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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Quadratic terms in QED lagrangian density

I recently learned that when we speak about a "free lagrangian", this actually means that the lagrangian is quadratic in the fields. When considering the Lagrangian density describing the coupling to ...
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$i\epsilon$ versus $2i \epsilon E_k$ in the propagator

The Fourier Transform of the propagator can be written as $$\tilde{\Delta}(k) = \frac{i}{k^2-m^2+i\epsilon} \tag{1} $$ which is then "factored" into $$ = \frac{i}{\left( k^0-E_k ...
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272 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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1answer
55 views

Excitation source in 2D grid coupled harmonic oscillator

In A. Zee's Quantum field theory in a Nutshell, he describes the QFT analogy of a matress, a 2D grid of points $q_a$ connected by springs (first page of first chapter, $q_a$ is the vertical ...
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64 views

What is Hawking Hartle vacuum state and why does the following Euclidean path integral gives the wave functional of it?

I am studying the wave function of black hole via the paper by Sergey Solodukhkin, Entanglement entropy of black holes,arXiv:hep-th: 1104.3712. In the paper, equation (53) is as follows: ...
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98 views

Relation of field creation operators to path integral?

Applying two field creation operators to a vacuum I get: $$\hat{\psi}^\dagger(x)\hat{\psi}^\dagger(y)|0\rangle = (\hat{\phi}(x)\hat{\phi}(y) - s^{-1}(x-y)) |0\rangle$$ where the quantum field ...
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1answer
23 views

Lifting an analogy of a pond to question signals at natural or artificial boundaries in space-time [closed]

I conjured up an idea to lift an analogy into the language of QFT and GR. I thought up the universe as a pond with a liquid. If we imagine a liquid poured into some pond (sort of bang and inflation ...
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2answers
111 views

Wavefunction collapse and relativity [closed]

In classical QM, when I measure the wave function of a system, e.g. the position of an electron somewhere in a box, its wave function collapses instantaneously to some classical position. But how fast ...
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3answers
188 views

How many electrons are there – quantum-wise?

If you consider that a particle exists as a quantum field, could you say that all the particles' fields combine into one field for that particle type? Why could you then not say there is no specific ...
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1answer
239 views

Peskin Schroeder and the general solution to Callan-Symanzik Equation

I have a couple of questions regarding Peskin and Schroeder's derivation of the solution to the Callan-Symanzik equation. First of all, they claim that using ...
3
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162 views

Phase transitions, Landau Ginzburg theory and Symmetry reduction

On one side of critical temperature (usually for $T<T_{c}$), symmetry is reduced w.r.t the symmetry on the other (usually $T>T_{c}$) regime. I heard on the road (near a theoretical physics ...
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20 views

Symmetry of retarded R-current correlator in $\mathcal{N}=4$ Super Yang-Mills

The retarded correlator of the R-current $J_\mu$ of $\mathcal{N}=4$ Super Yang-Mills theory is $$ C_{\mu\nu}(x-y)=-i\theta(x^0-y^0)\langle[J_\mu(x),J_\nu(y)]\rangle. $$ In this paper in eq. (2.4), I ...
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1answer
76 views

Two Point Correlator

I have a problem to reproduce the following identity: \begin{equation} \Pi_{\mu\nu}(q^2) = i \int d^Dx e^{iqx} \langle 0 | T \{j_\mu(x) j_\nu(0) \} | 0 \rangle = (q_\mu q_\nu - g_{\mu\nu} q^2 ) ...
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1answer
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Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
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26 views

What is therelation between nonlinear sigma model, complex projective group?

The O(N) nonlinear sigma model has topological solitons only when N=3 in the planar geometry. There exists a generalization of the O(3) sigma model so that the new model possess topological solitons ...
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1answer
97 views

Are quantum “virtual negative-energy particles” the same as “negative energy density” in EFEs?

Question is fairly straightforward. Quantum theory describes negative energy in the form of the Casimir effect and virtual negative energy particles. In the Einstein field equations, negative energy ...
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1answer
78 views

Is it possible to understand physics and make new discoveries using computer simulation? [closed]

I'm a computer science major and I want to learn Physics. I can create computer simulations of any type. I'm not good at math that is required to learn QFT or GR,but I'm thinking is it possible to ...
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30 views

What is the interpretation of coefficients in path integral

Say we want the amplitude for particles starting at x,y with distribution f(x,y) and ending up at w,z with distribution w,z. Given a functionals: $F[\phi] = \int f(x,y)\phi(x,t)\phi(y,t) dx^3 dy^3$ ...
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1answer
225 views

Scattering Amplitudes from Feynman Diagrams (Spinor Helicity Formalism)

$\require{cancel}$ I am trying to do an exercise from Scattering Amplitudes By Elvang (Exercise 2.9) which states: Show that $A_5(f^-\bar{f}^-\phi\phi\phi) = g^3\frac{[12][34]^2}{[13][14][23][24]} ...
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1answer
75 views

Spin sums in cross sections. Summing amplitudes or probabilities?

The context: I'm calculating the cross section for a scalar particle to decay into a fermion-antifermion pair in Yukawa theory, at tree level. In doing this, when calculating the amplitude from ...
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40 views

What is the current theory underlying the concept of fields? [duplicate]

When I went to school I was specifically told that fields are material (they occupy some region in space, and they "exist" there) and continuous. Recently, studying quantum physics I came across the ...
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73 views

Isn't is far more likely that general relativity, and not QFT, is “wrong?” [duplicate]

At the risk/certainty of both sounding super ignorant and talking out of my arse, I have always wondered why there is some big mystery about why there are contradictions between the predictions ...
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78 views

Dirac Delta in Field Theory

We start with a function $${\Delta(x) = \displaystyle \int \dfrac{d^3k}{(2\pi)^3 2k^0}}\left( e^{ik^\mu x_\mu} - e^{-ik^\mu x_\mu} \right).$$ It is obvious to me that for $t = 0$ the above expression ...
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1answer
968 views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
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3answers
163 views

Are field theories special?

