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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Nontrivial IR fixed point, mass dimension, and dimensional transmutation?

I am in the process of reading this paper http://arxiv.org/abs/hep-ph/0703260 by Georgi which indeed is a nice paper but I am running into slight difficulties comprehending some conceptual and ...
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2answers
86 views

How to mathematically describe a spin-0 particle

That simple. I can't buy anything; I am only 15. I don't know all the technical things like Eigenstates. I want to know, mathematically written out for beginners, how to make a quantum field theory of ...
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15 views

Non-pertubative renormalization and correctness of a theory

Even if I start to understand why perturbative renormalization is necessary, I'm not exactly sure why non perturbative renormalization is. After asking the question to several theorists, what I think ...
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17 views

Scarlar Yukawa theory derivation

I am using Tong's notes for QFT, and on page 59 there is a derivation for the scattering amplitude of $\psi\psi \rightarrow \psi\psi$ in Scalar Yukawa theory. It goes from here: $$\langle ...
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13 views

Higgs mass and EW precision tests

I'm trying to understand how the Higgs mass can influence EW precision tests. In order to do that I'm using the following document (section 4.3): http://arxiv.org/pdf/0706.0684v1.pdf There are a ...
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1answer
31 views

Realistic interacting QFT construction

May I ask is it true that all the interacting 4 dimension qft couldn't be constructed and defined consistently and rigorously? If we are able to rigorously constructed lower dimension qft, what are ...
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27 views

Why are the particles called irreps of Poincare group? [duplicate]

Why are particle excitations called irreducible representation of the Poincare group? It will be very helpful if someone can illustrate with one concrete example of a particle.
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14 views

Problem in the derivation of the Ward identities

This is a follow up to my previous Phys.SE question. The last equation in that question is $$-a\frac{1}{k^2+i\eta}k^{\lambda}i\Pi_{\lambda\rho}(k)iD^{\rho\nu}(k)=0$$ which we can further simplify as ...
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2answers
71 views

Is this symmetry factor in Peskin wrong?

I am trying to compute the symmetry factor of a Feynman diagram in $\phi^4$ but i do not get the result Peskin Claims. This is the diagram I am considering ...
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1answer
179 views

Is the exact form of the Higgs potential known?

Usually the Higgs potential is given as $$ \frac{1}{2}\mu^2\phi^2 - \frac{1}{4}\lambda^2\phi^4 $$ but I never quite understood if this just serves to give us an idea of how symmetry breaking works, or ...
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1answer
40 views

Topological entanglement entropy in transverse quantum Ising model?

I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
2
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3answers
86 views

Why are complex fields in the Lagrangian?

I know that a complex field has twice the number of degrees of freedom of a real field, and that fields (in QFT) aren't observables so we don't really care if they are real. But why the need for ...
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1answer
22 views

Multiply creation operator by a phase factor

A basic question, but I'm not completely confident what I'm doing is legit. I can multiply a creation operator by an arbitrary phase factor and it doesn't change any physics. True? I have a ...
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1answer
69 views

Scale invariance in QFT?

I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the ...
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52 views

Why can't I use Bloch's Theorem in Lattice QFT?

Let's take a really simple example: given a typical hamiltonian for a quantum field on a 1D lattice $X=\{0,\cdots,Na\}\subset \mathbb{S}^1$: $$H=\sum_{x\in X} ...
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1answer
70 views

Why does not Bhabha scattering contain u-channel diagram?

$e^+e^-\rightarrow e^+e^-$ is called Bhabha scattering. Let us only consider the tree level Feynman diagrams of this process. Apparantly, there are s-channel and t-channel diagrams as shown in the ...
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1answer
77 views

Poincaré' lemma and EM potential $A^{\mu}$

My lecturer said that given the sourceless Maxwell's equations $$ \partial_{\mu}\, ^ *F^{\mu\nu} = 0 $$, we can find a solution $$ F^{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu},$$ that ...
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3answers
189 views
+100

Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
4
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1answer
61 views

Why doesn't a renormalizable $\phi^4$ theory have odd diagrams?

