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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228 views

Is the form of the Lagrangian relevant before the renormalization procedure?

In the renormalization procedure, is writing things like $$\varphi=\sqrt{Z_{\varphi}}\ \varphi_R\ ,\ \ m_0^2=Z_m\ m_R^2\ ,\ \ g_0=Z_g \mu^{\epsilon}\ g_R$$ and $$Z_i=1+\sum_{\nu=1}^\infty ...
8
votes
2answers
214 views

Irrelevance of parastatistics for space dimension > 2

Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal ...
6
votes
1answer
326 views

Thermodynamic limit “vs” the method of steepest descent

Let me use this lecture note as the reference. I would like to know how in the above the expression (14) was obtained from expression (12). In some sense it makes intuitive sense but I would ...
0
votes
2answers
362 views

Anomalous magnetic moment of electron

It is known that the value of 2 of the electron g-factor arises from the Dirac equation. As far as I can see from the various sources, this value is obtained in non-relativistic limit, in particular ...
4
votes
2answers
272 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: ...
4
votes
1answer
179 views

Colour decomposition of $n-$gluon tree amplitude

I have here a $SU(N_c)$ Yang-Mill's theory and let the index $i$, label the $n$-gluons, and $\{k_i, \lambda_i, a_i\}$ be its momenta, helicity and colour index and $\cal{A}_n^{tree/1-loop}(\{k_i, ...
3
votes
2answers
567 views

Discreteness of Spacetime and Violation of Lorentz symmetry

It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows ...
2
votes
2answers
283 views

Does path integral and loop integral in a Feynman diagram violate special relativity?

Consider a correlation function between two points $A(x_1,t_1)$ and $B(x_2,t_2)$, we need to integrate over paths which could be infinite long. But the time length $(t_1-t_2)$ is finite, so if $A$ ...
0
votes
2answers
944 views

quantum optics of a polarizing beam splitter

I would like to use the Heisenberg picture in quantum field theory to model a polarizing beam splitter. Is there an easy way for someone to show me how the field operators ($a^\dagger_{input1}$, ...
2
votes
1answer
277 views

half Skyrmion vs Meron

Is there a difference between a half skyrmion and a meron? I'm asking this in regard to half skyrmion theories of High Tc Superconductors. It would be interresting to know if the proposed half ...
4
votes
1answer
174 views

Is the long range neutron-antineutron interaction repulsive?

I can model this interaction as Zee does in "Quantum field theory in a nutshell". In chapter I.4 section "from particle to force" he uses two delta functions for the source. The integral gives ...
4
votes
1answer
295 views

SU(2) yang-mills EOM

I'm just playing around tonight trying to better myself, but I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor $$ ...
7
votes
4answers
365 views

Different kinds of S-matrices?

It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
3
votes
3answers
580 views

Quantum harmonic oscillator

I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is ...
7
votes
2answers
563 views

Interesting topics to research in mathematical physics for undergraduates

I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on. I'm particularity fond of abstract algebra ...
6
votes
2answers
338 views

What is known about quantum electrodynamics at finite times?

I'm aware that we can describe the time evolution of states/operators (choose your favourite picture) of non interacting quantum fields and that perturbation theory is very effective in computing S ...
4
votes
3answers
425 views

Calculating lagrangian density from first principle

In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
11
votes
1answer
431 views

Derivation of the effective potential between a quark and an anti-quark

Typically in particle physics books (not in QFT books!) I have often seen this statement that the potential between a heavy quark and its anti-quark can be "empirically" represented as $V(r) = ...
2
votes
1answer
151 views

Electron shell bombardment

If you bombard an electron shell with a photon below the critical level to promote the electron to a higher state, will the shell absorb nothing and the photon get deflected with the same amount of ...
6
votes
1answer
322 views

Can a photon see ghosts?

Does it make sense to introduce Faddeev–Popov ghost fields for abelian gauge field theories? Wikipedia says the coupling term in the Lagrangian "doesn't have any effect", but I don't really know ...
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vote
0answers
118 views

Can we use only the observables of Fermion fields?

There are legion ways to consider fermionic Dirac spinor fields, but is it possible to consider the asymptotic free field only in terms of observables, which in the case of the Dirac spinor field must ...
2
votes
1answer
324 views

How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments?

How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments? I am having a hard time figuring the answer out. Please help.
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vote
2answers
103 views

Nonabelian gauge theories and range of the corresponding force

Do all nonabelian gauge theories produce short range force?
2
votes
2answers
147 views

Can the charge of particles spontaneously flip from positive to negative or vice versa?

I'm thinking of matter antimatter annihilation, are there reactions where normal matter converts to antimatter?
9
votes
1answer
370 views

Reduced density matrices for free fermions are thermal

Many recent papers study entanglement in eigenstates of fermionic free hamiltonians (normally on a lattice) using the basic assumption that the reduced density matrices are thermal (e.g. Peschel ...
18
votes
1answer
762 views

Why is there no theta-angle (topological term) for the weak interactions?

