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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Non Zero correlation function (for large separations) in one particle state?

So i computed the following equal time correlation function for a one particle state. The vacuum correlations give the function $$\langle \phi(\vec x)\phi(\vec y)\rangle_0=D(\vec x-\vec y)\\ ...
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39 views

How can one diagonalize the second variation of action?

Suppose we have action $S[q]$ and its stationary path $q_s$, I want to find the orthonormal paths $\psi_n$ that can diagonalize the second variation of the action $S[q]$. How to do that? Thanks
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578 views

Are gravitomagnetic monopoles hypothesized?

My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic ...
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28 views

Electron photon interaction potential in old fashioned perturbation theory (OFPT)

In this PDF on old fashioned perturbation theory (OFPT) we find from equation (14) the potential describing the interaction between the electron and photon: $$ V = \frac{1}{2}e \int \mathrm{d}^3x\, ...
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S-Matrix Elements in Path Integral Formalism

I have a question related to the connection between the S-Matrix elements and the path integral formalism. In order to formulate the question, I will just work with a scalar field theory for ...
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513 views

Physical interpretation of infinite total cross section

What does it tell us about a process, say A+B->C+D, if the calculated total cross section is infinite?
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69 views

What's the difference between energy and temperature in field theory?

I'm familiar with the formalisms for both zero temperature and finite temperature field theory, but (somewhat embarrassingly) I don't actually have a good physical intuition for when physical ...
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288 views

(Un)countability in QFT

I am a mathematician self-studying physics, and a currently working on QFT with Srednicki's book. One thing that bothers me is that for a scalar field (in the Hamiltonian version) there is a ...
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87 views

Non-local structure of field theory

Can someone explain what is non-local structure of field theory? I know you cannot have $\phi(x) \phi(y)$ term in Lagrangian which indicates the non-locality. However, why I cannot have the non-local ...
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67 views

Expansion in Quantum Fluctuations of the Path Integral

In this post: Dimensionless Constants in Physics there is a discussion about dimensionful vs. dimensionless constants in physics. In the context of this discussion, I'm wondering about the ...
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69 views

Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. ...
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69 views

The particle content of a given state

In Carroll's we read ...The Unruh effect teaches us the most important lesson of Quantum Field Theory (QFT) in curved spacetime, the idea that "vacuum" and "particles" are observer-dependent ...
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38 views

Properties of the Scalar Field in Scalar-Tensor Theories

I've been reading about scalar-tensor theories of gravity, such as Brans-Dicke theory, and I started thinking about the scalar field. Now, I know that the Higgs field is a scalar field, and of course ...
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131 views

What does this question about entanglement and classical geometry mean?

Below is the question from Andy Strominger's presentation at the String 2014 conference. The question was asked by credible physicist Ashoke Sen as an important question. "What is the precise ...
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38 views

What are differences between Spin(3,1), SL(2,C), SO(3,1) and SU(2) representations? Which one is correct exact representation for spinor fields? [duplicate]

I want to understand which group transformations exactly represent spinor fields. That is, do spinor fields transform under the Lorentz group $\mathrm{SO}(3,1)$ or under $\mathrm{Spin}(3,1)$? What ...
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329 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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77 views

What is the axial transformation of a group, i.e. $SU(3)$?

The Gell-Mann matrices $\lambda^\alpha$ are the generators of $SU(3)$. Applying an SU(3) - transformation on the triple $q = ( u , d, s )$ of 4-spinors looks like this: $$ q \rightarrow q' = e^{i ...
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103 views

Lagrangian and grassmann numbers

Why sometimes we remember that "classical" lagrangians of fermions are constructed from grassmann numbers, while sometimes don't? For example, for Majorana's field in terms of 2-component spinors ...
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1answer
52 views

A question about the asymptotic series in perturbative expansion in QFT

Related post I heard about the argument that the perturbative expansion in QFT must be asymptotic, such as http://ncatlab.org/nlab/show/perturbation+theory#DivergenceConvergence Roughly this can ...
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91 views

Proof of Connected Diagrams

If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only ...
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1answer
104 views

Understanding the four fundamental forces of the standard model - are they magic [closed]

Don't misunderstand the question, my purpose is exploration and understanding of what defines "mainstream physics". It is not asked idly, or with ill purpose.... My understanding of current ...
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36 views

U(1) local gauge transformation for Dirac spinor field

How can we define U(1) local gauge transformation for Dirac spinor field?, like scalar fields?
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29 views

Wick theorem applying to partly ordered operator

I symbolize $T$ as the time-ordered operator and $::$ as normal order symbol. I know that in quantum field theory generally we have: $$T\phi_1(x_1)\dots\phi_n(x_n)=:\phi_1(x_1)\dots\phi_n(x_n):+A$$ ...
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314 views

Does the the quantum field theoretic process of particle–antiparticle annihilation break the axioms of Special Relativity?

