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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What is crossover?

It is known that EW and QCD phase transitions in SM are so-called "crossovers". What is the difference between crossover and phase transition of the second kind?
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69 views

Time evolution of scalar field

Consider the quantized real scalar field acting on the vacuum state $\vert 0 \rangle $. We can interpret the state $\phi(\textbf{x})\vert 0 \rangle $ (defined in the Schrodinger picture at $t=0$) as a ...
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Massive Gauge Bosons without Higgs Effect

In a possible theory like our Standard model but without a Higgs i.e.: $$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$ where $b,f$ run over the typical ...
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Instantons and Fivebranes

What is the general relationship between instantons and fivebranes? In the paper ``Magnetic Monopoles in String Theory'' by Gauntlett, Harvey and Liu, the authors state the fivebrane ansatz of ...
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89 views

Equivalence principle for test fields

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...
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1answer
42 views

What is the energy-conserving delta function

I am reading about the S-matrix in QFT (Standard Model book by Burgess and Moore) and I came across the energy-conserving delta function, which is factored out of the S-matrix. I would greatly ...
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37 views

Supersymmetric transformation of general Wess-Zumino Lagrangian

I suspect that I might have understood something wrong here. I'm trying to show that the general Wess-Zumino Lagrangian \begin{align} \mathcal{L} &= \int d^2\theta d^2\bar{\theta} K(\Phi^*, \Phi) ...
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2answers
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Why do neutrino oscillations imply nonzero neutrino masses?

Neutrinos can pass from one family to another (that is, change in flavor) in a process known as neutrino oscillation. The oscillation between the different families occurs randomly, and the likelihood ...
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2answers
109 views

Identify for $f(\infty)+f(-\infty)$ in quantum field theory [duplicate]

In Matthew Schwartz's textbook, Quantum Field Theory and the Standard Model, equation 14.68 on page 266 says the following: ...
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38 views

How can I compute the orbit of a Higgs field?

In many papers that deal with symmetry breaking a concept called orbit is introduced: It is worth noting that if the potential is a minimum $\phi_0$ at a value of the field, then from (3.13) it is ...
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Can the photoelectric effect be explained without photons?

Lamb 1969 states, A misconception which most physicists acquire in their formative years is that the photoelectric effect requires the quantization of the electromagnetic field for its ...
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1answer
165 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
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1answer
93 views

Is the Klein-Gordon Hamiltonian unbounded below?

This question is about the Klein-Gordon Hamiltonian for simplicity, but the problem seems to remain when dealing with other fields (e.g. Dirac, photon...). One usually writes the Hamiltonian ...
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117 views

What is the Copenhagen interpretation of quantum field theory?

I am most interested in interpretational differences due to the fact that quantum field theory is relativistic while quantum mechanics is not. By "Copenhagen interpretation" I mean a minimal ...
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74 views

Weinberg Volume I Equation (10.5.10) on page 451

I copy it here: $$\Delta'_{\mu\nu}(q)=\Delta_{\mu\nu}(q)+\Delta_{\mu\rho}(q) M^{\rho\sigma}(q) \Delta_{\sigma\nu}(q)$$. $\Delta_{\mu\nu}(q)$ is the bare photon propagator, and $\Delta'_{\mu\nu}(q)$ ...
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44 views

Why does not the bare interaction potential appear in the Bogoliubov theory?

They use some effective potential defined by the s-wave scattering length, but not the bare atom-atom interaction $V(r)$. Why? It is standard practice in second quantization to use the bare ...
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150 views

How does Hawking radiation grow as a black hole evaporates?

The temperature of Hawking radiation is inversely proportional to the mass of a black hole, $T_{\rm H}\propto M_{\rm BH}^{-1}$, and so as the black hole shrinks the temperature of the radiation should ...
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73 views

Counterterm Lagrangian and Renormalisation?

I am going through the notes on QFT by M. Srednicki (online: http://web.physics.ucsb.edu/~mark/qft.html), and I am having a hard time to understand the "renormalised" Lagrangian. Consider a ...
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21 views

Which is the analogous of the unitarity constraint of chiral perturbation theory in superchiral perturbation theory?

I am trying to reconstruct something and I would appreciate omeone helping me filling the gaps. To motivate my question let's first consider chiral perturbation theory with up and down quarks. This is ...
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51 views

Vacuum to vacuum transition amplitude confusion

I keep seeing this for the vacuum to vacuum transition amplitude: $\langle 0,\infty|0,-\infty\rangle_J\,.$ What is $|0,-\infty\rangle_J?$ Am I to take the Hamiltonian with the source present, ie. ...
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1answer
279 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
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3answers
2k views

Do particles with exactly zero energy exist?

In my understanding, in Newtonian mechanics if something has no mass it cannot be said to "exist" since it cannot possibly have energy or momentum and thus cannot participate in interactions or be ...
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21 views

Large Spin operators and radial quantization

I've been reading the paper "Comments on operators with large Spin" (here) and I am having some trouble understanding the following: In section 2, they begin by studying, in a conformal field theory ...
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1answer
59 views

How are scale of renormalization and scale of symmetry breaking related?

