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
147 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 ...
1
vote
1answer
81 views
Degree of divergence of a Feynman diagram
I am studying the degrees of divergence of Feynman diagrams. I feel that I miss something but I don't really understand what. Please apologize if this question is silly. Anyway.
As an introduction to ...
3
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0answers
49 views
Questions about classical and quantum scale invariance
This is kind of a continuation of this and this previous questions.
Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an ...
4
votes
3answers
108 views
Associating a Unitary operator to proper Lorentz transformations?
If one reads eg page 32 of Srednicki where he says:
In quantum theory, symmetries are represented by unitary (or
antiunitary) operators. This means that we associate a unitary
operator U(Λ) ...
4
votes
2answers
546 views
A quantitative explanation of EM coherence domains in liquid with DNA
I've been looking with interest at a recent biology paper claiming that DNA molecules give off electromagnetic signals which can cause the same types of molecules to be reconstructed at a remote ...
4
votes
1answer
97 views
Soft Mass and Physical Mass in Softly-broken SUSY
In softly broken SUSY, the bare mass parameters may be specified at e.g. the GUT scale, and then we can run these down to another scale using RGEs, similar in form to the RGEs for gauge couplings, ...
0
votes
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
votes
1answer
111 views
Product of VEVs vs. VEV of product
How can we prove the following cluster decomposition formula
$$\langle \phi_1 \phi_2 \rangle ~=~ \langle \phi_1 \rangle \langle \phi_2 \rangle,$$
where brackets denote vacuum expectation value (VEV) ...
-1
votes
1answer
79 views
Symmetry breaking with Lagrangian
I have been studying the spontaneous symmetry braking from Zee (Quantum Field theory ) and found in the page 224, he wrote the lagrangian as
$$\mathcal{L}=
\frac{1}{2}\{
λ
(∂φ)^2 + μ^2φ^ 2\} − ...
-1
votes
0answers
43 views
Why action and velocity of a free particle has a limit? [closed]
I know that velocity is limited to speed of light (atleast in theory) and i found over here ( physics.stackexchange... ) that action is also limited to planck's constant.
why (or what is the reason ...
10
votes
4answers
651 views
Spinning Tachyons
In all examples that I know, tachyons are described by scalar fields. I was wondering why you can't have a tachyon with spin 1. If this spinning tachyon were to condense to a vacuum, the vacuum ...
0
votes
1answer
84 views
4
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1answer
82 views
Some questions about Ward-Takahashi Identity
I'm a learner of Peskin and Schroeder's textbook of quantum field theory.
I have proceeded to Ward-Takahashi identity and have one question when I look for Wikipedia for reference.
The following is ...
4
votes
2answers
147 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
1
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2answers
151 views
$\hbar \rightarrow 0$ in quantum mechanics
We often see a limit $\hbar \rightarrow 0$ in quantum mechanics and sometimes its related with Symmetry breaking. Can someone briefly write the story behind this limit.
Thanks in advance
0
votes
1answer
95 views
proper variation of action term
I have a term I want to vary by a field, $\phi$.
$$
`S' = \frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}\,\delta\left[h(\phi)\,\partial_{\mu}\phi\,\partial_{\nu}\phi \right].
$$
Is it correct to get this?
...
9
votes
1answer
322 views
False vacuum in axiomatic QFT
There is an elegant way to define the concept of an unstable particle in axiomatic QFT (let's use the Haag-Kastler axioms for definiteness), namely as complex poles in scattering amplitudes. Stable ...
2
votes
1answer
95 views
Getting rid of double delta function in Feynman rules
[1]
A very simple example of feynman rule for scalar fields.
After computing the diagram i have got the following:
$$
-i(2\pi)^4g^2\int d^4q \frac{i}{q^2 -m^2c^2}\delta^{(4)}(p_1 - p_3 -q)
...
6
votes
1answer
427 views
Definition and difference between the R-symmetry and the $U(1)_R$ internal symmetry
For a general ${\cal N}$ the R-symmetry group is $U({\cal N})$ but for the ${\cal N}=2$ case why is it $SU(2)$ ? I guess it is again different for ${\cal N}=4$. How does one understand this?
One ...
8
votes
1answer
187 views
What really are superselection sectors and what are they used for?
When reading the term superselection sector, I always wrongly thought this must have something to do with supersymmetry ... DON'T laugh at me ... ;-)
But now I have read in this answer, that for ...
13
votes
1answer
601 views
Classical and quantum anomalies
I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views:
Anomalies are due to the fact that quantum field ...
2
votes
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? ...
0
votes
1answer
419 views
Charge conjugation in Dirac equation
I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ .
Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix , $T$= ...
1
vote
0answers
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 ...
0
votes
0answers
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
votes
1answer
116 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 ...
1
vote
1answer
57 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 ...
5
votes
4answers
252 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
votes
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 ...
0
votes
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 ...
4
votes
2answers
99 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
...
1
vote
0answers
53 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 ...
5
votes
5answers
345 views
What is the path integral exactly?
I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
3
votes
1answer
80 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, ...
6
votes
0answers
80 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 ...
3
votes
1answer
338 views
If : V(Phi) : is nonlocal in space, does that mean interacting quantum field theory is nonlocal?
Free field theories are definitely local in .
In the interaction picture, we can decompose the fields into creation operator modes and annihilation operator modes. The product of operators can be ...
2
votes
0answers
61 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 ...
5
votes
1answer
137 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 ...
5
votes
2answers
2k views
The Spectral Function in Many-Body Physics and its Relation to Quasiparticles
recently, I stumbled accross a concept which might be very helpful understanding quasiparticles and effective theories (and might shed light on an the question How to calculate the properties of ...
3
votes
1answer
126 views
Straightforward questions about calculating SUSY F-terms
So in the Lagrangian for a SUSY theory we have the F-terms, which I have seen written (e.g., in Stephen Martin's SUSY primer) as
$F^*_i F^i$
where
$F^i = \frac{\partial W}{\partial \phi^i}$.
I ...
3
votes
0answers
58 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 ...
4
votes
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:
$$\psi = \sum\limits _{i} ...
2
votes
1answer
441 views
Interaction potential in standard $\phi^4$ theory
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
4
votes
1answer
111 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
votes
1answer
103 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 ...
17
votes
7answers
624 views
Is there a symmetry associated to the conservation of information?
Conservation of information seems to be a deep physical principle.
For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.
We may wonder if there is an underlying ...
6
votes
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 ...
-1
votes
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 ...
5
votes
0answers
120 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
votes
0answers
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 ...
