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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Gravitational Chern-Simons theory for bosons and fermions

Q1: What is the difference of boson and fermions for their Gravitational Chern-Simons theory? I suppose in general if the metric is not flat, we have vierbein ${e_{\hat{b}}}^{\nu}$, with $$ ...
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3answers
293 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
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74 views

Free Field theory to Interacting Field theory

Free field theory: Why is it said that different Fourier modes in case of a free field (say, real Klein-Gordon field) are independent of each other? Interacting field theory: How exactly does the ...
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1answer
105 views

Equations of motion for the Yang-Mills $SU(2)$ theory

I have an exercise for Yang-Mills theory. I can't find answer anywhere. Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar ...
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3answers
115 views

Is Space-Time a special form of energy?

I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of ...
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118 views

Duality behavior of light and effect of system scale on its behavior [closed]

Does an electromagnetic wave that makes by antenna behaves purely as wave for all the times? or it can change its behavior as photon? and does the scale of system effect on behaving as EM wave or ...
2
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1answer
72 views

Can symmetry generators anticommute with the S-matrix?

In Coleman and Mandula's proof of the Coleman-Mandula theorem, they define a symmetry transformation as an unitary $U$ which, turns one-particle states into one-particle states, acts on ...
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356 views

Why fermions have a first order (Dirac) equation and bosons a second order one?

Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion ...
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1answer
65 views

Distance and time measurement in the famous Superluminal Neutrinos Experiment

I tried to understand the technical aspects of the OPERA/CERN experiment, but apparently it takes some professional experience. Therefore I would like to ask someone better acquainted with such ...
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44 views

Changing Coordinate Systems in Two-Loop Integrals

Suppose we have the two-loop integral $\int \mathrm{d} ^ 4 k _ {2} \int \mathrm{d} ^ 4 k _ {1} \, f(k _ {1}, k _ {2})$, where $k _ {1}$ and $k _ {2}$ are four-dimensional vectors in Euclidean space. ...
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46 views

Coordinate Systems in Loop Integrals

Let us consider a two-point two-loop integral $\int \mathrm{d} ^ 4 k _ {2} \int \mathrm{d} ^ 4 k _ {1} \, f(k _ {1}, k _ {2}, p)$, where $k _ {1}$, $k _ {2}$ and $p$ are four-dimensional vectors in ...
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44 views

Jacobian in Loop Integrals

Let us consider a two-loop integral $\int \mathrm{d} ^ 4 k _ {2} \int \mathrm{d} ^ 4 k _ {1} \, f (k _ {1}, k _ {2})$, where $k _ {1}$ and $k _ {2}$ are four-dimensional vectors in Euclidean space. We ...
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1answer
127 views

Derivation of matrix element

I have tried to understand paragraph 10.7 (Kallen-Lehmann Representation) in Weinberg's Quantum theory of fields (vol.1). He calculated matrix element $$\langle0|\Phi(0)|p\rangle ...
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2answers
379 views

Yang-Mills CP violation

Why does a term proportional to $\left(F,\,\tilde{F}\right)\propto Tr\left[ F_{\mu\nu}\tilde{F}^{\mu\nu}\right]$ in the Lagrangian of the pure Yang-Mills theory violate CP?
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127 views

Momentum in Free Scalar Field

I have a few issues with making the transition between these: $\phi(x)=\int{\frac{d^3p}{2\pi^3}\frac{1}{\sqrt{2\omega_{\vec{p}}}}(a_{\vec{p}}e^{i \vec{p} \vec{x}}+ a^{\dagger}_{\vec{p}}e^{-i \vec{p} ...
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2answers
168 views

No monopoles in the Weinberg-Salam model

I'm reading Chapter 10.4 on the 't Hooft-Polyakov monopoles in Ryder's Quantum Field Theory. On page 412 he explains why magnetic monopoles cannot appear in the Weinberg-Salam model. I'm I right by ...
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1answer
50 views

Basic Field Calculations

I'm trying to derive the relation: $\phi(x)\phi(y)=:\phi(x)\phi(y):+\langle 0|\phi(x)\phi(y)|0 \rangle$ but struggling to see the first few steps I need to make. I've made the substitutions ...
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64 views

A question on IR cancellation caculation in peskin schroeder

In Peskin and Schroeder Introduction to Quantum Field Theory book, above equation 6.64 on pg. 200, it was said that "to gain better understanding, of the divergence, let us evaluate the coefficient of ...
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1answer
133 views

Casimir forces due to scalar field using Path integrals

I have just started learning QFT. I have just completed scalar fields, which I learnt in using Canonical Quantisation and Path integrals. I did calculation of Casimir force between two metal plates ...
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138 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
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42 views

Mass eigenstate of neutrinos [duplicate]

Isn't mass a fixed and an intrinsic property of a particle? How can we talk about eigenstates of the mass in the context of neutrinos?
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1answer
134 views

Why does a spurion analysis work independently of the UV physics?

In short, my question is why does a spurion analysis work to produce the correct symmetry breaking terms regardless of the high energy physics? The context that this question arose is from an ...
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1answer
113 views

are sub-atomic particles really particles or mere concepts in our minds? [closed]

are sub-atomic particles really particles or mere concepts in our minds? do they exist independently of human thought? In the tenth century, Ibn al-Haytham initiated the view that light proceeds ...
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50 views

Is there a soft Goldstino theorem?

