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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How Uncertainty Principle, Vacumm fluctuations and Energy Conservation coexist in QFT?
Recently I had a debate about the uncertainty principle in QFT that made me even more confused..
Because we use Furrier transforms in QFT we should have an analogue to the usual Heisenberg ...
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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 ...
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2answers
218 views
Can scattering amplitudes be simplified with 1PI diagrams?
I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
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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 ...
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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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62 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 ...
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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 ...
4
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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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8answers
594 views
Why do physicists believe that particles are pointlike?
String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories.
So why is it that it's popular ...
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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
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 ...
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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 ...
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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
268 views
About the definition/motivation/properties of the twisted chiral superfield in ${\cal N}=2$ theories in $1+1$ dimensions
The following is in the context of the ${\cal N}=2$ supersymmetry in $1+1$ dimensions - which is probably generically constructed as a reduction from the ${\cal N}=1$ case in $3+1$ dimensions.
In ...
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1answer
167 views
Calculation of Commutation in constraint analysis
During analysis the constraint from a theory,
suppose my canonical Hamiltonian is $$H_c=P^A\dot{A}+P^B\dot{B}-L$$
where $P^A=\frac{\partial L}{\partial \dot A}$ and $P^B=\frac{\partial L}{\partial ...
12
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3answers
703 views
No hair theorem for black holes and the baryon number
The no hair theorem says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge.
For me it is puzzling why ...
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2answers
348 views
Gauge invariance and diffeomorphism invariance in Chern-Simons theory
I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
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1answer
87 views
Density operator in second quantization
I would want to understand why the density operator in second quantization takes the form:
$$\rho_\sigma(\mathbf{r})=\Psi_\sigma^\dagger(\mathbf{r})\Psi_\sigma(\mathbf{r})?$$
Is this a definition or ...
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0answers
85 views
QFT: differential cross section from center of mass to lab frame
I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed $|M|^2$ and the differential cross section in the ...
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1answer
189 views
Why do irrelevant operators require infinitely many counterterms?
As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
2
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0answers
74 views
Vacuum to vacuum transition amplitude
I have two questions about Vacuum to vacuum transition amplitude.
Can any particle stay in $|0\rangle$?
I was studying this topic from Srednicki's QFT book. He writes in eq.$(6.22)$
$$\langle0|0 ...
2
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1answer
138 views
Tachyon vertex operator (Polchinski's book)
I would like to know how does Polchinski in his book "derive" what is the "tachyon vertex operator" (..as say stated in equation 3.6.25, 6.2.11..) I can't locate a "derivation" of the fact that ...
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2answers
207 views
Ward Takahashi identities from Z invariance
I'm trying to get Ward-Takahashi identities using the approach used in Ryder's book (pages 263-266). I like that he starts from demanding gauge invariance of Z in a explicit way and them explores the ...
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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 ...
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2answers
121 views
Definition of Free field or Noninteracting field
In QFT we can write a Hamiltonian operator for a free field. So, what is a free field/ noninteracting field?
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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 ...
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2answers
85 views
Heisenberg evolution equation for $\hat{\phi}$
Consider quantum Hamiltonian of free massive scalar particle:
$$\hat{H} = \int d^3x \left[\frac{1}{2} \hat{\pi}^2 (t, \vec{x}) + \frac{1}{2} \partial_i \hat{\phi}(t, \vec{x}) \partial_i \hat{\phi}(t, ...
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3answers
360 views
Noether theorem, gauge symmetry and conservation of charge
I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far.
First, the global gauge symmetry. I'm starting with the Lagragian
...
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1answer
103 views
A question about defining a classical CFT
This is kind of related to this,
Defining a CFT using beta-functions
So what would be the right definition of a CFT even classically?
Is it true that classically one will call a theory scale ...
11
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3answers
476 views
The interpretation of mass in quantum field theories
Consider a free theory with one real scalar field:
$$
\mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -\frac{1}{2}m^2\phi ^2.
$$
We write this positive coefficient in front of $\phi ^2$ ...