I've been reading Zee's QFT textbook and trying to follow some lecture notes online whenever I can't grasp something. I really don't understand one thing regarding the renormalization of theories, ...
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0answers
21 views

Correction to the residue in QED using $\overline{MS}$ contains IR divergence

I'm Calculating the next-to-leading orders in QED, but I'm using $\overline{MS}$ scheme, as known in $\overline{MS}$ the residue is no longer one and I have to calculate the correction to the residue ...
2
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0answers
105 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 ...
4
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1answer
57 views

Point splitting technique in Pesking and Schroeder

One of the cornerstones of point splitting technique of calculating chiral anomaly (Peskin and Schroeder 19.1, p.655) is a symmetric limit $\epsilon \rightarrow 0$. And this is the point that I don't ...
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2answers
66 views

Does the time ordering operator have a rigorous definition?

In quantum field theory, the time ordering operator (TOO) appears in the formal expressions for the scattering amplitudes. It acts upon a product of operators that each depends on time, and returns ...
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2answers
80 views

Covariant commutation relations in Mandl and Shaw

In page 47 of Mandl and Shaw, the $\Delta$-function can be written as $$ \Delta(x) = \frac{-1}{(2 \pi)^3} \int \frac{d^3k}{\omega_k} \sin(kx) \tag{3.43} $$ and as equation $$ \Delta(x) = ...
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0answers
15 views

What are instanton fugacities?

I have seen this term many times in various papers but I could not find anywhere a good explanation on what instanton fugacity is. Can you explain and provide some reference if possible please?
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43 views

Dropping creation/annihilation terms when quantising a field theory

There is something I don't understand in the procedure that is often done while quantising a field theory. Say, we have operators $a_k, a^{\dagger}_k, b_k, b^{\dagger}_k$ which obey the commutation ...
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19 views

SUSY without gaugino [closed]

In Minimal Supersymmetric Standard Model (MSSM) with $R$-parity, gauginos have Majorana mass. If we use $R$-symmetry instead of $R$-parity, gauginos do not have Majorana mass. But they can acquire ...
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1answer
32 views

QCD is able to reproduce the short range observations of deep inelastic scattering is it able to quantitatively explain quark confinement yet?

I tried to understand QCD a few years back but it was said that the force needed to confine quarks couldn't be calculated and was still in the process If a theory is so complicated that you need super ...
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64 views

If you are only interested in deriving Feynman diagrams can you skip path integrals and just compute greens functions?

I've been reading about the path integral approach to quantum field theory and I noticed that at the end you are just computing greens functions that you could have started computing in the beginning. ...
8
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2answers
239 views

The poles of Feynman propagator in position space

This question maybe related to Feynman Propagator in Position Space through Schwinger Parameter. The Feynman propagator is defined as: $$ G_F(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p ...
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0answers
26 views

How does the lagrangian derived if it has dependence on coordinate additional to field itself and derivative of itself? [on hold]

In book "QFT" By Lewis H. Ryder , page83~85 .i don't understand why he introduce so much variation,and it confuse me though.i am wondering what is the difference between total variation and ...
3
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1answer
46 views

Why can we not choose the stress tensor in a CFT to be identically symmetric?

The stress tensor for a conformal field theory (or any quantum field theory) can be derived from the action $S$ by the functional derivative $$T^{\mu \nu} ~=~ -\frac{2}{\sqrt{|g|}}\frac{\delta ...
4
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3answers
104 views

In QCD mass is caused by gluons and in electroweak it is caused by the Higgs field which is it?

