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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Yukawa potential, which is correct?

Sometimes I see Yukawa interaction term written as $$-g\bar{\psi} i \gamma^5 \phi \psi$$ and other times as $$-g \bar{ \psi} \gamma_5 \psi \phi $$ Which is the correct form?
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64 views

Help to understand vertex function

In Weinberg's book (the quantum theory of fields, volume 1, pag 446, equation (10.4.19) ) is stated that $\int \ dx \ dy \ dz \ exp(-i p x - ik y + i lz) \langle\Psi_0,T\{J^{\mu}(x)\Psi_n(y)\bar ...
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75 views

In QFT, do the fields evolve with determinism, in principle?

In quantum mechanics, the outcomes of a certain measurement might not be deterministic. However, the wavefunction evolves with determinism according to Schrodinger's equation. Is QFT analogous in ...
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2answers
103 views

Can we regard field operator $\Psi (x)$ as $a_{x}^{\dagger }$ ,$a_{x}$?

In real scalar CG-field, do we have $a_{x}^{\dagger }$ and $a_{x}$ operators? Because we have $a_{p}^{\dagger }$ and $a_{p}$ , also the relation $\Psi (x)=\int dp\, \, a^{\dagger }e^{-ipx-i\omega ...
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78 views

Are there QFTs in which a field cannot produce a real particle?

The usual mantra of a quantum field theory is that real particles (as opposed to virtual ones) are excitations of a field. Is this a necessary property of all (operator-valued) quantum field ...
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39 views

SU(2) kinetic term as a trace

Is there a easy way to rewrite the SU(2) kinetic term as a trace? As in $$\mathcal{L} = -\frac{1}{4}\vec{F}_{\mu\nu}\vec{F}^{\mu\nu}\\[1cm] = -\frac{1}{2}\mathrm{tr}\Bigg[\bigg(\vec{F}_{\mu\nu}\cdot ...
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55 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
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1answer
71 views

Guidance needed in finding scattering amplitude

If I have the Lagrangian $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How to find the scattering amplitude for $$ ...
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59 views

Range Of An Interaction

Why is the Compton wavelength $\lambda_c=\frac{\hbar}{mc}$ used as a sensible measure for the range of an interaction, where m is the mass of the corresponding mediator?
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2answers
161 views

Electron's self-energy in QED in arbitrary gauge

Recently I've tried to evaluate electron's self-energy in QED in the second order of perturbation theory by using dimensional regularization. Corresponding 1PI-diagram leads to $$ \Sigma_{1loop} = ...
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37 views

What's the importance of background field gauge?

Recently I've read that background field gauge is very convenient for gauge theories, because it fixes the connection between normalization constants of gauge field and gauge coupling constant one. I ...
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8answers
3k views

Is gravity just electromagnetic attraction?

Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the ...
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104 views

How to know if the pseudoscalar Yukawa Lagrangian is invariant under chiral transformation?

The pseudo-scalar Yukawa theory Lagrangian is $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How can I show it is ...
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2answers
58 views

Off-shell external line

In some QFT textbooks, an external line which is off mass shell also concerns us. But according to the motion equation, shouldn't the single external line be on the mass shell? Especially when we ...
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1answer
78 views

Weinberg QFT Chapter 5: gamma matrices consistency

Currently reading through Weinberg's QFT book (Vol. 1) [readable in parts here]. In his derivation of the causal Dirac field in Ch. 5, he chooses his gamma matrices as (5.4.17) \begin{align} ...
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4answers
2k views

Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula ...
4
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3answers
93 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. Suppose we ...
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5answers
493 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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4answers
206 views

What is the meaning of a state in QFT?

I guess this may be more of a mathematical than a physics question, but it comes down to physical interpretations, so I'm posting it here. In classical Quantum Mechanics, we can define a state ...
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1answer
154 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
5
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1answer
73 views

Baryon in terms of quark fields – spinor index structure

What is the most general way to write down a current describing a baryon made from quarks $\psi_i^\alpha$? Let's say we suppress flavour indices but want to write colour $(i,j)$ as well as spinor ...
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2answers
70 views

Vacuum to vacuum transition amplitude using functional integral

The vacuum to vacuum transition amplitude for a free particle with source $J$ is given by $$Z_0[J]=\int D\phi \mathrm{exp}\{-i\int [\frac{1}{2}\phi(\square +m^2-i\epsilon)\phi-\phi J]d^4x\}$$ Let ...
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1answer
164 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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2answers
30 views

Quantization conditions/ Real Scalar field

It is often written in books, the quantization conditions for classical field theory leading to Lagrangian of a real scalar field and thus to Klein Gordon equation. And these are introduced by ...
4
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2answers
131 views

Renormalization, integrating out high momenta Wilson way

In equation $(12.5)$ in Peskin and Schroeder, they write out the generating function but leave out all quadratic terms of the form $\phi\hat{\phi}$ arguing that they vanish since Fourier ...
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1answer
84 views

Apparent spacetime dependence of creation and annihilation operators

I'm currently going through An Introduction to Quantum Field Theory by Hartmut Wittig I've stumbled upon. Having trouble with equation (2.29), I'm asking the question: Do creation and annihilation ...
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1answer
91 views

How does conservation of energy manifest itself quantum mechanically?

