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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23 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:
$$
H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
3
votes
1answer
40 views
Proof of S-duality between Type IIB, IIB and Type HO, I string theories
About every source on string theory I've read which do mention S-duality state that:
$$\begin{array}{l}
\operatorname S:\operatorname{IIB} \leftrightarrow \operatorname{IIB}\\
\operatorname ...
3
votes
1answer
95 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 ...
4
votes
1answer
50 views
Differential equation (Greens function) satisfied by the kernel using path integrals
How do I show that the kernel $K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$, satisfies the differential equation
$$-\frac{\hbar}{i}\frac{\partial K(2,1)}{\partial ...
3
votes
1answer
53 views
Quantum Field Theory and Hilbert space dimensionality
Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis.
How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
3
votes
2answers
53 views
Can one define a “particle” as space-localized object in quantum field theory?
In Peskin and Schroeder, while discussing creation and annihilation operators for a Klein-Gordon field (p.22), the authors say, as we all know the creation operator $a_p^{\dagger}$ acts on vacuum to ...
4
votes
2answers
55 views
How to directly calculate the infinitesimal generator of SU(2)
We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial ...
1
vote
1answer
48 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
$$\delta\omega_{\rho\sigma}(g^{\sigma\mu}M^{\rho\nu} - g^{\rho\nu}M^{\mu\sigma})
...
2
votes
0answers
52 views
Categorizing solutions to Hierarchy problem
We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
7
votes
1answer
86 views
What is the reason that relativistic corrections for hydrogen atom work?
Here I cite part from Sidney Coleman's lectures on Quantum Field Theory:
It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
0
votes
0answers
44 views
Gradient involved commutator in $\phi^4$ theory
In a phi fourth theory, the Hamiltonian density is:
$$\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$$
Now I impose the usual equal time ...
5
votes
2answers
65 views
Calculating the the kernel using path integrals for quadratic lagrangians
I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
3
votes
2answers
89 views
Imaginary time in QFT
I'm reading chapter 4 of Introduction to Quantum Field Theory by Peskin & Schroeder. In the $\phi^4$ theory, the authors state that the ground state of the interaction theory $|\Omega\rangle$ can ...
0
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0answers
31 views
Scalar-fermion bound state
Is it possible to have a bound state between a scalar and a fermion? For example, a squark--anti-squark bound state, provided that the decay width is sufficiently small compared to the binding energy?
...
0
votes
1answer
71 views
Derivation of Dirac equation using the Lagrangian density for Dirac field
How can I find Dirac equation using the Lagrangian density for Dirac field?
4
votes
1answer
64 views
T-Duality between Type HE String theory and Type HO string theory
My question is regarding T-Duality between the 2 Type H string theories.
I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so
...
1
vote
1answer
30 views
what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
3
votes
1answer
62 views
Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?
Suppose we have an integral
$$\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
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 ...
4
votes
1answer
98 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
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 ...
3
votes
0answers
63 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
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
$$\beta(m^2) ...
2
votes
0answers
93 views
Quantum field theory alternatives
Quantum field theory arises from the requirement that the S-matrix is lorentz scalar and obeys the cluster decomposition principle.
I want to know if there are other ways to build invariant ...
0
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0answers
37 views
Question regarding operators and cylindrical coordinates
I have the following problem in my hand:
I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$
to this expression:
...
2
votes
0answers
27 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
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 ...
5
votes
0answers
74 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 ...
2
votes
1answer
69 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
159 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
vote
1answer
63 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
61 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
votes
0answers
50 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
37 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 ...
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votes
0answers
22 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
111 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?
3
votes
1answer
66 views
Spectra of the Type II String theories
The spectrum of the Type II string theory (both IIA and IIB) is given by:
\begin{array}{*{20}{c}}
\hline
& {{\text{Sector}}}& & {{\text{Spectrum}}}& & {{\text{Massless Fields}}} ...
3
votes
1answer
61 views
Four-gauge-boson vertex in non-Abelian gauge theories
In Peskin & Schroeder's book page 524, the following diagram is calculated for the gauge boson self-energy in order $g^2$:
In dimensional regularization, its contribution is given by
...
-1
votes
0answers
64 views
Interconnections between two equations
I have been trying to reconstruct mathematical formulations of the article
I have understand till article equation(25). When I am trying to get the equation(2) from (1) [article equations 26 from ...
1
vote
2answers
114 views
$\langle B|A \rangle$ expressed in terms of the Partition Function
Say you have an electron departing from point A and reaching poing B after a time t.
According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
4
votes
1answer
78 views
Can Divergences in Nonrenormalizable Theories Always Be Absorbed by (An Infinite Number of) Counterterms?
For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian:
$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$.
In 8 ...
3
votes
1answer
85 views
Field operator eigenvalues
For an harmonic oscillator we can write the Hamiltonian eigenvalues in the basis of the amplitude eigenvalues : for example the ground state is a gaussian : $⟨x|0⟩=a.e^{-b.x^{2}}$.
I was wondering ...
2
votes
0answers
85 views
quantization of Dirac field
The general solution to the Dirac equation is a sum of plane wave solutions
$$
\psi(x) \sim \int d^3k \sum_r b_r(k) u_r(k)e^{-ikx} + d^\dagger_r(k) v_r(k)e^{+ikx}
$$
The basis spinors $u_r$ and $v_r$ ...
2
votes
1answer
56 views
Is conservation of statistics logically independent of spin?
If the number of fermions is $n$, we expect the quantity $(-1)^n$ to be conserved, i.e., $n$ never changes between even and odd. This is known as conservation of statistics. In the normal context of ...
4
votes
0answers
58 views
I am trying to calculate the branching ration of higgs goes to 2 photons using the standard model [closed]
I need to use the three lowest order feynman diagrams to first calculate the squared matrix element to put into fermis golden rule formula and then from there get the branching ratio of higgs decays ...
1
vote
1answer
68 views
Renormalizibility by power counting
When testing a theory for its renormalizability, in practice one always calculates the mass dimension of the coupling constants $g_i$. If $[g_i]>0$ for any $i$ the theory is not renormalizable. I ...
3
votes
2answers
134 views
Renormalization condition: why must be the residue of the propagator be 1
In on-shell scheme, one of the renormalization conditions is that the propagator, say, a scalar theory
$$\frac{1}{p^2+m^2-\Sigma(p^2)-i\epsilon}$$
must have a unit residue at the pole of ...
4
votes
1answer
147 views
Yang-Mills instanton
How can instanton solution to Yang-Mills theory with gauge group $SU(3)$ or $SU(N)$ be obtained? For $SU(2)$ it is explained in textbooks but what about more general color gauge groups?
EDIT: How ...
1
vote
0answers
23 views
Is there anything connecting concrete connecting evaluating of non perturbative field theory correlation functions and solitons/instantons?
I keep reading about instantons and solitons being non-perturbative effects. Well it does make sense that mass of solitons goes inversly as coupling constants so their effects would not be seen in ...
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votes
0answers
54 views
A book recommendation for Quantum Field theory [duplicate]
I'm a novice in Quantum Field Theory and searching for a understandable good book for quantum field theory. I know some best book for Quantum field theory but I want to start these books after ...