I am trying to understand mass. The Standard model contains an electroweak field where mass of everything comes from the Higgs field. The Standard model also contains Quantum Chromodynamics with a ...
3
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2answers
51 views

What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
2
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1answer
63 views

Lorentz-invariance of step function

I was reading about the Lorentz invariant integration measure $\int \frac{d^3k}{2E_K}$, and ways to prove that this was Lorentz invariant. Many of the proofs I have read use the step function (or ...
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0answers
26 views

Experimentally realizable states for bosonic quantum fields

I would like to know which type of quantum states of a bosonic field, that have an explicit analytical expression as vectors/density matrices in a symmetric Fock space, can be prepared in an ...
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0answers
28 views

Computation of the partition function of a fermionic oscillator

I don't understand the following steps in the calculation of the partition function for a fermionic oscillator (Nakahara). The eigenvalues of the operator ...
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0answers
31 views

Fermionic oscillator and Hurwitz zeta function

Good resources for calculating Partition function of the fermionic oscillator using the Hurwitz zeta function? I liked the way Nakahara explain this, but some parts are really tricky for me (e.g. the ...
4
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0answers
95 views

Quantum Mechanics and Economics… What [migrated]

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: ...
3
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0answers
66 views

Field states, particles, QFT

I'm trying to self-study QFT and write a presentation paper on neutrinos. Regarding the $\left\{ \nu_L, \nu_R, \bar{\nu}_L, \bar{\nu}_R \right\}$ set of neutrino states, what is the correct word to ...
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59 views

Deriving effective model without integrating out degrees of freedom in path integral formalism?

In path integral formalism of quantum field theory (particle physics or condensed matter), one can in principle integrate out part of the degrees of freedom so as to attain an effective model ...
1
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1answer
26 views

Why IR divergences cancel by cross sections of next-to-leading diagrams?

I was reading QFT & Standard Model by Schwartz, Chapter 20 which is about IR divergences. He says that IR divergences only cancel cross sections for processes involving different initial or ...
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2answers
52 views

Understanding notation regarding particles states and wavefunctions

In the development in my notes of second quantisation I have a problem in understanding notation. We start by considering a basis $\psi_i(\mathbf{r})$ for the Hilbert space of single particle ...
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0answers
51 views

Spinor helicity formalism, exact form of the spinors

I am trying to understand how to perform computations with the spinor helicity formalism, I am studying on this review http://arxiv.org/abs/1308.1697. I have stumbled upon a problem though, in pag. ...
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0answers
44 views

Need help understanding Peskin&Schroeder QFT

I don't understand (19.73) in Peskin & Schroeder Introduction to QFT \begin{eqnarray} \sum_n \phi^{\dagger}_n(x) \gamma^5 \phi_n(x) &=& \lim_{M \rightarrow \infty} \sum_n ...
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0answers
38 views

Error in setting $m_{proton} = m_{neutron}$

Is the following reasoning correct, I'm doing mostly relativistic calculations so basically all masses come in squares. Suppose I have some expression that contains both the proton and the neutron ...
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39 views

What are the zero point energy densities of the individual quantum fields?

I'm reading through "General Relativity - An Introduction for Physicists", by Hobson, Efstathiou, and Lasenby, and I have a question regarding one of the statements related to the cosmological ...
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1answer
62 views

How to find the number of distinct contraction cases in Wick's Theorem?

Let $\mathcal{G}^8_{un}:=(t_1,t_2,t_1'^3,t_2'^3)=\langle 0 \mid T[Q_{un}(t_1)Q_{un}(t_2)Q(t_1')^3Q(t_2')^3] \mid 0 \rangle_{un}$ We want to use Wicks theorem to write this function as the sum of ...
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0answers
39 views

What insights does category theory offer in terms of grand unified theories?

What insights does category theory offer in terms of grand unified theories? Any references to books or papers that give categorical descriptions of any of the common grand unified theories would be ...
6
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1answer
78 views

Is Elitzur's theorem valid only in lattice field theory?

Elitzur's theorem, stating that spontaneous breakdown of a gauge symmetry is impossible, was originally proved for a lattice gauge theory. Is it valid in continuum field theory? Any ref?