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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8
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2answers
403 views

Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
-2
votes
0answers
18 views

Wick's theorem and

Please, help me to calculate this integral: $$\int\limits_{-\infty}^{\infty} \, d\vec{x} \, x_1 x_2 e^{-1/2 \cdot xkx}\left(1-\frac{g}{4!}\sum x_i^4 + \frac{g^2}{2!(4!)^2}\left(\sum x_i^4 \right)^2 - ...
0
votes
1answer
30 views

Placement of indices in canonical commutation relations of coordinates and conjugate momenta as well as fields and conjugate momenta

The canonical commutation relations between generalised coordinates $q_a$ and their conjugate momenta $p^a$ are given by $[q_a,q_b]=[p^a,p^b]=0$ $[q_a,p^b]=i\delta^b_a$. Furthermore, the canonical ...
5
votes
1answer
70 views

Spontaneous symmetry breaking of a spinor / vector field

Why does SSB deal only with scalar fields and not with fermion or vector fields? My professor told me that it's closely related to the Lorentz invariance of the theory, but I don't understand at all ...
3
votes
3answers
976 views

Why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
3
votes
1answer
399 views

Do we need virtual particles?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
6
votes
2answers
455 views

QFT question, scalar field and so on

$\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle} \newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle #1 |}$ I have a problem with a proof. I'm studying the two point correlation ...
7
votes
0answers
255 views

Regulating the sum in Casimir Force

I am trying to evaluate the Casimir force using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum $$ ...
3
votes
0answers
54 views

S-matrix and derivative interaction

I just read in some lecture notes that formally we can write the S Matrix as: $$S=T(e^{-\int_{-\infty}^{+\infty} H_{int}dt}) $$ Where $T$ is the normal product and $H_{int}$ is in the interaction ...
0
votes
0answers
16 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
1
vote
1answer
54 views

Time-ordered product of two normal-ordered products of fields

Suppose you have a scalar field theory with field operators $\phi(x)=\phi(x)_+ + \phi(x)_- $ that can be decomposed into terms of annihilation and destruction operators. Let $$ D(x-y) = ...
1
vote
0answers
54 views

Path integral (sum over paths where $v>c$) [on hold]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
5
votes
1answer
306 views

Antiparticles, charge conjugation and chirality

(Why/how) are antiparticles and charge-conjugates different things? I am trying to understand the effect of discrete symmetries on spinor fields (neutrinos in particular). In the article, Dirac, ...
0
votes
0answers
16 views

Superficial degree of divergence for scalar theories

I have a few questions regarding the derivation of the degree of divergence for feynman diagrams. The result is $$D = [g_E] - \sum_{n=3}^{\infty} V_n [g_n]$$ (following notation in Srednicki, $P118$) ...
0
votes
0answers
28 views

What is quantum foam?

Can someone please explain me what quantum foam is? Is it the space-time fabric or just any other field? Also please explain this image
0
votes
0answers
10 views

Deep Inelastic Scattering - electromagnetic current

When one tries to compute the deep inelastic scattering for the process: where $l$ is a lepton with incoming momentum $k$ and outgoing $k'$, $h$ is an hadron with momentum $P$, $q$ denotes some ...
0
votes
0answers
38 views

Entanglement in Quantum field theory [duplicate]

How is entanglement represented in a field theory? For instance how can I represent a maximally entangled state such as a Bell state? Would such an approach also apply in a Conformal field theory ...
1
vote
2answers
226 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
2
votes
1answer
91 views

What does it mean by “infinities” when dealing with QFT? [on hold]

I found this PDF online here while browsing Nobel Prize winner contributions, which explains a bit about renormalization (a concept for which Kenneth G. Wilson won the Nobel). However I was somewhat ...
6
votes
2answers
1k 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? ...
4
votes
2answers
106 views

Are the path integral formalism and the operator formalism inequivalent?

Abstract The definition of the propagator $\Delta(x)$ in the path integral formalism (PI) is different from the definition in the operator formalism (OF). In general the definitions agree, but it is ...
0
votes
1answer
42 views

Fine structure constant and unit conversion [on hold]

In a paper I'm reading, the author writes down the following formula: $$\Gamma=\dfrac{\alpha^2}{576\pi^3}\dfrac{\left(4+z\right)^2}{z}\dfrac{m^5}{m^2_\pi f_\pi^2}$$ $\Gamma$ is a function of $m$ (in ...
9
votes
1answer
460 views

Calculating $\mathrm{Tr}[\log \Delta_F]$

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
4
votes
2answers
198 views

Why do gauge bosons/leptoquarks not mediate proton decay in the Pati-Salam model?

In the Pati-Salam $\mathrm{SU}(4)_c\times\mathrm{SU}(2)_L\times\mathrm{SU}(2)_R$ model, I see Wikipedia and some slides mention this model doesn't predict gauge mediated proton decay without giving ...
2
votes
1answer
661 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
1
vote
0answers
24 views

Transverse and longitudinal random forces

I am trying to read following article: http://arxiv.org/pdf/1410.1262v1.pdf According to the equation (2.10) and (2.11), the random force is defined as $ \langle f_i(x) \ f_j(x) \rangle = ...
1
vote
1answer
109 views

What are skeleton diagrams and what is their use in qft and many-body physics?

How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, ...
3
votes
1answer
143 views

Is an electron technically a set of two particles?