If symmetry breaking, e.g. with a potential $V=-\mu^2\phi^2 + \lambda \phi^4 $ occurs at a certain energy scale, and I now evolve to another scale via the Callan-Symanzik equations, does that change ...
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Is there a useful way to represent the optical theorem in the parametric representation?

The usual way to represent the optical theorem for Feynman diagrams is through the Cutkosky rules. The proof of these rules works by considering the momentum representation and performing the iterated ...
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94 views

How does Lorentz invariance make $(\Psi_0,J_{\mu}\Psi_0)$ vanish?

Right before equation (10.4.7) in Weinberg's volume 1 on quantum field theory, he said $(\Psi_0,J_{\mu}\Psi_0)$ vanishes due to requirement of Lorentz invariance. As I understand, this term is a ...
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215 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...
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265 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 ...
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2answers
201 views

Why does the Walecka model not include pions?

The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?
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63 views

Why is the free field operator the same with interactions present?

In free scalar theory, the field would have the expression $$\phi(x)=\int \frac{d^3p}{(2\pi)^3\sqrt{2E_p}}a_p e^{-ip_\mu x^\mu}+a^\dagger_p e^{ip_\mu x^\mu}$$ Suppose we have an interaction with a ...
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2answers
37 views

Does the connected Green's function's decomposition into 1PI-s have connected contributions, or can it be written exclusively using 1PI-s?

While reading this article by Abbot on the background field method, in Fig 5. on page 38 (page 6 in the pdf file), we can see the relation between connected contributions to the two point function and ...
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145 views

What is $\phi(x)|0\rangle$?

Suppose for instance that $\phi$ is the real Klein-Gordon field. As I understand it, $a^\dagger(k)|0\rangle=|k\rangle$ represents the state of a particle with momentum $k\,.$ I also learned that ...
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2answers
201 views

Difference between locality and causality?

I ask this question as the two seem to be very closely related and are sometimes taken to be one and the same (in the notion of microcausality in QFT), which has left me confused as to what meaning of ...
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1answer
113 views

How to calculate the functional derivative of the functional integral?

I study by myself with the QFT, in the page 197 of book of Lewis H. Ryder (2nd edition), The author wrote that he take the functional derivative of equation 6.69: $$\frac ...
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1answer
116 views

Proper way to quantize the string in the light-cone gauge

In many books like Polchinski and Green-Schwarz-Witten the light cone quantization is carried out in a fast way. They just use the virasoro constraint in the light-cone gauge to get the ligh-cone ...
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18 views

Typical Momentum Invariants of a General 3-Point Function for Renormalization Conditions

According to Peskin, p.414, at the bottom, as part of calculating the $\beta$ functions of a theory, we need to fix the counter terms by setting the "typical invariants" built from the external leg ...
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1answer
747 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, ...
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2answers
65 views

How are quadruple gluon vertices related to $SU(2)$ and $SU(3)$?

I once read that the non-commutativity of the Lie Groups $SU(2)$ and $SU(3)$ is the reason that the weak and strong interactions have Feynman diagrams with quadruple vertices, where four gauge bosons ...
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53 views

Locality, unitarity & vacuum energy

I've read in a set of lecture notes that the requirement of locality and unitarity in QFT imply that the vacuum must have a non-zero energy associated with it (http://arxiv.org/abs/1502.05296 , top of ...
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260 views

How do gauge boson interact with elementary particles?

We know that gauge bosons are the force carriers of fundamental interactions, but how do the gauge bosons themselves interact with particles?
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1answer
161 views

Massless boson in 2D and its (retarded) propagator

I have the retarded propagator for a free scalar field in 1+1 dimensions. Inside the light cone, this looks like $J_0(m \sqrt(t^2-x^2))$, J being a Bessel function. When I take the massless limit, ...
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37 views

Symmetry breaking to a special subalgebra?

This is a follow-up to my question here. For regular subalgebras of some group's Lie algebra the root system of the subalgebra is a subset of the root system of the original's group algebra. In ...
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1answer
128 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?
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1answer
100 views

Singlet neutrinos decaying to Higgs bosons during leptogenesis

(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 ...
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5answers
3k views

Which is more fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: I lack an adequate understanding of ...
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34 views

How is the stability of Higgs vacuum affected? [duplicate]

What is meant by standard model vacuum? Is it same as the the vacuum of the Higgs potential? What is meant by the stability or instability of vacuum? And how is Higgs self-interaction responsible for ...
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1answer
515 views

Does gravity affect quantum fluctuations? [closed]

Empty space is filled with quantum fluctuations. My question is, since space is affected by the amount of matter contained in it (based on General Relativity), does gravity affect quantum ...
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1answer
144 views

Quantizing highly nonlinear field-theories?

I'm wondering how to go about quantizing a classical field theory which looks nothing like a free field theory plus a perturbation term. Suppose for concreteness I have the classical hamiltonian $ ...
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1answer
110 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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2answers
102 views

Ground state for interacting field thoeries

Are there references where the ground state of an interacting quantum field theory is explicitly written in terms of states of the underlying free theory? For example, let us suppose to have a self ...