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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11
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335 views

Apparent failure of SUSY nonrenormalization theorem

I am having trouble reconciling two pieces of information. Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, $h$ and $\hat{h}$. The ...
5
votes
1answer
190 views

What exactly is Weinberg's power counting theorem?

The massive gravity propagator goes like $\sim \frac{p^2}{m^4}$ at high energies and in this case we cannot apply Weinberg's standard power counting arguments. I have read something like that ...
5
votes
1answer
362 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
3
votes
1answer
161 views

Singlet neutrinos decaying to Higgs bosons during leptogenesis

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term $$f_{\alpha ...
5
votes
1answer
364 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
3
votes
2answers
295 views

Pauli Villars Regularization

Consider the t-channel diagram of phi-4 one loop diagrams. Evaluated it is, with loop momenta p, $\frac{\lambda^2}{2}\displaystyle\int\frac{d^4p}{(2\pi)^4}\frac{1}{(p+q)^2-m^2}\frac{1}{p^2-m^2}$ If ...
1
vote
1answer
38 views

$e^-e^-\rightarrow e^-e^-$ scattering relative negative sign quick computation

In the QED scattering process $e^-e^-\rightarrow e^-e^-$ there are two possible diagrams in the tree level. If I label the momenta I have, $$e^-(k_1)\quad e^-(k_2)\quad \longrightarrow \quad ...
8
votes
1answer
158 views

Intuition for S-duality

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
7
votes
1answer
197 views

Are there negative energy states in QED?

I was reading Weinberg I, when I came upon the following statement$^1$ (slightly edited by me): \begin{align} (\not p+m)u=ie\not A\\ (\not p-m)v=ie\not A \tag{1} \end{align} The minus sign on ...
-1
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0answers
36 views

Does the goldstone field really disappear? [on hold]

When we apply Higgs Mechanism to a Lagrangian which has say U(1) local gauge symmetry then then the goldstone boson disappear from the Lagrangian and the degree of freedom is absorbed by the massive ...
3
votes
0answers
32 views

Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
4
votes
1answer
157 views

Two conflicting definitions of chirality

Consider a Majorana fermion embedded in a Dirac spinor, $$\psi = \begin{pmatrix} \psi_L \\ i \sigma_2 \psi_L^* \end{pmatrix}.$$ The Majorana fermion $\psi_L$ is left-chiral, i.e. it transforms in the ...
4
votes
1answer
66 views

What is the Lorentz group representation for a general spin?

Setup, as I understand things so far: One way to think about where the spin of a quantum field comes from is that it is a consequence of the ways that different types of fields transform under ...
6
votes
2answers
62 views

SHO in QM and Klein Gordon field in 1+0D QFT

The SHO in QM with mass $m=1$ has action $$ S[x] = \int dt \frac{1}{2} \dot x^2 + \frac{1}{2}\omega^2 x^2 $$ by integration by parts we see this is the same as 1 dim Klein Gordon QFT action with ...
3
votes
1answer
124 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
4
votes
1answer
50 views

What is a slow-roll field?

I am studying inflation reading this article http://lanl.arxiv.org/abs/hep-ph/0406191 and in section 3 it states: This inflaton field may evolve slowly down its effective potential, or not. While ...
1
vote
1answer
188 views

How does Hawking radiation grow as a black hole evaporates?

The temperature of Hawking radiation is inversely proportional to the mass of a black hole, $T_{\rm H}\propto M_{\rm BH}^{-1}$, and so as the black hole shrinks the temperature of the radiation should ...
8
votes
1answer
133 views

Why does Landau theory not fail when dealing with a first order phase transition?

Here is a problem where I can do the calculation, but I am not understanding the philosophy behind it. It is about Landau theory: The Landau theory of phase transitions is based on the idea that the ...
12
votes
3answers
946 views

What really goes on in a vacuum?

I've been told that a vacuum isn't actually empty space, rather that it consists of antiparticle pairs spontaneously materialising then quickly annihilating, which leads me to a few questions. ...
5
votes
1answer
69 views

Why is the $D^0$ oscillation so different from the $K^0$ and $B^0$?

I have looked for this answer into many articles and books but I am not able to figure out why $D^0\to\bar{D}^0$ is so highly suppressed if compared to the $B^0 \to \bar{B}^0$ and $K^0 \to \bar{K}^0$ ...
3
votes
2answers
137 views

Spinor field normalisation from poles in the propagator

In the theory of free scalar bosons (KG field) it is a basic result that the propagator $\Delta(p)$ has poles at $p^2=m^2$, with residue $1$ (or any other constant, depending on conventions). Thinking ...
7
votes
1answer
264 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
4
votes
1answer
179 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
-1
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0answers
13 views

what are excited state spectra of particles?

Is it correct to see excited state spectrum as an indication of how much energy flow to respective coupled fields during collision? How can such spectra (if they can) be calculated from collision ...
1
vote
0answers
33 views

How to represent the spherical wave by using Fock basis?

