual space

I'm reading the section on Grassmann numbers in QFT for the Gifted Amateur and I'm confused by something said therein: First, they define a coherent state for fermions $\rvert \eta \rangle$ as \begin{...
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87 views

Why are coherent states necessary for defining the fermionic path integral?

I am following the discussion of fermionic path integrals and Grassmann variables in QFT for the Gifted Amateur (ch. 28). It defines a coherent state for fermions $\rvert \eta \rangle$ as \begin{...
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0answers
19 views

derivation of formula for number of closed loops in a Feynman diagram [duplicate]

How does one derive the formula $$V=I-L+1$$ where $V$=No. of vertices, $I$= No. of internal lines and $L$=No. of closed loops. I've seen it stated in several lecture notes on QFT but none (that I ...
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36 views

What is the form of Higgs potential, when written using higgs mass and quartic coupling.

Usually we write Higgs potential as $V=-\frac{1}{2}m^2 \phi^2 + \frac{1}{4}\lambda \phi^4$ What are the present reliable values of parameters '$\lambda$' and '$m$'? Is '$m$' used here Higgs mass? If ...
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32 views

Definition of vacuum and occupation number in expanding Universe

Suppose for simplicity we have theory of free quantum scalar field in expanding Universe (metric plays the role of background field) $g_{\mu \nu} = \text{diag}(1, -a^2,-a^2,-a^2)$, where $a(t) \sim \...
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45 views

What is the simplest chiral $U(1)$ theory that satistifies both gauge and gravity anomalies?

I've learned the chiral $U(1)$ theory that satisfies either gauge anomalies or gravity anomalies. But what's the theory satisfies both of them?
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64 views

$S$-matrix expansion and Feynman graphs for toy model

I have a toy model with three interacting particles $A$, $B$ and $C$ and $A$ can decay to $B$ and $C$. Looking at the process $AB\to BBC$ I just want to know which orders of the $S$-matrix expansion ...
0
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1answer
37 views

Interaction Hamiltonian and shifts

When we quantize a free field theory, we set $\phi(x)$ to be the operators and we take the Fourier transform to determine the creation and annihilation operators $a_\omega,a^\dagger_\omega$ such that $...
9
votes
2answers
275 views

Yukawa interaction between Dirac particles is universally attractive?

Can anyone provide me a specific reference to (or supply themselves) the derivation of the fact that the Yukawa interaction$$\mathcal{L}_{\text{int}} = -g\overline{\psi} \psi \phi$$between Dirac ...
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41 views

Calculate 1-point function from generating functional

I have a generating functional: $<exp[i \sum_k c_k x(t_k)]> = exp[-1/2 \sum_{k,k'} c_k c_{k'} G(t_k, t_{k'})]$ and I need to calculate the 1-point and the 2-point function. Does anyone ...
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0answers
62 views

Solving Weyl Equations

In my second taking of QFT we just finished the Dirac equation. As an exercise I tried applying what I have (re-) learned to the Weyl equations. I'd like someone to check if my work is correct. For ...
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0answers
35 views

Canonical definition of the integrand in planar $\mathcal{N}=4 \ \mathrm{SYM}$ theory

According to page 101 of Scattering Amplitudes (Elvang, Huang), one can use the zone variables $y$ to define a unique integrand, in the planar case. This is done by saying that the momenta associated ...
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1answer
63 views

How to impose canonical commutation relations when quantising a field

I believe this is a simple question, however I cannot find it explained anywhere what the term: "Impose canonical commutation relations" means. If I have a classical equation, and I wish to quantise ...
1
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1answer
67 views

Seiberg duality and IR fixed point

This question is related with Seiberg duality for $SU(N)$ gauge theory which states a duality between electric theory, $SU(N_c)$ gauge theory with $N_f$ flavors is dual to its magnetic theory, $SU(N_f-...
8
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1answer
998 views

The meaning of Goldstone boson equivalence theorem

The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the ...
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0answers
71 views

Definition of the charge conjugation operator

My question will be a bit provocative, I hope it will attract more interest (and hopefully no downvoting). I introduce the following notation: $u(p)\exp(-ipx)$ positive energy solution $v(p)\exp(ipx)$...
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0answers
34 views

Quantum Fluctuations [duplicate]

Energy is converted to mass and mass to energy. But during quantum fluctuations energy is created without mass, does this not violate the law of conservation of mass and energy?
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0answers
42 views

Books on path integral methods [duplicate]

Are there advanced books on applications to physics of the method of path integral? I am aware of some of the standard textbooks on QFT, but looking for more advanced applications of the method.
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1answer
206 views

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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117 views

Goldstone's theorem. What's the catch?

A theory of scalar field with SO(3) symmetry and Higg's potential is presented by Lagrangian $$ L=\frac{1}{2}\partial_{\mu}\phi^{a}\partial^{\mu}\phi^{a}-\frac{\lambda}{4}(\phi^{a}\phi^{a}-\mu^{2})^2$...
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1answer
60 views

Why the QED coupling constant is a continuous function? [closed]

In page 316 of 'Student friendly quantum field theory', when discussing Figure 12-4, it says that the QED coupling constant is a continuous function of $\ln(p)$. But I think it's disconnected at $p=...
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2answers
103 views

Why does number of photons fluctuate?

When counting photons (with, e.g., a CCD), there is the so-called ''photon noise'' (important at low photon numbers). What is the explanation in the framework of QED, QFT? Is it the Heisenberg ...
5
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1answer
219 views

Is a $SU(2)$ supergauge theory really a $SU(2)$ gauge theory?

Consider $SU(2)$ supergauge theory with $A$, a doublet of two chiral superfields in the fundamental representation. $$A= \begin{pmatrix} \Phi_1\\ \Phi_2 \end{pmatrix}$$ where $\Phi_1$ and $\Phi_2$ ...
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1answer
68 views

What's the bubble's wall made up of in false vacuum decay? [closed]

It is well known that for some kind of double well potentials, there are two minima with one is unstable called the false vacuum while the other stable one called the true vacuum. The tunneling is ...
4
votes
2answers
136 views

Determinant of a propagator

Say I have a path integral $\int D \phi \exp(i S_0)$. $S_0$ is the usual free action $$S_0=\frac{1}{2}\int\phi (-\Box-m^2) \phi=\frac{1}{2}\int \phi G^{-1} \phi,$$ and at the moment I'm not ...
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109 views

Scalar QED, are there any scalar-fermion vertices in this theory?

Consider QED with an additional charged (complex) scalar field, $\phi$:$$\require{cancel} \mathcal{L} = -{1\over4} F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^*(D_\mu \phi) - \mu^2 \phi^* \phi - \overline{\...