$\textbf{Note that this diagram hasn't anything to do with the question directly.}$ After a particle and its antiparticle annihilate, their energy is converted into a force carrier particle, such ...
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1answer
70 views

The n-point Green functions and Heisenberg picture

Let's have the S-matrix: $$ S_{\beta \alpha} = \langle \beta | \hat{S} | \alpha\rangle . $$ Here $|\alpha \rangle , | \beta \rangle$ are $t \to \mp \infty$ limit of the free states, $\hat {S} = ...
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1answer
114 views

Fermion Self-Interaction

I'm trying to think of a theory with a Fermion self-interaction, similar to the $\phi^4$ theory. The first difficulty is of course that such a theory would have a non-renormalizable mass dimension: ...
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256 views

Soliton Moduli Spaces and Homotopy Theory

The four-dimensional $SU(N)$ Yang-Mills Lagrangian is given by $$\mathcal{L}=\frac{1}{2e^2}\mathrm{Tr}F_{\mu\nu}F^{\mu\nu}$$ and gives rise to the Euclidean equations of motion $\mathcal{D}_\mu ...
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47 views

Irreducible representation for the massless particle with helicity 2 and the Weyl tensor

As it can be shown, the equations for the irrep with zero mass and helicity 2, -2 respectively can be given in a form $$ \tag 1 \partial^{\dot {b}a}C_{abcd} = 0, \quad ...
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1answer
47 views

How Chern-Simons gauge field transform fermion to scalar?

In A.Zee's "QFT in a nutshell"book Page 324, after he wrote down the general Lagrangian, he said "in previous chapter, we learned that by introducing a Chern-Simons gauge field we can transform $\psi$ ...
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What's the difference between correlation functions and S-matrix, and between in-in formalism (or “closed time path formalism”) and in-out formalism?

I was reading the "in-in" formalism (or "closed time path formalism" used in condensed matter physics) in cosmology created by Schwinger in 1961, and there is a saying: "they care about correlation ...
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1answer
55 views

Weak interaction violate charge conjugate

How can we show that the weak interaction violates the charge conjugation symmetry?
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71 views

Chiral Anomaly in Massless QED

Classical massless QED has axial current conservation. When quantizing the theory, we expect that suddenly $\partial_\mu \hat{j}^{\mu5}\neq0$ (as an operator equality). I have two questions regarding ...
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Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
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44 views

Size of an elementary particle [duplicate]

Do we have a well defined mathematical expression denoting the size of a fundamental particle with no internal structure (electron for example) ? If we do, how does it fit in with the uncertainty ...
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380 views

How many subatomic particles can absorb/emit photons?

Is the electron the only subatomic particle that can absorb and emit a photon?
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1answer
96 views

Regarding Non-renormalizatibility of GR

I've been doing some reading trying to get to a better understanding of some renormalization issues with the Einstein-Hilbert action. But, something odd came into mind that I'm hoping some users may ...
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70 views

Antiparticles as “holes” of the quantum fields? [duplicate]

If particles are simply regions of space where certain quantum fields have non-zero divergence, are anti-particles simply the corresponding regions of opposite divergence? This seems like the ...
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53 views

Time reversal operator symmetry of dirac lagrangian

I want to prove time reversal symmetry of Dirac Lagrangian, I have some problems with calculations. I start with \begin{eqnarray} T\psi T = U \psi \end{eqnarray} \begin{eqnarray} T\bar{\psi } T = ...
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3k views

Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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Interactions with high helicities particles

As it can be shown, there are no interacting helicity-3 (and higher) particles (i.e., massless spin-3 or higher particles) in soft limit (small momentums of emitting particles of given helicity). Сan ...
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202 views

How do we measure meson decay constants?

I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay ...
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71 views

Why do people say “Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon).”?

Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st ...
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1k views

Schrodinger equation from Klein-Gordon?

One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrodinger's equation from Klein-Gordon's one. Assuming a ...
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8answers
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Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
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62 views

target category of extended field theory

For a topological field theory to be a true “extension” of an Atiyah-Segal theory, the top two levels of its target (ie its $(n-1)^{\text{st}}$ loop space) must look like $\text{Vect}$. What other ...
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3answers
642 views

Creation of particle anti-particle pairs

I was reading some QFT notes and there is one point that I don't understand, they are justifying why we need QFT saying that the number of particles is not preserved once we consider special ...
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Naive questions on the concept of effective Lagrangian and equations of motion?

Let us consider a LC circuit containing an electric dipole moment, the quantum system (electric field $E$ coupled with a dipole moment) can be described by the path integral $$Z=\int DEDxe^{i\int ...
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“Dictionnary” between QFTs in D and D-1 dimensions?

Considering Einstein equations, suppose, for instance, that the RHS, the stress-energy tensor, is uniquely due to the electromagnetic field. Now, if we imagine a quantized version of these Einstein ...
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Quantum symmetries that are not classical symmetries

An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ...
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1answer
299 views

What does it mean to renormalize an effective field theory?

This is in reference to slide 19 of this talk "As always in Effective Field Theory, the theory becomes predictive when there are more observables than parameters" Can one explain what this exactly ...