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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The relationship between the structure of spacetime and the existence of spinor field?

We all know that the existence of spinor fields implies that spacetime must be time-orientable. Thus that spacetime is time-orientable is a necessary condition for existence of spinor fields. Geroch, ...
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9 views

Normal ordering for a two fermion case

I am trying to understand how normal ordering works. I am considering a system of two photons, with $\hat{f}_i$ and $\hat{f}_i^\dagger$ being the annihilation and creation operators, respectively. I ...
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1answer
55 views

Can the energy of the universe ever be infinite in qunatum physics?

Suppose that the universe runs under some variants of QFT, with universal wavefunction and Hamiltonian. Then would infinite energy of the universe ever be possible? According to what I am thinking, ...
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33 views

Why is only the third component of weak isospin used as conserved quantity?

Using Noether's theorem \begin{equation} \partial_0 \int d^3x \left(\frac{\partial L}{\partial(\partial_0\Psi)} \delta \Psi \right) = 0 \end{equation} we get three conserved quantites $Q_i$ from ...
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1answer
30 views

The contribution to the one loop beta function for the WZW model

When the Wess-Zumino-Witten model $$S_{WZW}=\frac{k}{4\pi}\int d^2 z \, \, \mathrm{Tr}[\partial u \bar{\partial}u^{-1} ]+ \frac{k}{12\pi}\int d^3 \sigma \epsilon^{ijk}\, ...
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54 views

Is there really such a thing as a left-chiral particle?

A chiral eigenstate is always a linear combination of a particle and an antiparticle state and a particle or antiparticle state is always a linear combination of chiral eigenstates. Now, how can we ...
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46 views

BRST quantization of point particle

Suppose we have Lie algebra $\mathfrak{g}$ with basis $t_a$ with a representation $$ t_a \mapsto K_a: V \to V. $$ Denote by $c^a$ the dual basis. Chevalley differential is defined as $$ Q = c^i K_i - ...
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1answer
35 views

Eigen-state in a coupled Boson system [on hold]

What's the eigenstate of the coupled system like $$ H=a^{\dagger}b+ab^{\dagger} $$ The system is Boson system and $a,b$ are annihilation operators of fock states and they are commute. In my opinion, ...
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4answers
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Are atoms made of protons, electrons and neutrinos?

If neutrons decay into proton, electron and (anti)neutrino of electron type, then is it safe to say that atoms are protons, electrons and neutrinos?
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27 views

Strong CP Problem

So, as far as I know, the Strong CP Problem in QCD results from the theta angle term in the action: $i\theta\int_X F_\nabla\wedge F_\nabla$ where $\nabla$ is the gauge connection and $X$ is a manifold ...
2
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1answer
25 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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67 views

Has confinement been experimentally observed? [on hold]

So, confinement has obviously been shown by lattice gauge theory to be a predicted aspect of QCD. However, to what extent has it been observed in experimental physics?
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14 views

Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
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29 views

Isolating the divergences in the stress energy tensor

In DeWitt's report "Quantum Field Theory in Curved Spacetime" (B. S. DeWitt, Phys. Rep. 19C, 292 (1975)), he states that in Eq.(175) $$\langle in, vac| T^{\mu\nu}|in,vac\rangle = 2 \frac{\delta ...
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2answers
174 views

Does the lagrangian contain all the information about the representations of the fields in QFT?

Given the Lagrangian density of a theory, are the representations on which the various fields transform uniquely determined? For example, given the Lagrangian for a real scalar field $$ \mathscr{L} = ...
2
votes
1answer
127 views

Fourier and inverse fourier transform in QFT

According to my lecture notes, the inverse Fourier transform of an operator $\phi(p)$ is given by $$\phi(x)=\int \frac {d^4p}{(2\pi)^4}\phi(p)e^{-ip\cdot x}.$$ As @WenChern pointed out below, Peskin ...
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42 views

How do Lorentz transformations act on position kets $|\mathbf{x}\rangle$?

The Hilbert space of one particle can be spanned by position kets $|\mathbf{x}\rangle$ or by momentum kets $|\mathbf{k}\rangle$. If we denote $|k^\mu\rangle = \sqrt{2E_{\mathbf k}}|\mathbf{k}\rangle$, ...
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14 views

Non-minimal coupling (Pauli Coupling) of gauge field with a non-relativistic scalar field

I am wondering if it makes any sense to non-minimally (say, Pauli-like) couple an external gauge field with a non-relativistic scalar field: \begin{equation} p_\mu \rightarrow p_\mu - e A_\mu + ...
3
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2answers
80 views

Why scalar function of vector can only depend on norm of vector?

