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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128 views
What if EM or QCD was spontaneously broken?
Suppose that Standard Model Higgs mechanism broke electromagnetism, by e.g. veving the charged component of the doublet, so that the photon was massive with $m_\gamma\sim v$. Could such a Universe ...
2
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1answer
126 views
+50
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 ...
5
votes
1answer
86 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 ...
2
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1answer
68 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 ...
1
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1answer
62 views
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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1answer
45 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 ...
6
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53 views
What is energy in $z \neq 1 $ theories?
In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
5
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0answers
83 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 ...
1
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1answer
65 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.
...
9
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0answers
144 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 ...
8
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1answer
101 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 ...
2
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0answers
45 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 ...
2
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1answer
87 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} +
...
1
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2answers
136 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 ...
5
votes
1answer
71 views
Gauge fields and strings: Loop equations
I am trying to derive Eq. (7.25) (p. 117) of Polyakov's book:
$$ \delta \Psi (C) = \int_{0}^{2\pi} {\rm P} \left(F_{\mu\nu}(x(s)) \exp \oint_C A_\mu dx^\mu \right)\dot{x}_\nu \delta x_\mu(x) \, {\rm ...
2
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0answers
41 views
Relevant operators in two dimensional O(n) models
The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written:
$$
H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
4
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1answer
67 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:
$$\begin{array}{l}
\operatorname S:\operatorname{IIB} \leftrightarrow \operatorname{IIB}\\
\operatorname ...
3
votes
1answer
121 views
Quantum field theory quote
I have read this in scientific American:
According to quantum field theory, all particles spend a little time as combinations of all other particles"
Is this right? How long? And how can they be a ...
3
votes
1answer
71 views
Quantum Field Theory and Hilbert space dimensionality
Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis.
How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
3
votes
2answers
79 views
Can one define a “particle” as space-localized object in quantum field theory?
In Peskin and Schroeder, while discussing creation and annihilation operators for a Klein-Gordon field (p.22), the authors say, as we all know the creation operator $a_p^{\dagger}$ acts on vacuum to ...
4
votes
2answers
83 views
How to directly calculate the infinitesimal generator of SU(2)
We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial ...
1
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1answer
53 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
$$\delta\omega_{\rho\sigma}(g^{\sigma\mu}M^{\rho\nu} - g^{\rho\nu}M^{\mu\sigma})
...
3
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0answers
63 views
Categorizing solutions to Hierarchy problem
We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
7
votes
1answer
108 views
What is the reason that relativistic corrections for hydrogen atom work?
Here I cite part from Sidney Coleman's lectures on Quantum Field Theory:
It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
1
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0answers
56 views
Gradient involved commutator in $\phi^4$ theory
In a phi fourth theory, the Hamiltonian density is:
$$\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$$
Now I impose the usual equal time ...
5
votes
2answers
75 views
Calculating the the kernel using path integrals for quadratic lagrangians
I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
3
votes
2answers
111 views
Imaginary time in QFT
I'm reading chapter 4 of Introduction to Quantum Field Theory by Peskin & Schroeder. In the $\phi^4$ theory, the authors state that the ground state of the interaction theory $|\Omega\rangle$ can ...
1
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0answers
36 views
Scalar-fermion bound state
Is it possible to have a bound state between a scalar and a fermion? For example, a squark--anti-squark bound state, provided that the decay width is sufficiently small compared to the binding energy?
...
0
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1answer
88 views
Derivation of Dirac equation using the Lagrangian density for Dirac field
How can I find Dirac equation using the Lagrangian density for Dirac field?
5
votes
1answer
88 views
T-Duality between Type HE String theory and Type HO string theory
My question is regarding T-Duality between the 2 Type H string theories.
I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so
...
1
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1answer
53 views
what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
3
votes
1answer
71 views
Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?
Suppose we have an integral
$$\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\ ...
2
votes
0answers
54 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 ...
4
votes
1answer
112 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 $H$, ...
2
votes
0answers
37 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 ...
3
votes
0answers
71 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 ...
4
votes
1answer
81 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
$$\beta(m^2) ...
2
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0answers
102 views
Quantum field theory alternatives
Quantum field theory arises from the requirement that the S-matrix is lorentz scalar and obeys the cluster decomposition principle.
I want to know if there are other ways to build invariant ...
0
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0answers
39 views
Question regarding operators and cylindrical coordinates
I have the following problem in my hand:
I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$
to this expression:
...
2
votes
0answers
31 views
5D Ricci Curvature
As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper ( http://arxiv.org/pdf/1107.5563v2.pdf ). I was wondering if there is some ...
2
votes
2answers
88 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 ...
5
votes
0answers
94 views
Setting of renormalization scale in field theory calculations
In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
4
votes
1answer
89 views
Flavour diagonal SUSY breaking
Because there is a single Yukawa matrix for the SM leptons, the lepton mass and flavour states can be aligned, by diagonalization, even if the Yukawa matrix had off-diagonal elements.
SUSY breaking, ...
7
votes
3answers
203 views
Many photons, one quantum field?
If a photon can be described as an excitation in a quantum field, is this the same field for all photons, or does each photon exist in its own field?
1
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1answer
68 views
Why doesn't one-photon-irreducible function have any pole at $q^2=0$?
I'm reading the QFT textbook by Weinberg. In volume one chapter 10 page 451, at the lower part of the page he says,
Now, because $\Pi^*_{\mu\nu}(q)$ receives contributions only from ...
3
votes
1answer
76 views
For mesons, or baryons, do sea quarks contribute to the angular momentum of the bound state?
The total angular momentum of a bound state of quarks, such as a meson say, can be done by studying the spin and orbital angular momentum of the 2 valence quarks.
What about the sea quarks why they ...
2
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0answers
55 views
About deriving the multi-trace index in terms of the single-trace index
This question is in reference to this paper
Combining their equations 5.2, 5.3, 5.6 and 5.7 one seems to be looking at the integral/partition function,
$Z(x) = \prod_{n=1}^{n =\infty}\left [ \int ...
3
votes
1answer
42 views
Parametrization of $U(N)$ non-linear sigma model
The motivation of this question actually comes from this (really old) paper of Weinberg. He considers a theory of massless pions. They have a chiral $SU(2)_{L} \times SU(2)_{R}$ symmetry. The pions ...
0
votes
0answers
25 views
What's the real value of screening length?
I know that the screening length (R) is an effective distance over which the nucleus of an atom is active, since it is screened by the orbiting electrons.Various derivations for R have been proposed, ...
3
votes
2answers
121 views
How to prove that the generator of proper vertices is the Legendre transform of $W(j) = \log \frac{Z[j]}{Z[0]}$
I'm studying QFT from Le Bellac's book, but I can't understand very well his proof for the generator of proper vertices. Can someone give a more readable and/or understandable proof?