Suppose I have two particles with opposite momentum: $$ |\psi \rangle_{\mathbf k} = |\mathbf k; -\mathbf k\rangle ,\quad |\mathbf k| = M $$ I want to represent the spherical symmetric distribution of ...
4
votes
3answers
356 views

Schroedinger field operators and their commutation relations

I've got several questions regarding the so called second quantization of the Schroedinger equation. My professor introduced the field operators for the Schroedinger field by simply stating them as ...
0
votes
1answer
186 views

Derivation of eq 6.17, Peskin and Schroeder

I am having trouble following a derivation in Peskin and Schroeder's textbook, namely equation 6.17 on page 182. It seems benign at first, but I am completely stuck. Essentially, we have an expression ...
1
vote
1answer
39 views

Structure of Mass Renormalisation

I'm currently working on the renormalisation part in Peskin, Schroeder QFT. There it is stated that non-logarithmic UV divergences give a mass renormalisation and thus are forbidden, e.g. for the ...
0
votes
1answer
45 views

Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
1
vote
1answer
88 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
8
votes
1answer
579 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
6
votes
1answer
165 views

Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
5
votes
1answer
50 views

Holevo Information and Quantum Mutual Information

This question is about the difference between Quantum Mutual Information and Holevo Information of quantum channels. From http://arxiv.org/pdf/1004.2495.pdf equation 7 we know that the sum of quantum ...
0
votes
0answers
19 views

Is absorption probality modulated by interferance instanteneous or retarded effect?

Let say the absorption probability at some atom 1 location is modulated by photo ionized electron wave (ionized from 1) that scatters by neighboring atom 2 and returns to the 1. (Around the absorption ...
1
vote
2answers
395 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
4
votes
1answer
92 views

A question about Fierz identities in Peskin's Quantum field theory

In Peskin's "quantum field theory", there is a identity of Pauli matrix which is connected to Fierz identity,(equation 3.77) ...
1
vote
2answers
56 views

Commutation Relations in Second Quantization

I understand that if I have the field operators $\psi(r)$ and $\psi^\dagger(r)$, then I have the canonical commutation relation (in the boson case) $$[ \psi(r) , \psi^\dagger(r')]=\delta(r-r').$$ My ...
2
votes
1answer
32 views

Computation of theta-term from triangle diagram

The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
2
votes
0answers
65 views

What is the meaning of SU(2) triplet scalar field? [closed]

The following is an about a Left-Right Symmetric model. $SU(2)\otimes SU(2)$ $(2\otimes 2=3\oplus 1)$ will generate a triplet, which in Left-Right Symmetric model is ...
1
vote
0answers
22 views

Spontaneous symmetry breaking of scalar multiplet theory

Consider a theory with two multiplets of real scalar fields $\phi_i$ and $\epsilon_i$, where $i$ runs from $1$ to $N$. The Lagrangian is given by: $$\mathcal L = \frac{1}{2} (\partial_{\mu} \phi_i) ...
3
votes
1answer
512 views

Scalar two loop diagram in $\varphi^4$ theory

Could someone explain how, or at least show me a link that explicitly shows the calculation of a two-loop corrections to scalar’s two-point function in $\varphi^4$ theory in the massless limit.
7
votes
1answer
223 views

Does it make sense to speak of amplitudes of finite closed boundaries in QFT?

A example of amplitude in Relativistic Quantum Mechanics or specifically in QFT is the amplitude of a field configuration on a space-like hyper-surface of space-time to "lead" to another field ...
1
vote
1answer
47 views

Is even the perturbative expansion of the QCD beta function expected to be divergent?

The usual QCD folklore tells us that perturbative expansions are (at best) asymptotic. Recently a colleague of mine told me that the expansion of the beta function is thought to be convergent because, ...
4
votes
1answer
39 views

Why do we exclude the quark condensate in the OPE?

In every QCD paper I open people say that in the OPE, the lowest order non-trivial condensate is the gluon condensate, whose dimensions are 4. Nonetheless, I knowof the existence of the quark ...
0
votes
0answers
22 views

Continuum of states after 2-particle states

In the Hilbert space of some free theory one can define single-particle states as $|\vec{p}>$, 2-particle states as $|\vec{p},\vec{q}>$ and so on. The $total$ 4-momentum eigenvalue of the ...
4
votes
1answer
251 views

Quantizing highly nonlinear field-theories?

I'm wondering how to go about quantizing a classical field theory which looks nothing like a free field theory plus a perturbation term. Suppose for concreteness I have the classical hamiltonian $ ...
0
votes
0answers
20 views

Reasoning behind the logarithm in the expansion during dimensional regularisation

In the calculation of integrals using dimensional regularisation, one often encounters an expression like $$I_n(m,\epsilon) \propto \left(\frac{4\pi\mu^2}{m^2}\right)^{\frac{\epsilon}{2}} \times ...
1
vote
0answers
31 views

Self-energy integral at (complex) polar coordinates [migrated]

I am trying to resolve the following integral where $x,y \in \mathbb{R}$ and $a,b$ are constants in $\mathbb{R}$. $$ I = \int \frac{dxdy}{(2\pi)^2} \frac{x-ia}{\sqrt{(x-ia)^2+(y-ib)^2}} $$ This ...
0
votes
0answers
14 views

Neutral pion mass correction from electroweak instantons

It is stated that the virtual process $$ \pi^{0}\to 2W \to \pi^{0}, $$ where $\pi^{0}$ is neutral pion and $W$ denotes $W-$boson, generates the small correction to the pion mass, namely $$ \delta ...
0
votes
0answers
27 views

Spontaneous Symmetry Breaking in global $U(1)$ symmetry

I was reading SSB from Ashok Das - Lectures on Quantum Field Theory. I have a couple of questions. First Question Equation (7.65) reads ...