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 ...

learn more… | top users | synonyms (1)

0
votes
0answers
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 ...
4
votes
1answer
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 ...
4
votes
2answers
243 views

Integrated Ward Identity

Suppose you have the following ward identity : $$\int_{M} d^4x\ \epsilon(x)\ \partial_{\mu} \langle j_{\mu}(x)O(y)\rangle = - \ \langle\delta O(y)\rangle$$ where $\delta O(y)$ can be written in the ...
0
votes
0answers
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 ...
0
votes
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, ...
1
vote
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 ...
0
votes
0answers
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 ...
4
votes
1answer
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 ...
1
vote
1answer
50 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?
4
votes
1answer
70 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, ...
4
votes
1answer
102 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
1answer
83 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 ...
1
vote
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 ...
9
votes
0answers
95 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 ...
4
votes
2answers
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]}, ...
1
vote
3answers
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. ...
2
votes
0answers
26 views

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?
11
votes
5answers
266 views

How is the ground state chosen in a spontaneous symmetry breaking process?

This question is about how the ground state is chosen in a spontaneous symmetry breaking process. Say we have a Mexican Hat potential (e.g. the one for the Higgs field) and are sitting at the unstable ...
3
votes
2answers
66 views

How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
0
votes
0answers
44 views

Lagrangian derivation of Thomson scattering cross section (ie photon-electron)

Does anyone know a quick way to obtain the classical Thomson scattering scattering cross section (for photons scattering on electrons) from quantum mechanics/quantum field theory, avoiding the lengthy ...
2
votes
0answers
53 views

Is a lagrangian with a background field interaction renormalizable ? If yes, when?

Consider the Lagrangian, $$ L = -\partial_{\mu} \chi \partial_{\nu} \chi^{\dagger} - m^2 \chi \chi^{\dagger} + g\chi \chi^{\dagger}\phi,$$ where $\phi$ is a background field and $\chi$ is a complex ...
7
votes
2answers
115 views

Lie groups with same algebra

I had a problem when considering symmetry breaking in an SO(4) gauge theory: $\mathcal{L} = \left| D_\mu\phi \right|^2$ where $D_\mu$ is the SO(4) covariant derivative. Then assuming there is some ...
1
vote
1answer
97 views

Does massive particle really move at speed of light? [closed]

According to this answer I understood that particles with mass also move at speed of light but interaction with higgs field make this movement zigzag. So average speed is below speed of light. But I ...
2
votes
0answers
39 views

Contour integral of the retarded Klein Gordon propagator

I've been trying to prove by hand the Peskin's formula for the retarded propagator of the Klein Gordon equation, that is, $$\int_{x^0 > y^0} \frac{d^4p}{(2\pi)^4} \frac{-e^{-ip(x-y)}}{i(p^2 - ...
4
votes
0answers
37 views

Has anyone studied anomalous supersymmetry?

In this paper (and others), the authors study a supersymmetric model where the supercharge suffers an ABJ anomaly. Has anyone studied a supersymmetry with a 't Hooft anomaly (gauging the ...
3
votes
2answers
77 views

Bilinears in adjoint representation

Below are two statements from my notes and I am trying to verify them explicitly. In both cases the fields are assumed to transform under the fundamental representation of $O(N)$ - --'The kinetic ...
3
votes
1answer
100 views

Quantum field theory: zero vs. finite temperature

I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero ...
8
votes
2answers
332 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 ...
1
vote
1answer
61 views

Cutoff-dependent “inverse propagator” for renormalization

In Zee's QFT in a Nutshell, when introducing mass renormalization, he calculates the "inverse propagator" for a $\phi^4$ scalar field theory to order $\lambda^2$ by considering the two diagrams shown: ...
0
votes
0answers
47 views

Gravity modeled by warping of spacetime or by field field theory?

I've recently read "Fields of Color" by Rodney Brooks who states that there are currently two ways of understanding the phenomenon of gravity. One involves a warping of 4D spacetime a la Einstein, ...
7
votes
0answers
53 views

Why would renormalization be necessary without divergent integrals? [duplicate]

Weinberg uses the LSZ reduction formula to introduce field renormalization,and on page 441, he says: As this discussion should make clear: the renormalization of masses and fields has nothing to ...
0
votes
0answers
29 views

Electroweak instanton calculations

Consider an electroweak instanton in a model beyond the Standard Model with explicit baryon plus lepton number ($B+L$) violation. This instanton decays into nine quarks $q$ and three leptons $l$, ...
3
votes
0answers
30 views

Polarization vectors in Quantum Electric Field

The quantum electric field is written as, \begin{equation} \mathbf{E}(\mathbf{r})=i\sum_{\mathbf{k},\lambda}\sqrt{\frac{\hbar \omega}{2 V ...
5
votes
2answers
128 views

Is the Noether charge always a Hermitian operator?

