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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$e^-e^-\rightarrow e^-e^-$ 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 ...
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214 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 ...
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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 ...
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161 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 ...
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71 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 ...
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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 ...
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130 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 ...
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69 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 ...
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190 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 ...
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141 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 ...
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3answers
957 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. ...
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140 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 ...
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35 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 ...
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370 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 ...
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1answer
40 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 ...
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54 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 ...
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91 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 ...
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60 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 ...
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21 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 ...
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101 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) ...
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2answers
60 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 ...
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1answer
34 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 ...
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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 ...
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26 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) ...
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525 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.
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226 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 ...
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51 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, ...
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40 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 ...
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25 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 ...
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21 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 ...
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17 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 ...
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30 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 ...
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219 views

Expanding free scalar field in terms of ladder operators

I'm having some difficulty with the finer points of expanding a field in terms of ladder operators. Note that this is not identical to the other related question I asked. From Peskin / Schroeder; ...
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569 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
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1answer
365 views

Conservation of BRST current in QED

I am trying to understand the conservation of the BRST current in QED but am having some trouble. This is what I have so far, QED lagrangian density in Lorenz gauge is, $$L = ...
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75 views

What is a soft photon?

I accidentally came across the words "soft photon" today after reading a few blogs. There was some discussion of special situations involving gauge redundancies and a theorem by Weinberg. What is a ...
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1answer
37 views

Why do the different lepton generations have different masses?

I've been reading Mark Srednicki's book on Quantum Field Theory, and toward the end (Chapter 88), he describes how the different generations of leptons acquire mass via Yukawa interactions. However, ...
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1answer
54 views

Preference of Chirality

I was interested to see that , $$ \gamma^5 \psi = \psi_R - \psi_L $$ By the definition of chirality projection operator and that $\psi = \psi_R + \psi_L$. since $\gamma^5 \psi$ pops up a lot in ...
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53 views

SUSY Multiplets

Why is it that in vector supermultiplets, the left and right chiral components of the gauginos must transform in the same representations of all gauge groups, i.e a chiral theory for such fermions is ...
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49 views

Magnetic field of rotating capacitor [duplicate]

Does the rotating charged capacitor (both plates) produce magnetic field? and what about rotating both plates in opposite directions?
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69 views

How could we describe the electric bound state like hydrogen by QED? [duplicate]

We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, ...
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1answer
413 views

Why do we assume local conformal transformations are symmetries in 2D CFT

The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional. However, when ...
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1answer
81 views

Deriving the Spinor Completeness Relation without using a Representation

Reference: DAMTP problem set 3, question 5 but ignore the spinor solutions given. To preface, this has taken up 1 entire day and a further 2 afternoons of work so I will just list the most promising ...
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1answer
63 views

Heisenberg Representation of Dirac Equation Quantization

I am wondering exactly how to apply the following method to the Dirac equation (and even electromagnetism if it is easy to type up). It is a method of deriving the momentum-space Hamiltonian without ...
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93 views

Stimulated Emission in QED

The explanations of stimulated emission which I have found all describe the phenomenon in terms of non-relativistic quantum mechanics. How might you describe it in a field theory such as QED? In ...
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3answers
747 views

The virtual particles are only a fictive tool in equations? DO they exist or DON'T? And if they exist, why do we call them VIRTUAL?

There is no "action at a distance" in nature. Attraction of a piece of iron by a magnet, attraction between distant electric charges of opposite sign, have to be mediated by something. The virtual ...
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2answers
331 views

The Origins of the Second Quantization

I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
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314 views

Physical meaning of partition function in QFT

When we have the generating functional $Z$ for a scalar field \begin{equation} Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\Big[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\Big]}, ...
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76 views

What force prevents particles from penetrating other particles?

I understand that what prevents objects from penetrating each other is the electromagnetic force between the electrons in the respective objects. But if we don't have electrons, for example a proton. ...
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Gauge mediated SUSY breaking

I have seen it claimed that in SUSY gauge mediated breaking there can be no flavour changing terms because the mediation is flavour blind. What does this mean and how does it work?