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 ...
2
votes
0answers
25 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
29 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 ...
2
votes
0answers
23 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 ...
0
votes
1answer
39 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
votes
0answers
27 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
67 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
54 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
29 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
61 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: $$\mathrm{d}^4k = \mathrm{d}k^0\ ...
1
vote
0answers
42 views
de Sitter versus Minkowski QFT and cosmological constant
WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the ...
4
votes
1answer
96 views
Mass gap for photons
I am puzzled by the answers to the question:
What is a mass gap?
There, Ron Maimon's answer gives a clear-cut definition, which I suppose applies to any quantum field theory with Hamiltonian $H$, ...
2
votes
0answers
33 views
Intuition behind the notion of reflection positivity
I came across Yuji's question. I'm finding it difficult to parse the meaning behind what's said on Wikipedia. Could someone give an explanation of the concept involved? I would also appreciate ...
3
votes
0answers
59 views
Bosonic-Fermionic interactions in supersymmetry
There are a lot of supersymmetric theories, and, sometimes,in the Lagrangian, there are interacting terms between bosonic and fermionic degrees of freedom, and sometimes not. Why ?
For instance, for ...
4
votes
1answer
71 views
Beta-function non-zero at classical level?
In Jaume Gomis's lecture 5 on CFT at Perimeter Institute, he says (at 27:40 minute mark) that the beta function, classically, of the $m^2$ parameter in massive $\lambda \phi^4$ theory is
$$\beta(m^2) ...
2
votes
0answers
91 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
votes
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
72 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
68 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
157 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
60 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
49 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 ...
0
votes
0answers
20 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
65 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
59 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
74 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
55 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
66 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
129 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
145 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 ...
0
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 ...
3
votes
2answers
205 views
Irreducible Representations Of Lorentz Group
In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64.
He define states as ...
2
votes
1answer
75 views
Plane waves in QFT
Suppose we work in the metric $(-1,+1)$.
How do we describe an incoming particle with a plane wave; $\exp(-\mathrm ikx)$ or $\exp(+\mathrm ikx)$?
What's the difference?
Does it change if we work in ...
2
votes
0answers
26 views
``integrated vertex operators" in 1-loop open/closed bosonic string amplitude
This question is in reference to the first ~15 minutes of this String Theory lecture by Prof.Shiraz Minwalla,
http://theory.tifr.res.in/Videos/strings28_24sep08.mp4
Can one give a reference ...
3
votes
0answers
46 views
A particlar normal ordering problem
Say we have an expression of the form:
$$
\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,
$$
where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating ...
5
votes
2answers
108 views
What is the exact relationship between on-shell amplitudes and off-shell correlators in AdS/CFT?
In this answer to a question, it is mentioned that in the AdS/CFT correspondence, on-shell amplitudes on the AdS side are related to off-shell correlators on the CFT side.
Can somebody explain this ...
3
votes
1answer
90 views
What is the math showing that the time reversed version of an electron is a positron? (+general time reversal question)
As in Wheeler's One Electron Universe idea, how do you show that electrons and positrons are time-reversed versions of each other? Do you just apply time reversal to an electron and out pops a ...
0
votes
1answer
79 views
QED photon propagator to one-loop order gets different answers
I'm a self-studying 14-year-old who has a passion for particle physics. I'm currently trying to calculate the QED photon propagator to one loop. However, in all the places I've looked, even with the ...
4
votes
2answers
231 views
Definition of Casimir operator and its properties
I'm not sure which is the exact definition of a Casimir operator.
In some texts it is defined as the product of generators of the form:
$$X^2=\sum X_iX^i$$
But in other parts it is defined as an ...
1
vote
1answer
52 views
Casimir force using Pauli-Villars regularization
In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that:
$$
\sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
