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
61 views
How does this paper relate to standard QED?
This paper proposes a microscopic mechanism for generating the values of $c, \epsilon_0, \mu_0$. They state that their vacuum is assumed to contain ephemeral (meaning existing within the limits of ...
0
votes
1answer
126 views
is really an atom stable?
Half filled and fulfilled atomic orbitals are stable because of :
high exchange energy.
The problem is with exchange energy. We have learnt that the half and fulfilled orbitals have maximum no. of ...
3
votes
3answers
297 views
Quantum field theory, particle interpretations and path integrals?
I am trying to find some names or models of a particle interpretation of quantum field theory which isn't a literal path integral approach? Are there any particle interpretations of quantum field ...
1
vote
0answers
42 views
QFT basics for Klein-Gordon fields
I am teaching myself QFT from Peskin for next years maths course and I have two questions:
What is a c-number? Is it a complex number, and if so why does it mean, ...
2
votes
0answers
129 views
Field content and symmetry groups of Minimal Composite Higgs Models
I'm trying to teach myself the Composite Higgs Model, both its theory and its LHC phenomenology (particularly the 4DCHM). Unfortunately, I'm struggling; the literature is contradictory and/or omits ...
5
votes
1answer
78 views
Significance of Poles of Correlation Function in QFT
In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
2
votes
2answers
258 views
Correlation functions in thermal field theory etc
Suppose I am studying a field theory at finite temperature or some black hole formation scenario from boundary theory perspective in the sense of AdS/CFT. How is it possible to gain information about ...
2
votes
0answers
50 views
Helicity for Zero Rest Mass Field Equations
I'm trying to reconcile the usual definition of the helicity operator, namely
$$ h = \hat{p}.S$$
with the definition of a massless helicity $n$ field as a symmetric spinor field $\phi^{A\dots B}$ ...
9
votes
1answer
108 views
Why are topological solitons present in some phases for lattice models?
Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
6
votes
3answers
177 views
supressing certain decay paths and enhancing others with interference
In a scattering reaction, there are many possible final states for the products, each with different production rates.
Question: Is there a way in which we could in general supress certain rates ...
4
votes
1answer
184 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
98 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
votes
0answers
54 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
120 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
550 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
102 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
114 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
82 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
$$\mathcal{L}=
\frac{1}{2}\{
λ
(∂φ)^2 + μ^2φ^ 2\} − ...
10
votes
4answers
658 views
Spinning Tachyons
In all examples that I know, tachyons are described by scalar fields. I was wondering why you can't have a tachyon with spin 1. If this spinning tachyon were to condense to a vacuum, the vacuum ...
0
votes
1answer
86 views
4
votes
1answer
96 views
Some questions about Ward-Takahashi Identity
I'm a learner of Peskin and Schroeder's textbook of quantum field theory.
I have proceeded to Ward-Takahashi identity and have one question when I look for Wikipedia for reference.
The following is ...
4
votes
2answers
155 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
1
vote
2answers
153 views
$\hbar \rightarrow 0$ in quantum mechanics
We often see a limit $\hbar \rightarrow 0$ in quantum mechanics and sometimes its related with Symmetry breaking. Can someone briefly write the story behind this limit.
Thanks in advance
0
votes
1answer
97 views
proper variation of action term
I have a term I want to vary by a field, $\phi$.
$$
`S' = \frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}\,\delta\left[h(\phi)\,\partial_{\mu}\phi\,\partial_{\nu}\phi \right].
$$
Is it correct to get this?
...
9
votes
1answer
325 views
False vacuum in axiomatic QFT
There is an elegant way to define the concept of an unstable particle in axiomatic QFT (let's use the Haag-Kastler axioms for definiteness), namely as complex poles in scattering amplitudes. Stable ...
2
votes
1answer
102 views
Getting rid of double delta function in Feynman rules
[1]
A very simple example of feynman rule for scalar fields.
After computing the diagram i have got the following:
$$
-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
433 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
194 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
636 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
68 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
426 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 , $T$= ...
0
votes
0answers
82 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
140 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
66 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
276 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
131 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
86 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
104 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
57 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 ...
3
votes
1answer
88 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
89 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
339 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
63 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
140 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
133 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
60 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 ...
5
votes
1answer
209 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:
$$\psi = \sum\limits _{i} ...
2
votes
1answer
449 views
Interaction potential in standard $\phi^4$ theory
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
