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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Physical Interpretation of Lorentz-transformed Single Particle states being linear
As in this question, let $\psi_{p,\sigma}$ be a single-particle 4-momentum eigenstate, with $\sigma$ being a discrete label of other degrees of freedom.
Weinberg discusses the effect of a homogenous ...
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31 views
How (why!?) does one introduce an UV cut-off in dimensional regularization?
This question is in reference to the confusing equation 3.7 (page 14) of this paper.
One sees the 1-loop answers in their theory as given in their A.7 and A.8 on page 20. Each of the terms is a ...
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32 views
Why do single particle states furnish a rep. of the inhomogeneous Lorentz group?
Following up on this question: Weinberg says
In general, it may be possible by using suitable linear combinations of the $\psi_{p,\sigma}$ to choose the $\sigma$ labels in such a way that ...
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55 views
What is the reason why anyons escape spin-statistic theorem?
I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem.
I've read somewhere (the wikipedia page is ...
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36 views
Quantum master equation in the Batalin-Vilkovisky formalism
I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have
$$
\begin{split}
\delta ...
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19 views
Why are non-momentum DoFs of single-particle states discretely labeled?
Following the treatment of Weinberg, chapter 2, we consider $\psi_{p,\sigma}$ as single-particle eigenstates of the 4-momentum. Weinberg says that $\sigma$ labels all other degrees of freedom and we ...
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90 views
Unitary quantum field theory
What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
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56 views
What goes wrong when one tries to quantize a scalar field with Fermi statistics?
At the end of section 9 on page 49 of Dirac's 1966 "Lectures on Quantum Field Theory" he says that if we quantize a real scalar field according to Fermi statistics, the quantum Hamiltonian is no ...
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78 views
Complex masses for Dirac and Weyl spinors
I'm trying understand how to rotate Dirac fields to absorb complex phases in masses. I have a few related questions:
With Weyl spinors, I understand, $$ \mathcal{L} = \text{kinetic} +
...
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1answer
41 views
Anti-particle problem for Dirac sea
According to the Dirac hole theory we know that Dirac sea is completely filled with negative energy, called vacuum. We will need $2mc^2$ or greater to get electron and a positron by incident photon.
...
7
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1answer
188 views
Introductory examples of AdS/CFT duality
I would like to know, what are the simplest/starting/basic examples that are typically used to introduce students to how AdS/CFT really works? (not the MAGOO paper, as I am not sure it has concrete ...
5
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1answer
224 views
Spin-Statistics Theorem (SST)
Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
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1answer
69 views
Alternative methods to derive the static potential in the NR limit of QED
In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level ...
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38 views
Alternative interpretation of Off-shell internal QFT propagators?
In Quantum Field Theory in a (1, D - 1) space-time, to calculate transition amplitudes, we are using Feynman diagrams, where internal lines (internal propagators) corresponds to momenta which are said ...
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1answer
90 views
Path Integral Quantization
I was reading through my notes on the path integral quantization of bosonic string theory when a general question about path integral quantization arised to me.
The widely used intuitive explanation ...
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32 views
Gauge fields and strings: Loop equations
I am trying to derive Eq. (7.25) (p. 117) of Polyakov's book:
$$ \delta \Psi (C) = \int_{0}^{2\pi} {\rm P} \left(F_{\mu\nu}(x(s)) \exp \oint_C A_\mu dx^\mu \right)\dot{x}_\nu \delta x_\mu(x) \, {\rm ...
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1answer
204 views
Energy spectrum of a Dirac electron
How do you explain easily "The spectrum of an electron in a repulsive potential " and hence "bound state of charge conjugation" in Dirac hole theory ?
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1answer
100 views
Quantum field theory quote
I have read this in scientific American:
According to quantum field theory, all particles spend a little time as combinations of all other particles"
Is this right? How long? And how can they be a ...
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1answer
54 views
Proof of S-duality between Type IIB, IIB and Type HO, I string theories
About every source on string theory I've read which do mention S-duality state that:
$$\begin{array}{l}
\operatorname S:\operatorname{IIB} \leftrightarrow \operatorname{IIB}\\
\operatorname ...
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29 views
Relevant operators in two dimensional O(n) models
The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written:
$$
H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
3
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2answers
62 views
Can one define a “particle” as space-localized object in quantum field theory?
In Peskin and Schroeder, while discussing creation and annihilation operators for a Klein-Gordon field (p.22), the authors say, as we all know the creation operator $a_p^{\dagger}$ acts on vacuum to ...
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2answers
66 views
Calculating the the kernel using path integrals for quadratic lagrangians
I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
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2answers
91 views
Imaginary time in QFT
I'm reading chapter 4 of Introduction to Quantum Field Theory by Peskin & Schroeder. In the $\phi^4$ theory, the authors state that the ground state of the interaction theory $|\Omega\rangle$ can ...
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1answer
60 views
Quantum Field Theory and Hilbert space dimensionality
Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis.