Noether's theorem tells us that to every continuous symmetry of the Lagrangian there corresponds a conserved current $j^\mu$. From the time component of this current, we can then define the Noetherian ...
3
votes
1answer
61 views

Is Lorentz invariant differential measure arbitrary?

In Srednicki, we chose a function $f(\mathbf k)$ to make $d^3\mathbf k/f(\mathbf k)$ Lorentz invariant. The way to do this is to first start from a 4 dimensional measure and multiply it by a Dirac ...
0
votes
0answers
23 views

relation between operator and matrix

Recall that in quantum mechanics, the three components of s of a spin-$\frac{1}{2}$ particle satisfied the anticommute relation: $$ \{s^i, s^j\}=\delta^{ij} $$ and we could parametrize the operators ...
3
votes
1answer
49 views

Feynman Propagator in Peskin & Schroeder

To prove Wick's Theorem, Peskin & Schroeder define the contraction of two fields: \begin{align} \text{Contract}[\phi(x)\phi(y)]\equiv \begin{cases} [\phi^+(x),\phi^-(y)] & \text{for ...
3
votes
1answer
79 views

Does there exist finite dimensional irreducible rep. of Poincare group where translations act nontrivially?

I read several textbooks of QFT and find that there are two ways to classify the particles or fields. The first one is to study the irreducible representation of Lorentz group (or exactly the ...
1
vote
0answers
28 views

Single particle state in $\phi^4$ theory

I'm quite happy with the idea that a multi-particle state in a free scalar field theory has a discrete energy spectrum, and that turning on a quartic coupling $\frac{\lambda}{4!}\phi^4$ acts as a ...
2
votes
1answer
68 views

What is the axial current?

The axial current is defined as $$j^\mu_5 = \bar{\psi} \gamma^\mu \gamma_5 \psi.$$ This quantity is important when studying anomalies. Explicitly working out components, the axial current is just the ...
0
votes
0answers
59 views

Decay width in 2 & 3 body decays, calculating momentum integrals

I'm considering a toy model with two types of scalar particles, one massive $(\Phi)$ and one massless $(\phi)$ with an interaction of the form $$L_{int}=-\lambda \phi\phi\Phi$$ I'm interested in a ...
2
votes
0answers
73 views

Feynman rules from interaction Lagrangian with electromagnetic tensor (vertex)

I am currently studying for my QFT exam and in particular learning the methods of reading the Feynman rules directly off the Lagrangian. However, I'm still a bit uncertain how to deal with ...
0
votes
0answers
38 views

Confusion over trying to understand spinor components

I've been reading about the quantisation of the Dirac field $\psi(x)$ and it is stated that the general solution to the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi(x)=0$ is given by the ...
0
votes
1answer
82 views

Replica trick for calculating Entanglement Entropy?

This is probably a simple question. Von Neumann entropy is defined to be $$S_A=-tr_A\rho_A \log\rho_A$$. And it's said that it can be calculate from the "Replica trick": $$S_A=\lim_{n\to 1}\frac{tr_A ...
0
votes
0answers
43 views
2
votes
1answer
45 views

Why is the symmetric phase in a Bose gas not superfluid?

In the theory of superfluidity in weakly interacting Bose gases, one finds that in the symmetric phase the exctitations have the dispersion relation $\omega = \frac{k^2}{2m}-\mu$ with gap ...
0
votes
0answers
28 views

can different force fields interfere (create interference patterns)

Edit: I have rewritten the question for clarity. I know waves of photons can interfere eachother. What about if you mixed waves of photos with w and z bosons? What about gravitons (if they exist) ...
0
votes
0answers
32 views

$\mathcal{N} = 4$ Super-Yang Mills propagators

In $\mathcal{N} = 4$ Super-Yang mills there are only massless particles. If one wishes to obtain a heavy quark one can see the SYM theory as a stack of (N+1)-branes in AdS$_5 \times$S$^5$ where one ...
0
votes
0answers
33 views

Obtaining the $s,t,u$ Feynman diagrams by Wick contraction

Consider a real scalar field described through the following lagrangian $$\mathcal L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi - \frac{1}{2}m^2 \phi^2 - \frac{g}{3!}\phi^3$$ The second ...
0
votes
0answers
35 views

Why is the bosonic Casimir force attractive while the fermionic CF is repulsive?

Why is the bosonic Casimir force (CF) attractive while the fermionic CF is repulsive? I looked up for many papers and books but all are focused on boundary conditions. I didn't find any conceptual ...