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 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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1answer
107 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
63 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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3answers
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
108 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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37 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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31 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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317 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
73 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
116 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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1answer
258 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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49 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
48 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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0answers
38 views

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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3answers
1k views

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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2answers
390 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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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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0answers
59 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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31 views

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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2answers
208 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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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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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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64 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
647 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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2answers
167 views

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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45 views

“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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135 views

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 ...
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1answer
220 views

Chiral perturbation theory: what is the Quark Condensate? why expand in $U$ rather than Goldstone fields?

I'm studying Chiral Perturbation Theory ($\chi PT$) from Scherer's Introduction to Chiral Perturbation Theory. What I am currently having some trouble understanding are two things: The quark ...
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0answers
79 views

How to describe hadron-hadron strong interactions from QCD?

I'm trying to set up the problem of deriving the thermodynamics of hadronic matter. I know how to proceed in the case of an effective description such as mean field (Walecka/linear sigma model) but ...
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2answers
210 views

Nuclear physics from perturbative QFT

Is there a renormalizable QFT that can produce a reasonably accurate description of nuclear physics in perturbation theory? Obviously the Standard Model cannot since QCD is strongly coupled at nuclear ...
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1answer
80 views

Why is baryon or lepton violation in standard model is a non-perturbative effect?

The baryon number B or lepton number L violation in the standard model arise from triangle anomaly. Right? Triangle diagrams are perturbative diagrams. Then why the B or L violation in Standard model ...
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3answers
703 views

Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory

I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local ...
8
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1answer
93 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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1answer
84 views

Does spin-0 or spin-2 describe massive or massless particles?

spin-0 is massive or massless? How does we separate the massive and massless degrees of freedom for spin-2? What is the partially massive?
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2answers
112 views

CPT invariance of Dirac equation

We know that Dirac equation is \begin{equation} ( i \partial _\mu \gamma ^\mu - m ) \psi ~=~0. \end{equation} How can we show that Dirac equation is invariant under CPT transformation?
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3answers
113 views

Complex Dirac field in antiparticle description

I understand that the Dirac equation has negative and positive sets of solutions and this contributes to its quantization by a superposition of two Fourier modes represented as creation and ...
6
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3answers
668 views

Aharonov-Bohm Effect and Flux Quantization in superconductors

Why is the magnetic flux not quantized in a standard Aharonov-Bohm (infinite) solenoid setup, whereas in a superconductor setting, flux is quantized?
3
votes
1answer
108 views

Local number operators in quantum field theory

Redhead claims in his paper "More ado about nothing" (http://link.springer.com/article/10.1007%2FBF02054660) that number operators associated with different space points (at fixed time) fail to ...
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0answers
45 views

Can the rate of virtual pair production from vacuum be computed?

Consider for instance the QED Lagrangian. Is it possible to compute the rate of virtual electron-positron creation from the vacuum?
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1answer
61 views

Does this photograph portray double muon impact with nanogold atoms?

1PHOTO 1: Macro-photograph of an NIH/FDA TEM of a nanogold dark stained biological sample projected onto Silver Halide (AgX) photographic gel paper. On June 10 I questioned if PHOTO 1 ...
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1answer
240 views

What is the source of Quantum fields [duplicate]

In the beginning of "Quantum Field Theory for the Gifted Amateur," there is the statement: Every particle and every wave in the Universe is simply an excitation of a quantum field that is defined ...
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3answers
824 views

Dirac spinor and Weyl spinor

How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor? EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed ...
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1answer
62 views

Importance of the Higgs field being formulated in quantum gauge theory

As far as my knowledge goes, Higgs field is only currently formulated in term of classical gauge theory. What is the importance of Higgs field being formulated in term of quantum gauge theory? In ...
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1answer
119 views

Is quantum field operator $\psi$ same as quantum field $\psi$?

So in QFT, quantum field operator $\psi$ is there. $\psi$ seems to take the role of wavefunction in QM, which now acts upon vacuum state. Then, in lagrangian of various quantum field theories, $\psi$ ...