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 ...

learn more… | top users | synonyms (1)

0
votes
0answers
33 views

Which one to choose for theoretical physics phd: SISSA or IMPRS? [on hold]

I am a non-EU student, did my MS in physics and want to work in theoretical physics for my PhD. My major areas of interest are in theoretical particle and astro-particle physics, quantum field theory ...
0
votes
1answer
22 views

wave-particle duality and entanglement

By fundamental definition of a entangled system we can say that if we know the quantum state of one subsystem then we can describe the state of another subsystem. A particle possess wave-particle ...
1
vote
1answer
87 views

Proof of Dyson-Schwinger Equation

Assuming that the functional integral of a functional derivative is zero, so $$ \int \mathcal{D}[\phi] \frac{i}{\hbar}\left\{ \frac{\delta S[\phi]}{\delta \phi}+J(x) \exp \left[ {i \over \hbar} ...
0
votes
0answers
24 views

How to calculate relative branching fractions of the $Z$ boson to specific pairs of “neutral lepton and anti-lepton”?

The PDG is listing values of "$Z$ couplings to neutral leptons" as $$ \begin{eqnarray} g^{\nu_{\ell}} & = & 0.5008 \, \pm \, 0.0008 \\ g^{\nu_{e}} & = & 0.53 \, \pm \, 0.09 \\ ...
3
votes
1answer
74 views

Interpretation of Conjugate Momentum in Field Theory

The conjugate momentum density, following as a conserved quantity with Noethers Theorem, from invariance under displacement of the field itself, i.e. $\Phi \rightarrow \Phi'=\Phi + \epsilon$, is given ...
3
votes
1answer
56 views

W + jets at NLO

I would like to calculate $pp \rightarrow W (\rightarrow \ell \nu)$ + n-jets (n=2, maybe also 3) at NLO, with some cuts and plot some distributions. I used MadGraph extensively for LO processes and I ...
1
vote
1answer
39 views

Qustion about the appearance of $\Delta_{FP}[A_{\mu}]$ in the path integral of gauge field

Why is the Faddeev-Popov quantization of a $U(1)$ gauge field not the naive solution $$\int {\cal D}A \, \, \delta\left[F(A_\mu) \right]\exp \left\{ -\frac{i}{4}\int \mathrm{d}^4 x \, ...
5
votes
0answers
70 views

What is the connection between Conformal Field Theory and Renormalization group in QFT?

As I know, the fundamental concept of QFT is Renormalization Group and RG flow. It is defined by making 2 steps: We introduce cutting-off and then integrating over "fast" fields $\widetilde{\phi}$, ...
0
votes
0answers
20 views

What's the difference between particle's helicity, spinor's helicity and chirality?

What's the difference between particle's helicity, spinor's helicity and chirality ? I read a saying that right-handed spinor correspond to the left-handed positron, right-handed spinor correspond to ...
5
votes
1answer
99 views

Eigenstate of field operator in QFT

Why don't people discuss the eigenstate of the field operator? For example, the real scalar field the field operator is Hermitian, so its eigenstate is an observable quantity.
1
vote
1answer
102 views

Why isn't the $\lvert\phi(x)=0\rangle$ Fock eigenstate the vacuum state?

If, in a QFT of a scalar field $\phi$, a Fock space $n$-particle position eigenstate $\lvert x_1\cdots x_n\rangle $ is given by $$ \lvert x_1\cdots x_n\rangle ...
7
votes
1answer
87 views

A graphical proof that the $SU(2)/\mathbb{Z}_2$ vortex is non-orientable

The text, see [1], compares the vortex solutions of a spontaneously broken symmetry $U(1) \rightarrow 1$ and $SU(2)\rightarrow U(1) \rightarrow \mathbb{Z}_2$. The vortices can be classified by ...
4
votes
2answers
361 views

Virtual particles and physical laws

Recently, I was reading about Hawking Radiation in A Brief History of Time. It says that at no point can all the fields be zero and so there's nothing like empty space(quantum fluctuation etc.). Now, ...
3
votes
1answer
80 views

S-operator lorentz invariance

How to show that $\hat {S}$-operator must be lorentz-invariant operator? $$ |\Psi (t)\rangle = \hat {S} | \Psi (0) \rangle , \quad \hat {S} = \hat {T}e^{-i\int \hat {H}_{I}d^{4}x}. $$ I have read ...
2
votes
0answers
63 views

Why is $\vert I=1,I_3=1\rangle = -p\bar n$

My book doesn't explain well how to build a doublet of antiparticles that transforms the same way the particle doublet $(p,n)^T$ (proton neutron) does. They claim $$\tag 1 \vert I=1,I_3=1\rangle = ...
3
votes
1answer
72 views

Effective theories and dimension six operators

What is the importance of dimension six operators in the study of physics beyond the Standard Model? Are these operators more relevant than dimension five operators like $HHFF$ or operators with ...
2
votes
1answer
48 views

What are threshold corrections?