In Field Quantization by Greiner and Reinhardt as well as The Qunatum Theory of Fields by Weinberg, concerning the spectral function, the authors say a scalar function of the four-vector $p^\mu$ can ...
3
votes
1answer
89 views

Proving $[a_k^\dagger, a_q^\dagger]=0$

I am trying to prove the commutation relations between the creation and annihilation operators in field theory. I was already able to show that $[a_k, a_q^\dagger]=i\delta(k-q)$. I want to show that ...
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23 views

Normalization constant of the Vacuum polarization

In the article "On gauge invariance and vacuum polarization" by Schwinger, at some point the equation $$\frac{C}{s^2}\int e^{i\frac{x^2}{4s}} \, dx =1$$ is said to have the solution ...
3
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1answer
55 views

What are the definition and examples of topological excitation?

I read topological excitation in wiki, while it's too brief. What is the precise definition of topological excitation? And can give me some examples and explain why they are topological excitation? ...
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2answers
73 views

How to handle the potential $V(x)$ or $V(\phi)$ which is not analytic in QM and QFT

In QM, $$\hat{x}\phi(p)=i\frac{\partial}{\partial p} \phi(p)$$ and when $V(x)$ is an analytic function of $x$, then $$V(\hat{x})\phi(p)=V(i\frac{\partial}{\partial p} )\phi(p)$$ and we can do Taylor ...
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42 views

Staying up-to-date on modern physics [closed]

Not necessarily a science question, but I was hoping for advice as to what journal I should read online to stay more up-to-date on modern physics discoveries. To be specific: I'm an undergrad in ...
3
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1answer
66 views

Infinitely many scalar fields

Suppose I have the following Lagrangian density: $$ \mathcal L = -\frac{1}{2} \sum_{i = 1}^N \left [ \partial_\mu \phi_i\partial^\mu \phi^i +m^2 \phi_i^2\right ] + \frac{g}{2N}\sum_{i=1}^N ...
5
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3answers
109 views

Why every state evolving infinite time becomes the ground state in QFT?

For any state $|\phi \rangle $ evolving infinite time $$\lim\limits_{t\rightarrow \infty} e^{-iHt}|\phi\rangle=\lim\limits_{t\rightarrow \infty} e^{-iHt}|n\rangle\langle n|\phi\rangle$$ Let ...
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1answer
50 views

Eigenstates of a bosonic field operator

Even though related questions are discussed here and here, I am still confused about the eigenstates of the field operator of a bosonic field $$ ...
3
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1answer
112 views

Why use a particular regularization for $\int_0^\infty \mathrm{d}x\,e^{i p x}$?

There are many badly defined integrals in physics. I want to discuss one of them which I see very often. $$\int_0^\infty \mathrm{d}x\,e^{i p x}$$ I have seen this integral in many physical problems. ...
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0answers
61 views

Simplify QCD Lagrangian

How we can derive the electric charge of the field theory for each field ? For example lets say that we have the u quarks(3-colors) and electron that we know that has charge -e) free Lagrangian ...
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1answer
124 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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3answers
208 views

Why aren't purely Dirac neutrinos ruled out?

It is common knowledge that in neutrinos can be Dirac particles without any Majorana masses as given a mass matrix, \begin{equation} \left( \begin{array}{cc}\nu _L & \nu _R \end{array} \right) ...
2
votes
1answer
46 views

1-particle non-interacting Green function

At $T=0$ in the non-interacting case the $1$-particle Green function for an electron in the excited state $\lambda$ (empty band) is of the form \begin{eqnarray} G^{(0)}(\lambda,t-t') = -i \theta(t-t') ...
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0answers
43 views

Interpretation of all eight solutions of the Dirac equation

There are eight solutions of the Dirac equation. $u_1, u_2, u_3 , u_4$ and $v_1,v_2,v_3,v_4$. Conventionally the four solutions ($u_3 , u_4,v_3,v_4$.) following from $E=- \sqrt{ (\vec p)^2 +m^2}$ are ...
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0answers
46 views

What is really interacting in weak interactions?

