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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1answer
62 views
Invariance, covariance and symmetry
Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
4
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1answer
144 views
One-loop $\phi^4$ theory in $d = 3$
I'm trying to calculate the 1 loop correction to the propagator in massless $\phi^4$ theory, in $d = 3$, just for fun. The diagram just looks like a straight line with a circle touching tangently to ...
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57 views
A fundamental equation for solitary wave and dimension analysis
According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
What I want to do is ...
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66 views
How would I apply Wick's theorem to expand the time-ordered product of three quantum fields? [closed]
I think I understand how to use Wick's theorem to expand the time-ordered product of quantum fields, but I'd like to confirm that. Could you apply Wick's theorem to:
...
4
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1answer
115 views
What does it mean to integrate out fields from a theory?
I've done a fair bit of reading on this subject and I'm still confused about the basic principle of integrating out fields in QFT. When we have a function of 2 fields a and b, f(a,b), and we integrate ...
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4answers
237 views
Physical Interpretation of the Integrand of the Feynman Path Integral
In quantum mechanics, we think of the Feynman Path Integral
$\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action)
as a probability amplitude (propagator) for getting from $x_1$ to ...
3
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1answer
118 views
Photon as the carrier of the electromagnetic force
My physics background goes as "far" as reading popsci books on QM, Particle Physics, and Cosmology so pardon my ignorance in the below questions.
I've read that the photon is the particle (quanta in ...
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52 views
What is the fundamental difference between ghost and auxiliary fields?
I am somehow confused by the notion of auxiliary fields, such as for example the fields F and D which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
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1answer
130 views
Solving the soliton equation without energy
In this passage from Srednicki's Quantum Field Theory (page 576)
The solution of interest is time independent, so we can set $\dot\varphi = 0$. We can also rewrite the remaining terms in $E$ as
...
2
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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 ...
3
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1answer
79 views
Transformation law for fermionic measure in functional integral
I am reading the paper "Bosonization in a Two-Dimensional Riemann-Cartan Geometry", Il Nuovo Cimento B Series 11
11 Marzo 1987, Volume 98, Issue 1, pp 25-36, ...
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1answer
55 views
What is paramagnetic current-current correlation?
I know what paramagnetism is. But first I want to know about the paramagnetic current and then the above-mentioned correlation?
Actually, I am working on a paper on superconductivity where I have ...
2
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0answers
60 views
About the seesaw mechanism
I was reading about the seesaw mechanism in my Lecture notes and got a technical question. See for example
http://www.lhep.unibe.ch/img/lectureslides/9_2007-11-30_SeeSawMechanism.pdf
page 13.
There ...
8
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1answer
145 views
Correlated three-particle Green Function
I know the relationship between normal and correlated two-particle Green Functions for fermions:
$$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$
Also known as irreducible ...
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1answer
84 views
Comparing interaction potential in standard $ϕ^4 $theory
I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory.
I have been studying about solitions so I had ...
3
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0answers
56 views
How does one write eigenstates of field operators in terms of particle states in scalar field theory?
I am reading the first paper in Schwinger's QED anthology, where he discusses his action principle. In this, he writes down states that are simultaneous eigenkets of the field operators at all points ...
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1answer
134 views
Is the Hilbert space of $\phi^4$ theory known?
Consider free, real scalar field theory in $d=1+3$ dimensions: $H = \frac{1}{2} \partial_\mu \phi \partial^\mu \phi + \frac{1}{2} m^2 \phi^2$. The Hilbert space of this theory is known; it is just ...
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2answers
98 views
Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$
Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$?
I don't know if it's possible to define
...
4
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1answer
110 views
Lorentz invariance of positive energy solutions to the Klein-Gordon equation
I am reading Arthur Jaffe's Introduction to Quantum Field Theory. (You can find it here.) There is an interesting question posed in Exercise 2.5.1:
Solutions to the Klein-Gordon equation propagate ...
6
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1answer
101 views
Why is $R^2$ gravity not unitary?
I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?
My naive ...
6
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1answer
68 views
Are observables associated to spacetime regions?
In the Haag-Kastler approach to axiomatic quantum field theory, it is assumed that observables are 'associated' to spacetime regions. What this actually means is that there is a map $\mathcal{A}: R ...
4
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1answer
201 views
Second quantization
In second quantization we use Hamiltonian in form:
$$H=\int d^3x [ \psi^{\dagger}(x) h \psi(x)],$$ where $h$ is Hamiltonian density. The field operators have following form:
$$\psi = \sum\limits _{i} ...
5
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0answers
119 views
How does Haldane conjecture follow from the topological $\Theta$ term
The one dimensional SU(2) Heisenberg quantum spin chain is known to be described by the 1+1d O(3) nonlinear $\sigma$ model with a $\Theta$ term, following the action
...
4
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55 views
No mixing in light cone perturbation theory
In hep-ph/0609090, Triumvirate of Running Couplings in Small-x Evolution, Kovchegov et. al. calculated the running coupling correction to the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and ...
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1answer
66 views
Coupling constant problem
In the scalar $φ^4$ theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}(\partial_t\phi)^2 -\frac{1}{2}\delta^{ij}\partial_i\phi\partial_j\phi - \frac{1}{2}m^2\phi^2-\frac{g}{4!}\phi^4. $$
I want ...