As the title goes, what are threshold corrections in quantum field theory? In particular, I would be glad if a good reference is provided. Standard QFT books such as Peskin, Weinberg, etc seem to ...
1
vote
1answer
50 views

Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
4
votes
0answers
42 views

Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?

In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity $$ \overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}. $$ Here, I am using 4 ...
2
votes
1answer
64 views

Goldstone boson couple to conserved current

The Goldstone boson in spontaneous symmetry breaking problem couples naturally to the associated conserved current of the broken symmetry. How can I see a rigorous (mathematical) derivation for that?
4
votes
2answers
76 views

Higgs mechanism and neutral fields

Consider a Lagrangian $L(\phi,A_{\mu})$ with $\phi$ being some scalar field and $A_{\mu}$ some dynamical U(1) gauge field that minimally couples to $\phi$. Under a global U(1) symmetry the field ...
9
votes
2answers
135 views

In what sense do Goldstone bosons live in the coset?

Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. ...
2
votes
1answer
54 views

Can weakness of gravity explore new dimensions

Since gravitational force is weakest force out of the four fundamental fources at the microscopic level. Is it possible that gravitational force is strong in a particular direction at a new ...
1
vote
0answers
32 views

Thermal propagator for a scalar field (KMS condition)

I'm having some troubles following the derivation of the scalar field thermal propagator. I'm following the article "Finite Temperature Quantum Field Theory in Minkwoski space" by Niemi and Semenoff ...
1
vote
0answers
64 views

QFT in curved space [closed]

Can someone exactly tell me what one gains from doing QFT in curved space, and how reliable these new results are. I want to know if it is worth while putting some man hours towards this. Please ...
1
vote
0answers
42 views

Conflict between Lippmann–Schwinger equation and Gell-Mann and Low theorem about energy

Lippmann–Schwinger equation states that scattering state will have the same energy as free state, while Gell-Mann Low theorem says that they have different enery. Lippmann–Schwinger equation says: ...
3
votes
1answer
59 views

Photon Angular Momentum

Essentially I am wanting to evaluate $$\langle j\, m \mid a^\dagger(\mathbf{k}, \lambda) \mid 0 \rangle \,,$$ where $\lambda$ indicates the circular polarization (about $\mathbf{k}$). We have that ...
3
votes
2answers
273 views

Where does this term “shell” with prefix “on-/off-” come from?

Is there some historical reasons or is there a specific reason behind it? This question is connected to: Why on-shell vs. off-shell matters?
1
vote
0answers
15 views

Entropy of Reeh-Schlieder correlations

Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown ...
10
votes
0answers
133 views
+50

Polar Decomposition of a Complex Scalar Field

People often write a complex scalar field via polar decomposition. What does this parametrization precisely mean? To be more explicit consider the following Lagrangian of a complex scalar field with ...
3
votes
1answer
97 views

Finding the creation/annihilation operators

Using Minkowski signature $(+,-,-,-)$, for the Lagrangian density $${\cal L}=\partial_{\mu}\phi\partial^{\mu}\phi^{\dagger}-m^2\phi \phi^{\dagger}$$ of the complex scalar field, we have the field ...
0
votes
0answers
37 views

Is it possible to define a notion of temperature in a microcanonical ensemble?

I am thinking of a mircrocanonical ensemble as a finite system for which the number of particles, volume and the total energy is fixed. Is there a more refined view of this? Can I think of ...
1
vote
1answer
52 views

$\mathrm{d} \Omega_{CM}$ for a $1\rightarrow 2$ particle decay?

The differential solid angle is described in e.g. Srednicki's QFT text but only for the case of scattering. Because in the case of scattering it's defined with respect to the incoming three-momentum ...
2
votes
2answers
74 views

How to get conserved currents of a theory which are not Noether currents?

In the first SuSy lecture last week following theory of two real scalar fields has been considered as a first example: $$\mathcal{L}=(\partial_\mu \phi_1)^2/2+(\partial_\mu ...
4
votes
1answer
57 views

How use the Higgs branching ratio plot to extract information about the Higgs mass compared to experiment?