How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
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2answers
60 views
How to directly calculate the infinitesimal generator of SU(2)
We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial ...
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92 views
What is the reason that relativistic corrections for hydrogen atom work?
Here I cite part from Sidney Coleman's lectures on Quantum Field Theory:
It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
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1answer
50 views
Lie algebra of lorentz group
I'm stuck in following calcualtion from sredniki's QFT book.(Its actually in the solution manual)
How can i get from
$$\delta\omega_{\rho\sigma}(g^{\sigma\mu}M^{\rho\nu} - g^{\rho\nu}M^{\mu\sigma})
...
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1answer
258 views
What is the meaning of the concepts of “operator mixing” (and anomalous dimensions) [closed]
I am looking for an explanation about the idea of "operator mixing" and its associated concept about when anomalous dimension has to be thought of as a matrix.
For example this idea is slightly ...
2
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0answers
57 views
Categorizing solutions to Hierarchy problem
We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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45 views
Gradient involved commutator in $\phi^4$ theory
In a phi fourth theory, the Hamiltonian density is:
$$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$
Now I impose the usual equal time ...
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33 views
Scalar-fermion bound state
Is it possible to have a bound state between a scalar and a fermion? For example, a squark--anti-squark bound state, provided that the decay width is sufficiently small compared to the binding energy?
...
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1answer
75 views
Derivation of Dirac equation using the Lagrangian density for Dirac field
How can I find Dirac equation using the Lagrangian density for Dirac field?
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1answer
81 views
How to find the Higgs coupling with a mixing matrix?
It is known that the couplings to the Higgs are proportional to the mass for fermions;
$$g_{hff}=\frac{M_f}{v}$$
where $v$ is the VEV of the Higgs field. I'm trying to figure out why this is true ...
5
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1answer
152 views
How is the 'cluster decomposition principle' implemented in holographic theories?
Since holographic theories are non-local by definition, how is this principle implemented?
Naively, it seems to me it is not, at least, in some sense.
I would appreciate an explanation as simple ...
6
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1answer
90 views
Some more questions about the BCFW reduction
This question is a continuation of this previous question of mine and I am continuing with the same notation.
One claims that one can actually split this $n$-gluon amplitude such that there is just ...
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2answers
408 views
Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT
Below are the scan copies of some pages of Weinberg which are relevant to my doubts. My doubts basically concern the determination of normalization constant defined in (2.5.5).
Isn't (2.5.12) true ...
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1answer
86 views
Hawking Radiation as Tunneling
Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
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1answer
69 views
T-Duality between Type HE String theory and Type HO string theory
My question is regarding T-Duality between the 2 Type H string theories.
I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so
...
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1answer
31 views
what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
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48 views
de Sitter versus Minkowski QFT and cosmological constant
WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the ...
3
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1answer
63 views
Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?
Suppose we have an integral
$$\int \mathrm{d}^4k \,\ f(k)$$
we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$.
Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ ...
1
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1answer
159 views
Two photons transition
if an atom in its ground state is coupled to an electromagnetic field it can absorb a photon if the EM field contains one with the right frequency. These transitions depends on $⟨f|H_i|i⟩$ (from ...
3
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2answers
311 views
Recipe for computing vertex factors in Feynman diagrams
I am currently studying quantum field theory from Srednicki. In class we have covered till chapter 14 and then skipped to IR divergences. So my knowledge of quantum field theory is limited to those ...
4
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1answer
102 views
Mass gap for photons
I am puzzled by the answers to the question:
What is a mass gap?
There, Ron Maimon's answer gives a clear-cut definition, which I suppose applies to any quantum field theory with Hamiltonian $H$, ...
5
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2answers
224 views
Quantum field theories with asymptotic freedom
QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it:
(1) Are there other theories with ...
2
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34 views
Intuition behind the notion of reflection positivity
I came across Yuji's question. I'm finding it difficult to parse the meaning behind what's said on Wikipedia. Could someone give an explanation of the concept involved? I would also appreciate ...
4
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1answer
72 views
Beta-function non-zero at classical level?
In Jaume Gomis's lecture 5 on CFT at Perimeter Institute, he says (at 27:40 minute mark) that the beta function, classically, of the $m^2$ parameter in massive $\lambda \phi^4$ theory is
$$\beta(m^2) ...
4
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3answers
351 views
Special conformal transformations and locality
In the conformal symmetry, used in some QFT theories, the infinitesimal generators, applying to space-time, are all linear (translations, rotations, boosts, dilatation), except the special conformal ...
3
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65 views
Bosonic-Fermionic interactions in supersymmetry
There are a lot of supersymmetric theories, and, sometimes,in the Lagrangian, there are interacting terms between bosonic and fermionic degrees of freedom, and sometimes not. Why ?
For instance, for ...
2
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2answers
76 views
Question on the Hagedorn tower in Type I string theory
In a previous question (Mass spectrum of Type I string theory), I had asked about the mass spectrum of Type I string theory. I got a response saying that it is a Hagedorn tower. However, my source ...