Why is there no analog for $\Theta_\text{QCD}$ for the weak interaction? Is this topological term generated? If not, why not? Is this related to the fact that $SU(2)_L$ is broken?
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votes
0answers
173 views

Intuitive sketch of the correspondence of a string theory to its limiting quantum field theory

I'm looking for an intuitive sketch of how one shows the correspondence of string theory to a certain QFT. My best guess is that one calculates the scattering amplitudes in the string theory as a ...
3
votes
3answers
897 views

what causes virtual particle pair production to not occur in the space occupied by matter?

Are virtual particles only popping in and out of existence where the local energy density is below a certain point? What I wonder is, does any kind of matter prevent the pairs from appearing? Is ...
7
votes
1answer
768 views

Vacuum Wavefunctional

I am having this problem in understanding the vacuum wavefunctional in QFT. Hence this naive question. I mean, if someone say vacuum wavefunctional, I can think of an element like wavefunction as in ...
7
votes
2answers
838 views

Some questions about Wilson loops

Let $G$ be the gauge group whose Yang-Mill's theory one is looking at and $A$ be its connection and $C$ be a loop in the space-time and $R$ be a finite-dimensional representation of the gauge group ...
3
votes
1answer
339 views

An odd relation with the epsilon/delta invariant tensors of SO(3)

The rotation group SO(3) can be viewed as the group that preserves our old friends the delta tensor $\delta^{ab}$ and $\epsilon^{abc}$ (the totally antisymmetric tensor). In equations, this says: ...
3
votes
1answer
454 views

Feynman rule 4-point vertex WW -> ZZ

I am looking for the Feynman rule of the 4-point gauge boson interaction of W+ W- -> Z Z. I am guessing it looks like the Yang Mills 4-point vertex for gluons, but with helicity included. Equation ...
16
votes
3answers
833 views

Quantum Field Theory Variants

I am a math guy, so sorry for the naivety. When I peruse the wikipedia I see many "variants" of quantum field theory...conformal quantum field theory, topological quantum field theory, ...
10
votes
1answer
561 views

Time reversal symmetry and T^2 = -1

I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
3
votes
1answer
270 views

A dimensional regularization identity

I had a question on a dimensional regularization identity. A reference or a quick sort of derivation will be greatly appreciated. I looked at some textbooks of QFT, but couldn't find the one I was ...
4
votes
0answers
61 views

functional representations of free quantum fields

The free real quantum field, satisfying $[\hat\phi(x),\hat\phi(y)]=\mathrm{i}\!\Delta(x-y)$, $\hat\phi(x)^\dagger=\hat\phi(x)$, with the conventional vacuum state, which has a moment generating ...
12
votes
1answer
597 views

Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...
2
votes
1answer
258 views

Why is a gaussian fixed point called gaussian?

I know what a gaussian fixed point is, and I did read the wikipedia entry, but it wasn't helpful. It says because the probability distribution is gaussian, but what probability distribution?
6
votes
3answers
661 views

Gauge invariant Chern-Simons Lagrangian

I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$): $$\mathcal L= -\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + ...
18
votes
2answers
184 views

Values of SM parameters at one certain scale

The general question is: What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
6
votes
1answer
71 views

References for phase-transitions in supersymmetric field theory

Apart from other reasons, recently my interest in this area got piqued when I heard an awesome lecture by Seiberg on the idea of meta-stable-supersymmetry-breaking. I am looking for references on ...
6
votes
3answers
291 views

Modular invariance for higher genus

As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories: Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
9
votes
2answers
317 views

How to prove equivalence of RG flow of QFT coupling constant and diagrammatic resummation at fixed renormalization scale?

QFT books say that solving the RG equation $\frac {dg} {d\textbf{ln} \mu}=\beta(g)$, using the one-loop beta function, is to the "leading log" approximation equivalent to resumming infinitely many ...
6
votes
1answer
483 views

Time reversal symmetry and T^2 = -1

I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
15
votes
3answers
792 views

Simple (but wrong) argument for the generality of positive beta-functions

In the introduction (page 5) of Supersymmetry and String Theory: Beyond the Standard Model by Michael Dine (Amazon, Google), he says (Traditionally it was known that) the interactions of ...
4
votes
0answers
286 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
10
votes
3answers
784 views

What was missing in Dirac's argument to come up with the modern interpretation of the positron?

When Dirac found his equation for the electron $(-i\gamma^\mu\partial_\mu+m)\psi=0$ he famously discovered that it had negative energy solutions. In order to solve the problem of the stability of the ...
8
votes
2answers
215 views

Wilson Loops in Chern-Simons theory with non-compact gauge groups

VEVs of Wilson loops in Chern-Simons theory with compact gauge groups give us colored Jones, HOMFLY and Kauffman polynomials. I have not seen the computation for Wilson loops in Chern-Simons theory ...
12
votes
4answers
2k views

QM and Renormalization (layman)

I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
9
votes
3answers
2k views

Energy momentum tensor from Noether's theorem

in the book Quantum Field Theory by Itzykson and Zuber the following derivation for the stress-energy tensor is proposed (p.22): Assume a Lagrangian density depending on the spacetime coordinates $x$ ...