What does the plot of higgs branching ratio (see figure below) say about the higgs mass anyway? How can one use it as a guide to find the higgs mass experimentally? If we e.g. go to $M_H=126$ GeV ...
2
votes
1answer
48 views

All angle dependence in $\mathrm{d}LIPS_2$?

Recall that $\mathrm{d}LIPS_2$ (one particle decaying into two particles of the same mass) is given by $$\mathrm{d}LIPS_2 = \frac{\vert{\bf k_1'}\vert}{16\pi^2\sqrt{s}}\mathrm{d}\Omega_{cm}.$$ In a ...
3
votes
1answer
105 views

Mandelstam variables 1 positive 2 negative

The three Mandelstam-variables are defined as: $$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the ...
2
votes
0answers
51 views

One question about Weinberg's derivation of arbitrary spin fields expressions

In his book "QFT" (vol. 1) Weinberg writes the expression for an arbitrary spin massive field: $$ \hat {\Psi}_{a}(x) = \sum_{\sigma = -s}^{s} \int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2 ...
2
votes
0answers
51 views

Epsilon Tensor in FeynCalc

A few days ago I started to use the Mathematica package FeynCalc and one thing confuses me: Assume we have a four-vector $p_\mu$ and we contract it with the epsilon tensor. FeynCalc produces ...
3
votes
1answer
57 views

Dirac operator Feynman propagator

Is it true that the following identity holds for the Feynman prescription Dirac propagator: $$ S_F(x) \stackrel{?}{=} \gamma^0[S_F(-x)]^\dagger\gamma^0 $$ where $S_F$ is defined as the Green's ...
2
votes
3answers
177 views

why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value(vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
4
votes
4answers
76 views

why do the electroweak vacuum have to be charge and color neutral?

My question is why the electroweak vacuum of the Standard Model have to electroweak charge and QCD color neutral? What goes wrong if electroweak vacuum has either non-zero charge or color quantum ...
1
vote
0answers
30 views

Regulating a particular function

I am interested in computing the integral of this function: \begin{align} \int_0^\infty\frac{2du(u^2+1)}{(1-e^{2\pi u})}, \end{align} which of course at first sight, does not converge. But in QFT ...
0
votes
1answer
38 views

can interaction between a massless fermion and external sourse exist?

For example, let's consider the electromagnetic interaction between a massless fermion and a electromagnetic externel sourse $A^\mu$, then the lagrangian is ...
4
votes
1answer
71 views

Lorentz transformations of fields evaluated at a point

I'm am sure that I must be missing something very simple, so apologies in advance. Considering the Lorentz transformation $\Lambda$ of a spinor fields, for the plane-wave solution $u(p)$, I cannot ...
6
votes
1answer
65 views

About the recent discovery of 4-quark boundstates.

I am referring to this, http://home.web.cern.ch/about/updates/2014/04/lhcb-confirms-existence-exotic-hadron So how does this work if we stick to keeping quarks in the 3 dimensional fundamental ...
0
votes
1answer
50 views

Fermion propagator is not a Grassmann-odd object?

Is the following differentiation correct: $$ \frac{\delta}{\delta\eta\left(z\right)}\int d^{4}yS_{F}\left(z-y\right)\eta\left(y\right) = S_F\left(z-z\right)$$ where $\eta$ is a Grassmann-valued ...
1
vote
1answer
38 views

Defining quantum effective action (Legendre transformation), existence of inverse (field - source)?

Given a Quantum field theory, for a scalar field $\phi$ with generic Action $S[\phi]$, we have the generating functional $$Z[J] = e^{iW[J]} = \frac{\int \mathcal{D}\phi e^{i(S[\phi]+\int d^4x ...
5
votes
1answer
55 views

$P$ symmetry that is apparent with one definition of fields but not with another

Suppose that we have a Lagrangian density like $$\mathcal L = -\frac{1}{4} \operatorname{tr} F_{\mu\nu}F^{\mu\nu} + \frac{\theta}{32\pi^2} \operatorname{tr} \big( \epsilon^{\mu\nu\rho\sigma} ...
0
votes
1answer
63 views

Is $\langle k \vert k_1k_2\rangle=0$

Using that $$ \vert k_1k_2\rangle = a^\dagger({\bf k_1})a^\dagger({\bf k_2})\vert 0 \rangle$$ and the commutation relations $$[a({\bf k}),a^\dagger({\bf k'})]=(2\pi)^32\omega\delta^3(\bf {k}- \bf ...