For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission. If I break ...
5
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1answer
111 views

Why is the Yang-Mills Comparator unitary?

In chapter 15.2 of Peskin, the comparator is defined, as some object $U\left(y,\,x\right)$ which transforms as: $$ U\left(y,\,x\right) \mapsto V\left(y\right) U\left(y,\,x\right) ...
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1answer
212 views

Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
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1answer
151 views

Phase factors under rotations of strong and weak isospin

The strong isospin raising operator changes a $d$ quark into a $u$: $$ \tau_+ \big|d\big> = \big|u\big> $$ However, for antiquarks, there is an additional phase factor: $$ \tau_+ \big|\bar ...
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1answer
33 views

Relativistic Dynamical System

I have read in a paper that: A relativistic dynamical system must be invariant under infinitesimal inhomogeneous Lorentz transformation. A dynamical system is characterized by the ten generators, ...
5
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1answer
126 views

How to compute the propogator for Chern-Simons on a torus?

I'm looking to better understand Chern-Simons theory on a torus. We are given the action $$ S(\phi) = \int_E (\partial \phi)(\overline\partial \phi) + \frac{\lambda}{6}(\partial \phi)^3 $$ which ...
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0answers
31 views

Casimir Effect - Other force cause plates to attract

How do we know that virtual-particle's virtual-pressure differences caused the plates to collide in the Casimir Effect Experiments. What about micro-gravitation-fields produced but the plates ...
3
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1answer
70 views

Is there a way to compute (trivalent) Feynman integrals inductively from smaller diagrams?

Suppose that I would like to compute the Feynman integral associated to the trivalent graph One can argue that this diagram comes from two copies of the smaller diagram glued together at the ...
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1answer
330 views

Does Fermi-Dirac Statistics explain anti-particles?

I wondered whether the Fermi-Dirac Statistics describes the anti-fermion particles. Does it include the anti-particles?
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1answer
30 views

Decay width average in the isospin invariant limit

Suppose we have the following experimental values for $\eta' \rightarrow \eta \pi \pi$ decay width: $\Gamma_{\eta' \rightarrow \eta \pi^+ \pi^-} = 0.086 \pm 0.004$ $\Gamma_{\eta' \rightarrow \eta ...
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2answers
948 views

Is frequency quantized?

I'm aware that there're some questions posted here with respect to this subject on this site, but I still want to make sure, is frequency quantized? Do very fine discontinuities exist in a continuous ...
6
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1answer
159 views

Why does local gauge invariance suggest renormalizability?

I'm reading Gauge Field Theories: An Introduction with Applications by Mike Guidry and this particular remark is not obvious to me: A tempting avenue is suggested by the QED paradigm, for if a ...
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1answer
67 views

Ground State Energy in Euclidean Spacetime

Calculating the transition amplitude in Euclidean spacetime is useful because from it we can extract the ground state energy and ground state wave-functions values. For example, let's assume we are ...
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0answers
47 views

path integral quantization of EM field derived from canonical quantization?

In Peskin's QFT book page 294, he formally addressed the quantization of EM field, $$propagotor_{EM}=\frac{-ig_{\mu\nu}}{k^2+i\epsilon}$$ Now that we have the functional integral quantization ...
5
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2answers
212 views

Wick rotation in field theory - rigorous justification?

What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a ...
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1answer
76 views

Why can we simply absorb the positive coefficient of $i\epsilon$ in a propagator?

As far as I know, absorbing of the positive coefficient of $i\epsilon$ in a propagator seems to be a trivial operation without even the need of justification. In Peskin page 286, he did this: ...
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40 views

microcausality and locality

There is this thing I got confused: Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete ...
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0answers
151 views

Differential geometry of Lie groups

In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they ...
9
votes
2answers
307 views

Power divergences from loops

I do not know what I should think about power divergences from loops. Most QFT textbooks tell us how to deal with logarithmic divergences from loops $\sim\ln(\Lambda^2/\Delta)$: we can set a ...
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1answer
57 views

Equality of masses of particle and antiparticle

Usually we say that equality of masses of particle and antiparticle follows from CPT-theorem. But do we need it for showing this equality? The first method to show that is following. The equation ...
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2answers
106 views

Can we treat $\psi^{c}$ as a field independent from $\psi$?

When we derive the Dirac equation from the Lagrangian, $$ \mathcal{L}=\overline{\psi}i\gamma^{\mu}\partial_{\mu}\psi-m\overline{\psi}\psi, $$ we assume $\psi$ and ...
3
votes
2answers
98 views

Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
3
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1answer
107 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
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1answer
98 views

Functional field integral in condensed matter field theory (Altland)

This is the action for the 1+1 dimensional interacting electron system; $$S_{cl}[\theta , \phi]= \frac{1}{2\pi} \int dxd\tau \left(g^{-1}v(\partial_x \theta)^2 + gv(\partial_x \phi)^2 + ...
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2answers
146 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 ...
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1answer
108 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} ...
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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 \\ ...