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
12 views

Closed form expression for the partial decay widths of Higgs boson in massive vector bosons

Can anybody help me obtain a closed form expression for the Higgs partial decay width into massive vector bosons (off shell decays)? I am writing code for the partial decay widths of the Higgs and ...
0
votes
1answer
47 views

Feynman diagram elementary vertex with 4 lines?

Are there processes that require vertices with 4 lines in a Feynman diagram? (And cannot be written as composition of 3-line vertices?) If not, is it matter of models we use (where there are no ...
6
votes
1answer
93 views

Which inverse of $-(\partial^2 + m^2)$ should be used in the path integral?

The partition functional for free scalar field is $$Z=\int D\varphi e^{i\int d^4x[-\frac{1}{2}\varphi (\partial^2+m^2)\varphi+J\varphi]}.\tag{1}$$ To evaluate this functional integral, we usually ...
1
vote
2answers
46 views

An integral in mass renormalization in Peskin and Schroeder

I cannot figure out an integral (which involves certain approximations) in the textbook Quantum Field Theory by Peskin and Schroeder. On P.220 Eq.(7.28-29), it is mentioned that the integral (7.28) ...
0
votes
1answer
48 views

An Integral involving solid angle in Peskin and Schroeder

I cannot figure out an integral in the textbook Quantum Field Theory by Peskin and Schroeder. On P.201 the integral above Eq.(6.70), the relevant part in question reads $$\int\frac{\mathrm d\Omega_k}...
1
vote
0answers
15 views

How can tree level amplitudes have poles? And how can amplitudes have dimensions?

Consider the $\phi^{3}$ theory, whose lagrangian is $\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{3!}\phi^{3}$ The amplitude for tree level (2->1) process is simply ...
1
vote
0answers
34 views

irrational conformal dimension

I know examples of Conformal Field Theories in which the scaling dimension of certain operators is an integer number or a fractional number. However I do not know any example in which the scaling ...
1
vote
1answer
52 views

Spinors in 2+1 dimensions

I am trying to understand representations of the Poincare/Lorentz group, and in particular spinors, in 2+1 dimensions. I know some of the math, but I'm not sure about the physical interpretation of it ...
1
vote
0answers
50 views

Superfields in 2D SUSY

Many textbooks present expressions for superfields in $4$ dimensions. For my current project, I have to find out how things work in $2$ dimensions. Let me summarise in short what we know about $4$d (...
-2
votes
0answers
66 views

why exactly do we use regulators for infinite sums? [duplicate]

Disclaimer: I really apologize for not being educated in QFT a priori. Im trying to learn. I really really am. I am a doctor of physics but i sadly never took QFT in my program and so im now ...
-4
votes
1answer
78 views

Where do people go (online) to present big ideas they have discovered? [closed]

I can't realistically travel, but is there somewhere online where I can present some ideas? Or do I just put it on arXiv and hope someone important reads it?
5
votes
1answer
167 views

When particle number can change in quantum physics?

Let me write a paragraph from D.Tong lecture notes on QFT-chapter2 when he is talking about non-relativistic limit of scalar quantum field theory : A related fact is that the conserved charge $Q=\...
4
votes
1answer
82 views

Lie Algebra for fermion fields

A key identity (e.g. when deriving BRST symmetry for gauge fields) is that: $$[c,d]_a =f_{abc}c_b d_c$$ where $c$ and $d$ are both Fermion Fields. How do I derive this from the lie algebra ...
3
votes
1answer
168 views

How are Clifford algebras related to Dirac Equation

Given a vector space $V$ and a quadratic form $q$ for the vector space. The tensor algebra is defined as $\mathcal{T}(V)=\sum_{i=1}^{\infty} V^{\otimes i}$. The set $\mathcal{I}=\{x\otimes x-q(x)\cdot ...
5
votes
1answer
69 views

Shifting integration variable and taking derivative seemingly giving problem

I am doing loop integral in quantum field theory, and an issue in shifting integration variable is giving me a problem. Let me illustrate with an example. I have an integral that looks approximately ...
-5
votes
0answers
62 views

Does string theory predict QFT? [duplicate]

Does string theory predict QFT? Or is it only consistent with it? Or is it build-in from the start?
1
vote
0answers
41 views

Vertex renormalization and the probability to produce $n$ soft photons

On P. 208 of the book An Introduction of Quantum Field Theory by Peskin and Schroeder, the probability of production $n$ soft photos all with with energies between $E_- < E < E_+$ is discussed (...
0
votes
0answers
45 views

Examples of other hierarchy problems

The commonly quoted version of the hierarchy problem (at least, the one that I have heard), is concerned with the surprisingly low mass of the Higgs. We would expect the Higgs mass squared to have ...
1
vote
2answers
80 views

De Broglie- Bohm Quantum Theory

From what I have read the Standard Model of Particle Physics uses quantum mechanics,special relativity, along with other assorted mathematics to make predictions and provide a framework for QED, QCD, ...
1
vote
1answer
37 views

Why can precomputed sets of lattice QFT field configurations be used to measure arbitrary observables?