The electron - described as a four-spinor in the Dirac equation - transforms according to the $(1/2,0)\oplus(0,1/2)$ representation of the Lorentz group, so it is actually a direct sum of a left- and ...
0
votes
1answer
49 views

Coulomb law and photons

When we consider process like $e^- e^- \to e^- e^-$ in QED, we see that from exchanges of one photon (tree-level diagrams) one can obtain Coulomb's law, while loop-diagrams give quantum corrections ...
0
votes
1answer
29 views

Differential cross-section for a 2-particle process in the LAB frame

This should really be a straightforward calculation, but somehow, I keep confusing myself and failing over and over again. I did the calculation so many times that I don't even know what I'm looking ...
3
votes
1answer
65 views

Limits used to find non-rel limit of the Klein-Gordon equation

I just have a question regarding assessing the non-relativistic limit of the Klein-Gordon equation. In the book I'm following (Quantum Mechanics by Bransden & Joachain) they use the limits (Chpt. ...
10
votes
1answer
201 views

Why is the strong CP term $ \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$ never considered for $SU(2)$ or $U(1)$ interactions?

The Lagrangian one would write down naively for QCD is invariant under CP, which is in agreement with all experiments. Nevertheless, if we add the term \begin{equation} \theta \frac{g^2}{32 \pi^2} ...
3
votes
1answer
106 views

How do (and don’t) particles emerge from fields?

I am aware of the following field- and particle-like notions: QFT particle, a unit of excitation in (the Fock space of) a QFT; SR field, an extremal $A = A(\mathbf x)$ of a Lorentz-invariant action; ...
0
votes
0answers
31 views

Wick contraction in proton-pion production

Proton-pion production $\gamma + p \rightarrow \pi^0 + p$ occurs through the interaction hamiltonian $$\mathcal H_{int} = ig \bar \psi^{(p)} \gamma_5 \psi^{(p)} \phi + e \bar \psi^{(p)} \gamma_{\mu} ...
17
votes
3answers
3k views

Equivalence of canonical quantization and path integral quantization

Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance $$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t ...
0
votes
0answers
24 views

Representation of $P_\mu$ on a field [on hold]

So I've been going through a QFT past paper and I seem to be having a particular problem with this one. Consider the space-time transformation of translation $x^\mu\to x^\mu+a^\mu$ where $x^\mu$ is ...
3
votes
1answer
76 views

Symmetry breaking to a special subalgebra?

This is a follow-up to my question here. For regular subalgebras of some group's Lie algebra the root system of the subalgebra is a subset of the root system of the original's group algebra. In ...
0
votes
0answers
38 views

Klein-Gordon field quantization [on hold]

I'm taking my first QFT course and I have a problem when solving the Klein-Gordon equation for a free, non-interacting, field. When solving it, it's made a Fourier transform and expand the field in ...
5
votes
1answer
475 views
5
votes
1answer
71 views

Where does the matching condition for $U(1)$ subgroups come from in unified models?

The matching conditions for a breaking $G \rightarrow \prod_i G_i$ are $$\omega_G-\frac{C_2(G)(\mu)}{12 \pi}=\omega_{G_i}-\frac{C_2(G_i)(\mu)}{12 \pi} ,$$ where $C_2(g)$ denotes the quadratic ...
1
vote
1answer
279 views

Simple QFT simulation - how to do it

I would like to write a simple QFT simulation for a free scalar field with a cubic interaction term. However, I got stuck a bit. I will try to describe what I think I understand. I want to have a ...
10
votes
1answer
294 views

Why can't a real scalar couple to the electromagnetic field?

If we have a complex scalar $\phi$ we know that the gauge-invariant interaction with $A$ is given by $A^\mu J_\mu$, where $J$ is the Noether current of the $U(1)$ symmetry of the Lagrangian $$ ...
6
votes
0answers
65 views

Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
4
votes
0answers
83 views

Two-point function of a free massless scalar field in Euclidean space-time

Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
0
votes
0answers
49 views

Weinberg's QFT I Chapter 1 Problem 1 [closed]

I'm trying to solve the following problem: Suppose that observer $\cal O$ sees a $W$-boson (spin one and mass $m \neq 0$) with momentum $\textbf{p}$ in the $y$-direction and spin $z$-component ...
4
votes
0answers
24 views

Perturbation expansion of effective action

Chapter 11.4 of Peskin & Schroeder's book discussed the computation of effective action, but I don't understand some details of derivation. The book first split the Lagrangian into normal ones and ...
5
votes
1answer
47 views

Supersymmetric background and fermion variations

I'm trying to understand some basic questions about supersymmetric theories in curved backgrounds and supergravity. If I understand it correctly, there's a condition for a background to preserve SUSY, ...
1
vote
1answer
32 views

Estimate mass of exchange boson by decay time

I have made a rough estimate that the minimum lifetime $\tau$ of the proton must be $10^{23} \, \mathrm{s}$. From this I would like to estimate the mass of the X boson which would mediate this decay ...
1
vote
1answer
22 views

Crossing Symmetry in Bhabha scattering and Moller scattering

Given the amplitude for a particular process, it may be possible to obtain the amplitude for another similar process by a so called crossing symmetry. I know there is a $s \leftrightarrow u$ crossing ...
2
votes
1answer
48 views

1-Loop Mass Splitting of vector-like Fermions

In this paper the author argues that for a vector-like fermion doublet, with degenerate mass $M$ at tree level, we always have a mass splitting between the charged component of the doublet $L$ and the ...