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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Can the Higgs condensate be described in terms of creation operators?

In superconductivity, the BCS condensate can be described in terms of 2 creation operators (the 2 electrons of the pair) acting on the vacuum. I'm wondering whether a similar description can be given ...
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18 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 ...
5
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2answers
467 views

Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
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1answer
679 views

Wick rotation and spinors

I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; ...
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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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66 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. ...
5
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1answer
250 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) = ...
8
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3answers
982 views

Majorana zero mode in quantum field theory

Recently, Majorana zero mode becomes very hot in condensed matter physics. I remember there was a lot of study of fermion zero mode in quantum field theory, where advanced math, such as index ...
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4answers
184 views

What is the difference between the Higgs Boson particle and an electron moving through the Higgs field?

I am watching a lecture by Sean Caroll titled "Particles, Fields, and the Future of Physics". I am not a physicist by any means but enjoy the subject in my spare time hoping to understand it. This ...
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1answer
114 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
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3answers
106 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 ...
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2answers
58 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 $\mu$?
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1answer
66 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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1answer
149 views

Path integral in quantum mechanics

I am confused by the derivation in Srednicki QFT's chapter 6 from (6.8) to (6.9). In (6.8), we have $$<q'',t''|q',t'>~=~\int DqDp \exp[i\int_{t'}^{t''}dt(p\dot{q}-H(p,q))],\tag{6.8}$$ and ...
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0answers
30 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
30 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 ...
3
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1answer
180 views
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2answers
565 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
0
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1answer
170 views

QFT question, scalar field and so on

$\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle} \newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle #1 |}$ I have such a problem with a proof. I'm studying the two point correlation ...
8
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3answers
926 views

Are electrons just incompletely evaporated black holes?

Imagine a black hole that is fast-approaching its final exponential throws of Hawking evaporation. Presumably, at all points in this end process there there will remain a region that identifiably ...
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0answers
32 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 ...
2
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1answer
132 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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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: ...
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1answer
2k views

How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) Show, by explicit calculation, that ...
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0answers
61 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 ...
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2answers
224 views

The integral is zero! $\int \frac{\mathrm{d}^d k}{(2\pi)^d} = 0$

In using dimensional regularization in QFT calculations, one comes across integrals over propagators, they might look like $(d = \text{dimension of spacetime}, n = \text{a number})$ ...
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1answer
29 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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1answer
133 views

Why are right hand neutrinos unaffected by all forces except gravity

I'm curious as to something I read on Berkeley's website. Does anyone happen to know why, according to this model,right hand neutrinos are unaffected by all forces except gravity? (Model taken from ...
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2answers
54 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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5answers
1k views

What exactly is regularization in QFT?

The question. Does there exist a mathematicaly precise, commonly accepted definition of the term "regularization procedure" in perturbative quantum field theory? If so, what is it? Motivation and ...
3
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2answers
85 views

Functional integral in spontaneous symmetry breaking

So, functional integral is defined to be (with $\lvert\Omega\rangle$ is the vacuum state): $$\frac{\langle\Omega\rvert ... \lvert\Omega\rangle}{\langle\Omega\vert\Omega\rangle} = \int \mathcal{D} ...
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0answers
56 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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46 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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1answer
69 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
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 ...
2
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1answer
203 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
2
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1answer
267 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 ...
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0answers
41 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
76 views

Is $SU(2)$ really broken by the Higgs VEV or just hidden?

It's generally stated in the textbooks that whent the Higgs field acquires a certain vev the corresponding symmetry is spontaneously broken. For example in A. Zee - QFT in a Nutshell: But none of ...
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43 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 ...
2
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1answer
75 views

Leptogenesis with singlet neutrinos

(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 ...
2
votes
1answer
54 views

Charge conservation in the complex Klein-Gordon Field

This is an extremely naive question (based on a knowledge of chapter 2 of peskin and schroeder) so apologies for any things that seem obvious. The complex scalar field, when quantized, has a conserved ...
16
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1answer
308 views

Quantum symmetries that are not classical symmetries

An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ...
6
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95 views

Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All tbe Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason forbid, say, Lagrangians with logarithms or exponentials of the fields?
2
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1answer
135 views

Photon polarization sum prescription in $e^-e^+\to{}2\gamma$

In calculating the amplitude for the process $e^-\gamma\to{}e^-\gamma$ the substitution $\sum\epsilon_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$ is useful to sum over photon polarizations. If we ...
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1answer
49 views

Photons and EM Fields

I started learning the basic ideas of QFT in an intuitive manner ( withouth any math, only with mental videos and pictures ) some days ago, and i'm finding it completely beautiful [ the idea of ...
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3answers
438 views

What is meant by the term “single particle state”

In a lot of quantum mechanics lecture notes I've read the author introduces the notion of a so-called single-particle state when discussing non-interacting (or weakly interacting) particles, but none ...
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32 views

Scattering Amplitude Not Invariant under Little Group?

I am trying to make sense of scattering amplitude recently. In some literature people say that if some number of massless particles collide together, one can theoretically express the scattering ...