2
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1answer
94 views
Symmetries in Wilsonian RG (2)
This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG
In the liked paper why do the equalities in equation ...
6
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0answers
79 views
Dimensional regularization and IR divergences and scale invariance
I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant.
Does dimensional regularization see "all" kinds of divergences?
I mean - what ...
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1answer
139 views
$\phi ^4$ theory explaining [closed]
In $φ^4$ theory we often write the Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
If I want to write from the ...
2
votes
1answer
52 views
Given expectation values for E and B, can you find an associated state?
When we quantize the electromagnetic field, we develop the concept of the field operator $A(\vec{r},t)$ and the simultaneous eigenstates of momentum and the free field Hamiltonian (i.e., each ...
2
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0answers
58 views
Light Front Dynamics and Infinite Momentum Frame
What is the the relationship between Light Front Dynamics (One of the forms of dynamics pioneered by Dirac), and the infinite momentum frame?
In the literature, it is claimed that the two are very ...
2
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3answers
60 views
Valid theory in all dimensions for solitary waves
I'm studying soliton (solitary waves). They are many theory which explain the phenomenon, like sine-Gordon model. But sine-Gordon model has limitations when it applies to 4 dimension because it is ...
3
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0answers
59 views
Contact Term and Schwinger Term
In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'.
When deriving the quantum equations of motion for time-ordered ...
4
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1answer
40 views
Higgs VEV in terms of measurements on an ensemble?
Let $A$ be a Hermitian operator corresponding to some observable. If we prepare $N$ identical systems in the state $\psi$ and measure this observable in each system, the average of the measurements ...
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92 views
Mirror Matter Hypothesis?
What is the current state of the hypothesis of mirror matter today?
Are there any experimental data or theoretical arguments that exclude it by now, or is it still considered viable among physicists?
...
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0answers
70 views
Noether currents for the BRST tranformation of Yang-Mills fields
The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
...
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1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
3
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0answers
100 views
Quantum Electrodynamics
I was wondering if anyone could give a simple explanation of how light interacts with matter. From what I have read in QED, electrons will repel each other because of their ability to emit and ...
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0answers
40 views
Lagrangians for non-local equations of motion
Say I have a multicomponent field $X_a(x,t)$ such that I know it Fourier modes satisfy the following equation of motion,
$(\delta_{ab} \partial_t + \Omega_{ab}(t))X_b(k,t) = e^t \int \frac{d^3p ...
2
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0answers
39 views
CP-symmetry and Ward identities and finite temperature
I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature.
Wikipedia states about Ward-identities:
The ...
3
votes
0answers
96 views
exercise books for Feynman diagrams [duplicate]
I know QFT at graduate level but I'll like to master the skill of working with Feynman diagrams. I'm looking for a book of solved exercises on this topic.
Specifically, I'm looking for the kind of ...
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1answer
86 views
Density operator in second quantization
I would want to understand why the density operator in second quantization takes the form:
$$\rho_\sigma(\mathbf{r})=\Psi_\sigma^\dagger(\mathbf{r})\Psi_\sigma(\mathbf{r})?$$
Is this a definition or ...
1
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0answers
84 views
QFT: differential cross section from center of mass to lab frame
I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed $|M|^2$ and the differential cross section in the ...
2
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0answers
74 views
Vacuum to vacuum transition amplitude
I have two questions about Vacuum to vacuum transition amplitude.
Can any particle stay in $|0\rangle$?
I was studying this topic from Srednicki's QFT book. He writes in eq.$(6.22)$
$$\langle0|0 ...
1
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1answer
87 views
Quantum Mechanics of Lenz's Law?
I've searched the internet and two famous QM books (Sakurai and Messiah) for Lenz's Law, but haven't found anything. So my question is what the quantum mechanical explanation to Lenz's law is? Can ...
3
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0answers
102 views
Meaning of spin
I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things:
Mechanical spin (apparently a ...
2
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2answers
85 views
Heisenberg evolution equation for $\hat{\phi}$
Consider quantum Hamiltonian of free massive scalar particle:
$$\hat{H} = \int d^3x \left[\frac{1}{2} \hat{\pi}^2 (t, \vec{x}) + \frac{1}{2} \partial_i \hat{\phi}(t, \vec{x}) \partial_i \hat{\phi}(t, ...
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1answer
103 views
A question about defining a classical CFT
This is kind of related to this,
Defining a CFT using beta-functions
So what would be the right definition of a CFT even classically?
Is it true that classically one will call a theory scale ...
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5answers
189 views
Derivation of $ E=h\nu$
Is it possible to derive the relation $ E=h\nu$ from Schrodinger equation or the basic principles of quantum mechanics or is it something which is considered to be an axiom with no explanation?
4
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1answer
246 views
Why on-shell vs. off-shell matters?
The definitions between on- and off-shell are given in Wikipedia.
Why is it so important in QFT to distinguish these two notions ?
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0answers
71 views
How to charge a field?
In a previous post [ Noether theorem, gauge symmetry and conservation of charge ] we were discussing the different ways to demonstrate the current conservation: via the first Noether theorem applied ...