Only particles with chirality $-1$ do interact weakly. The corresponding eigenstate in the Dirac basis is $ \Psi_L = \begin{pmatrix}f \\ -f \end{pmatrix} = \begin{pmatrix}u_r {\mathrm{e}}^{-imt} \\ ...
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40 views

Background field expansion in normal coordinates

Background field expansion following form $Y= X+\pi$ where $X$ is my background field and $\pi$ is the fluctuation. From the Normal coordinates we have the expansion of $\pi^{\mu} = ...
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1answer
77 views

Feynman rule for propagator with derivatives

Suppose you have an interaction term of the form $$\mathcal{L}_{int} = \frac{h g}{3!}\phi^3\partial^2\phi$$ where $h $ and $g$ are both couplings. Now if I draw a diagram of the form given in the ...
5
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4answers
923 views

What are Quarks made of and will they ever decay to this? [duplicate]

What is it that quarks are actually made of? Will they decay into this substance? As the up and down quarks are the lightest type of quark do they not decay? I was thinking that if this could happen, ...
2
votes
2answers
307 views

Are virtual particles limited by the speed of light? [duplicate]

I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing. I understand photons mediate the electromagnetic force and interactions between ...
0
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0answers
29 views

Everything moves at the speed of light? [duplicate]

Whatever happened to that idea? Presumably it came from a concept known as Zitterbewegung. As wiki says, a theoretical rapid motion of elementary particles, in particular electrons, that obey the ...
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0answers
28 views

Is there an analytical expression for the conductivity of the surface of topological insulators?

I have a question about the conductivity on the surface of Topological Insulators (TI): Is it accurate to model the conductivity by the Drude model (I read a paper that modeled the conductivity with ...
3
votes
1answer
72 views

Relationship between the on-shell and BPHZ renormalization schemes

In his book Quantum Field Theory - A Tourist Guide for Mathematicians, Gerald Folland introduces the on-shell renormalization scheme for the $ \phi^{4} $-scalar field theory. According to my ...
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votes
2answers
75 views

Can an elementary particle be reduced to its properties?

For instance, is an up quark merely its particular mass, 2/3 electrical charge and 1/2 spin? I was wondering if there was a 1:1 correspondence with a particle and its properties, but I noticed a gluon ...
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56 views

What is the current situation of the Yang-Mills existence problem?

What is the current situation of the Yang-Mills existence and mass gap problem? And who are the physicists and mathematicians working in this nowaday?
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27 views

Are there Planck units for weak or strong “charge”, similar to the electromagnetic Planck charge $\sqrt{4~\pi~\epsilon_0~\hbar~c}~$?

Are there Planck units for "charge" of weak or strong interaction, similar to the Planck unit of electromagnetic charge: $\sqrt{4~\pi~\epsilon_0~\hbar~c}$ ? Are there perhaps direct substitutes, ...
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33 views

Definition of mass gap [duplicate]

Why do we say that a system with mass gap has correlation function which decays exponentially and one without a mass gap has a slower power law decay?
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0answers
35 views

Interpretation of Dirac Spinor components in Chiral Representation?

I failed to find any book or pdf that explains clearly how we can interpret the different components of a Dirac spinor in the chiral representation and I'm starting to get somewhat desperate. This is ...
2
votes
1answer
61 views

How does interpreting negative energy electrons as positrons solve the negative energy problem?

How does interpreting negative energy electrons as positive energy positrons solve the negative energy problem? How does change of “interpretation” without fixing the mathematics have such a profound ...
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0answers
21 views

Bulk Symmetry corresponding to Yangian Symmetry of Planar N=4?

4D N=4 Super Yang Mills in the planar limit has an infinite dimensional symmetry known as Yangian symmetry. Dualities respect symmetries, so what does this symmetry correspond to in the $AdS_5\times ...
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0answers
32 views

Minimization of a quaradic-like expression when calculating the generating functional for free Dirac field

The generating functional for a free Dirac field is $$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$ where ...
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1answer
35 views

What are Maximally Helicity Violating (MHV) Amplitudes?

Definition of MHV amplitudes on Wikipedia: In theoretical particle physics, maximally helicity violating amplitudes are amplitudes with n external gauge bosons, where n-2 gauge bosons have a ...