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5answers
190 views
Derivation of $ E=h\nu$
Is it possible to derive the relation $ E=h\nu$ from Schrodinger equation or the basic principles of quantum mechanics or is it something which is considered to be an axiom with no explanation?
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1answer
249 views
Why on-shell vs. off-shell matters?
The definitions between on- and off-shell are given in Wikipedia.
Why is it so important in QFT to distinguish these two notions ?
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71 views
How to charge a field?
In a previous post [ Noether theorem, gauge symmetry and conservation of charge ] we were discussing the different ways to demonstrate the current conservation: via the first Noether theorem applied ...
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2answers
248 views
Algebraic/Axiomatic QFT vs Topological QFT
Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
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1answer
224 views
Did the Feynman heuristic of “simple effects have simple causes” fail for spin statistics?
Someone here recently noted that "The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated."
...
3
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2answers
154 views
Ordering Ambiguity in Quantum Hamiltonian
While dealing with General Sigma models (See e.g. Ref. 1)
$$\tag{10.67} S ~=~ \frac{1}{2}\int \! dt ~g_{ij}(X) \dot{X^i} \dot{X^j}, $$
where the Riemann metric can be expanded as,
$$\tag{10.68} ...
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1answer
84 views
Multiple vacua vs. vev's in qft
Take a (possibly supersymmetric) relativistic quantum field theory:
when we construct it, we suppose that there is a unique vacuum state $|0\rangle$ which is Lorentz invariant, vector of some Hilbert ...
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2answers
375 views
Particle as a representation of the Lorentz group
In QFT one may refer to a particle as a representation of the Lorentz group (LG). More accurately - every particle is a quantum of some field $\phi(x)$ that belongs to some representation of the LG. I ...
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76 views
Do instantons support quantum bound states?
When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
8
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2answers
500 views
Regularisation of infinite-dimensional determinants
Can a regularisation of the determinant be used to find the eigenvalues of the Hamiltonian in the normal infinite dimensional setting of QM?
Edit: I failed to make myself clear. In finite ...
3
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1answer
73 views
Gell-Mann Low Theorem and Vacuum Energy
I know that the sum of vacuum bubbles can be related to the Vacuum energy, but I'm trying to understand how this follows from the Gell-Mann Low theorem/equation. My question will use equations from ...
6
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0answers
150 views
Regulator-scheme-independence in QFT
Are there general conditions (preservation of symmetries for example) under which after regularization and renormalization in a given renormalizable QFT, results obtained for physical quantities are ...
2
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0answers
91 views
Counterexamples in quantum theory [closed]
I'm looking for counterexamples in quantum theory, in the spirit of books like Counterexamples in topology and Counterexamples in analysis. A practically identical post, but for PDEs, can be found ...
6
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2answers
266 views
Dirac equation in curved space-time
I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$
This ...
4
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1answer
91 views
What's vison in Z2 resonating valence bond (RVB) state?
I have a problem on the "vison" exitation in the Z2 RVB state. The vison exitation is a topological exitation of the system like topological defect in nematic liquid , if I got it right. Because the ...
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1answer
87 views
QFT in Quantum Computing and Control Theory?
Is QFT being applied to quantum computing and control theory?
I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it ...
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2answers
199 views
Does the existence of dualities imply a more fundamental structure?
I was wondering if the existence of some kind of duality in physics always implies the existence of some underlying more fundamental structure/concept?
Let me give a few example from history:
...
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1answer
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Lagrangian formulation for relativistic case
Lagrangian for a real scalar field:
$$\mathcal{L}=\frac{1}{2}\eta^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-\frac{1}{2}m^2\phi^2 $$
Can someone simply drive me how can I write it from ...
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2answers
49 views
What can be the smallest chaotic system?
As I am talking about 'smallest' can I expect that it should be a quantum system? I understand that we use quantum chaos theory instead of perturbation theory when the perturbation is not small. For ...
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4answers
323 views
The Schwinger model
The Schwinger model is the 2d QED with massless fermions. An important result about it (which I would like to understand) is that this is a gauge invariant theory which contains a free massive vector ...