Our best descriptions of the microscopic world, that satisfy many fundamental requirements (as we know them today), are field theories. Is there something fundamental about field interactions, or are ...
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1answer
64 views

Boosting massless particles

How does one calculate the boost matrix to go from a photon of (standard) four-momentum $k^\mu = (k,0,0,k)$ to $p^\mu = (p,0,0,p)$? (in terms of $|p|/|k|$) Weinberg in his Quantum Field Theory Vol.1 ...
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1answer
98 views

Wightman axioms. Are test functions injectively mapped to operators

In AQFT test functions f are mapped to operators $\phi(f)$. This operator is said to obey a Klein Gordon equation KG ($\phi(f)$) = 0 if $\phi(KG(f))$ = 0. This means that if the map is injective it ...
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1answer
79 views

A derivation in Schwinger's proper time approach

I have a question in derivation of Schwinger's proper time method in chapter 2.1 of http://link.springer.com/book/10.1007%2F3-540-45585-X from Eq.(2.20)-Eq.(2.23) to the classical action expression ...
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2answers
132 views

Simulation of everyday life based on standard model [closed]

If I were to model the standard model, say on a super powered computer (which does not necessarily have to exist in the real world), would I get molecules, chemistry, life? I want to understand the ...
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3answers
834 views

What is meant by a “c-number”?

In Chapter 2 of David Tong's QFT notes, he uses the term "c-number" without ever defining it. Here is the first place. However, it's easy to check by direct substitution that the left-hand side ...
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1answer
80 views

Why are the odd point green functions in free field theory zero?

I don't understand why the $(N=\mathrm{odd})$-point Green functions calculated in free field theory are identically zero. Is it because the Green functions are odd? If so, then how do I prove it? Is ...
2
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1answer
73 views

What is the interpretation of a wave function of the Universe in Hawking's no boundary proposal?

In the path integral formalism we have an in state $\Psi_{in}[\phi]$ and and out state and we find the amplitude for going from one to the other: $$\Delta[\Psi_{in},\Psi_{out}] = \int ...
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2answers
90 views

Baryogenesis via Leptogenesis

Baryon number is directly violated through electroweak anomaly and so does the Lepton number, for each transition from one vacuum to another. The two violations are of equal amount $\Delta B=\Delta ...
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0answers
91 views

Schwinger-Dyson equation from the Heisenberg formalism?

All the derivations of the Schwinger-Dyson equation I can find are done using either the path integral formalism, or for the oldest papers, Schwinger's own quantum action principle formalism, which, ...
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2answers
408 views

Complex coordinates in CFT

The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric $ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. It seems to me that ...
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3answers
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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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0answers
169 views

Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
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30 views

Phase-space average equal to the quantum mechanical average in the early universe

I was reading Mukhanov's book of cosmology http://www.amazon.com/Physical-Foundations-Cosmology-Viatcheslav-Mukhanov/dp/0521563984 , specifically about symmetry restoration in the early universe ...
9
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2answers
447 views

What is the algebraic property that corresponds to a topological term?

Warning: This question will be fairly ill-posed. I have spent a lot of time trying to make it better posed without success, so please bear with me. A single $SU(2)$ spin may be represented by the ...
6
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3answers
334 views

What happens when you apply the path integral to the Einstein-Hilbert action?

The Einstein Field Equations emerge when applying the principle of least action to the Einstein-Hilbert action, and from what I understand the path integral formulation generalizes the principle of ...
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0answers
42 views

“Zero overlap” of initial and final states in meson to nucleon + antinucleon scattering of scalar Yukawa

I'm currently studying QFT from David Tong's lecture notes and video lectures. In meson to nucleon + antinucleon decay (section 3.2.1 in this ) in scalar Yukawa theory to order $g$, without using ...
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1answer
191 views

Feynman Diagrams for Yukawa Theory

I am trying to draw the Feynman diagram for the following scattering amplitude (f a fermion) $$ i\mathcal{M}(f\overline{f}\phi\phi\phi) $$ Given the following interaction term in the Lagrangian: $$ ...
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3answers
214 views

What is the connection between gravitons and geometry?

I know there are two ways to do quantum gravity. One can pick a background space-time (usually Minkowski flat space-time) and then at any time slice one can define the state of the universe as the ...
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1answer
59 views

OPE of parity even theories in CFT.

If I consider an OPE of some operators, which belong to a theory where parity is not violated, will I have a constraint on the kind of operators appearing in the right hand side ? For example, I ...
11
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3answers
2k 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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81 views

Higgs mechanism in 1+1 spacetime dimensions

I know there are problems with Goldstone's theorem, as stated by Coleman in http://projecteuclid.org/download/pdf_1/euclid.cmp/1103859034. What about Higgs mechanism? Can I possibly think of a ...
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1answer
93 views

Is it okay to put singularities into the wave function to test behavior around unstable potentials? [closed]

$$ \psi(r)=\sqrt[4]{\frac{ a}{8\pi^3 }}\frac{ \exp (-a r)}{r^{1.25}} $$ The wave function above is an example of a function that is normalizable in 3D space and $r=\sqrt{x^2+y^2+z^2}$. $$ -\psi ...
4
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1answer
230 views

Momentum eigenstates in an interacting quantum field theory

Context for the following questions: two widely stated claims hinge on what appears to be an inconsistent argument. The claims are that (1) an interacting field can produce, in addition to ...