We know that classically, if we have some theory $\mathcal{L}$ such that the action $\int d^4 x \mathcal{L}$ is invariant under time translation, then we can use Noether's theorem to find that (the ...
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2answers
246 views

Number of gravitons launched by a proton

The wikipedia article http://en.wikipedia.org/wiki/Gauge_bosons describes how in QM exchanges of gauge bosons carry force, and describes how the graviton may also be a gauge boson. If the observable ...
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1answer
205 views

The problem in Sredniki's textbook: How do I calculate loop corrections for $\phi\phi\to\phi\phi$ with this Lagrangian?

The problem in Sredniki's textbook 10.5 : For a free scalar field $\psi$, the Lagrangian is $$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$ Here we use the metric ...
2
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1answer
412 views

Time-ordering in QFT

In Srednicki QFT page 37. In the derivation of LSZ reduction formula, he introduces the time-order operator $T$, so no time-dependent creation/annihilation operators are left in the transition ...
2
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0answers
42 views

particle and antiparticle notation

This may be a very simple question but I'm really confused. If $\psi$ represents a particle (a Dirac fermion). What is an anti-particle represented by? Is it $\bar\psi=\psi^\dagger\gamma^0$ or ...
9
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1answer
169 views

Mathematical motivation of OPE?

In Peskin & Schroeder (and also Cheng which I have skimmed through) they motivate the Operator Product Expansion with a lot of words. Is there any way to motivate it mathematically, e.g. Taylor ...
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1answer
66 views

Can the strings in string theory be thought of as troughs in a field?

I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module, however my question is that since elementary ...
8
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1answer
91 views

What does an excitation in a field mean?

The term "field excitation" is used a lot especially when I hear about the Higgs boson. However, I cannot find an explanation of what precisely that means. I have a few questions relating to this. ...
0
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1answer
52 views

breitenlohner freedman stability condition

I am looking for a simple way to derive the breitenlohner-freedman bound. Actually I can't understand why we have stability above the BF bound and instability below the BF bound,while both have ...
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0answers
31 views

Pair production and initial separation

I was looking at the wiki article on electron-positron pair production (http://en.wikipedia.org/wiki/Pair_production) and have a question. The article states that the photon energy needs to exceed ...
2
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1answer
79 views

What is the four-dimensional representation of the $SU(2)$ generators?

Recently, I have been learning about non-Abelian gauge field theory by myself. Thanks @ACuriousMind very much, as with his help, I have made some progress. I am trying to extend the Dirac field ...
4
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1answer
309 views

Switching from sum to integral

I'm specifically asking about an equation in An Introduction to Quantum Field Theory, by Peskin and Schroeder. Example from page 374: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
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3answers
183 views

How is a photon measured?

If photons transmit the electromagnetic force, which is observable: the photon or the electron? Do we ever directly measure a photon, or do we only measure it's effect on electrons. For example ...
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0answers
39 views

Why is the effective action $\Gamma[\phi_c] \propto -(VT)$ (spacetime volume)?

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by $$\tag{11.50}\Gamma[\phi_c] = -(VT)\cdot ...
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1answer
96 views

Why do we believe in a “force” driven universe? [closed]

Why do we not believe in the potential for a "unified force field" universe, to the exclusion of the belief in the potential for a mechanical, gear driven universe, if the correct shape for the gear ...
1
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1answer
32 views

Deconfinement at high T $\leftrightarrow$ spontaneous breaking of the center of the gauge group

I am reading Witten's "Anti-de Sitter Space, Thermal Phase Transitions, And Confinement In Gauge Theories" (see here), in which he connects the confinement-deconfinement transition in $\mathcal{N}=4$ ...
3
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1answer
1k views

Why/How is this Wick's theorem?

Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$. $$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$ ...
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0answers
58 views

Is QED valid for arbitrarily short length scale?

Solving the Renormalization Group equation the running coupling constant in quantum electrodynamics is given by $$\bar{\alpha}(q)=\frac{\alpha}{1-\frac{\alpha}{3\pi}\ln{\frac{q^2}{M^2}}}$$ (i) It is ...
4
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1answer
142 views

Energy conservation of Virtual Particles - Quantum Fluctuation?

I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the ...
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1answer
68 views

Integration by parts [closed]

Zee in his book, Quantum field in a nutshell mentioned the following, p. 22: Equation (14): $$Z=\int{D\phi}e^{i\int d^4x{ {\frac{1}{2}[(\partial \phi)^2-m^2\phi^2]+J\phi}} }$$ He said then, ...
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1answer
144 views

What is the physical meaning of anti-commutator in quantum mechanics?

I gained a lot of physical intuition about commutators by reading this topic. What is the physical meaning of commutators in quantum mechanics? I have similar questions about the anti-commutators. ...
6
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2answers
120 views

Gauge choice after Spontaneous Symmetry Breaking

After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called ...
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1answer
256 views

QED Vertex Factor/Rule

On page 303 in Peskin&Schroeder they give the vertex factor as $$V = -ie\gamma^\mu \int d^4x$$ while on page 304 they write $$V_\times = -ie\gamma^\mu\int d^4x A_\mu(x).$$ Why are the ...
3
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1answer
52 views

How is $\varepsilon_+^\mu(p) = \bar{v}(k) \gamma^\mu u(p)$ derived?

The relation $$\varepsilon_+^\mu(p) = \bar{v}(k) \gamma^\mu u(p)$$ is sometimes used to ease calculations of Feynman amplitudes with external gluons (see for example here at (2.13)). Where does this ...