My knowledge of quantum mechanics is rusty and my understanding of (lattice) quantum field theory on a very novice level at best, so it is likely my whole question is based on completely wrong ...
0
votes
1answer
27 views

Can CP-violation arise due to interference between two tree-level diagrams in a QFT?

In Leptogenesis, CP-asymetry arises due to the interference of the tree-level amplitude $N\rightarrow l_\alpha\phi$ (where $N$ is heavy sterile neutrino, $l_\alpha$ is a lepton flavour, and $\phi$ is ...
3
votes
1answer
268 views

Understanding CP-violation from a toy model of two fermions and a scalar boson

Consider a field theory given by the following Lagrangian $$\mathcal{L}_{int}=y\overline{\psi_1}\psi_2\phi+y^*\overline{\psi}_2\psi_1\phi^\dagger$$ where $\phi$ is a complex scalar field, and $\psi_1,\...
2
votes
4answers
123 views

How can fields interaction give rise to particles?

We say light a matter-wave, meaning along with its wave property it shows particle nature. But how can fields interaction (electric and magnetic) give rise to particles (photon)? I wish someone could ...
0
votes
1answer
32 views

constraints on quartic interaction coefficients in double scalar field Lagrangian

Consider the 4-dimensional Lagrangian density with two real scalar fields $\phi_1$ and $\phi_2$: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi_1 \partial^{\mu}\phi_1 + \frac{1}{2}\partial_{\mu}\phi_2 \...
2
votes
0answers
40 views

Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
4
votes
1answer
115 views

What is the matrix representation of the momentum operator (generator of translations) that is used in the commutators of the Poincaré Group?

So the commutators of the Poincareé group are given by \begin{eqnarray} [J_{i},P_{j}]=i\epsilon_{ijk}P_{k}, \quad [J_{i},J_{j}]=i\epsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\epsilon_{ijk}K_{k}, \quad [...
1
vote
1answer
39 views

Is the reduction of tensor loop integrals to scalar integrals using Passarino Veltman Functions, theory dependent?

While reducing the tensor integrals to scalar integrals all that we use are Lorentz covariance and the physical interpretation of the result. Thus I think that the Pa Ve Reduction of Tensor integrals ...
0
votes
0answers
39 views

Why must the Vacuum Manifold contain the quotient group?

For a symmetry breaking pattern $G \rightarrow H$, the vacuum manifold must contain the quotient space $G/H$. In most cases, we take the vacuum manifold to be the quotient space. My question is, Is ...
1
vote
2answers
65 views

Interpretation of the mass of the field

Before QFT I had never thought if a field should or should not have any mass. Now it turns out that either case is possible. It might be naive to think this way, but I picture the mass of the field in ...
-1
votes
0answers
30 views

Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...
1
vote
1answer
74 views

Euler-Lagrange Equation in Quantum Field Theory

The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a ...
1
vote
0answers
24 views

Construction of Primaries of WZWN CFT

Is it possible to construct primaries of $SU(2)_{k+1}$ by using primaries of lower levels?. E.g. If I have a primary of $SU(2)_2$, let's say $\Phi^{(1/2)}$, the field with spin $1/2$ and another ...
9
votes
3answers
111 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
1
vote
0answers
106 views

Are strings in string theory actually little black holes? [closed]

I sometimes read that strings in string theory are actually little black holes, or can be interpreted that way. Is this true? How is that consistent with that the particle that a string represents ...
1
vote
1answer
69 views

What is the difference between worldsheet supersymmetry and spacetime supersymmetry?

What is the difference between worldsheet supersymmetry and spacetime supersymmetry? For worldline formulation of fermions quantum mechanics, there is a supersymmetry. But the corresponding spacetime ...
2
votes
1answer
73 views

R-matrix and S-matrix in QFT

In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-...
1
vote
1answer
50 views

Vacuum persistance amplitude

E. Fradkin's Field Theories in Condensed Matter Physics formulas 3.57 and 3.58: I feel really sad about it, but all my tries of getting from formula $$ Z = \operatorname{tr} \hat{T} \prod_{j=1}^{...
6
votes
3answers
249 views

Are there Gauge fields that are not 4-vectors?

In my understanding Gauge fields are fields that have some kind of redundancy, i.e. a transformation that does not change the physical state. As far as I can see all the Gauge fields in the Standard ...
2
votes
2answers
129 views

What is the meaning of the size of an elementary particle in QFT? What is the meaning of a point particle? [duplicate]

I have often seen people refer to the size of a particle being at most a given value, or a particle being a point particle, in the context of quantum field theory. Examples are the Wikipedia entry on ...
3
votes
0answers
25 views

Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
4
votes
0answers
53 views

Does Feynman parametrization commute with derivative?

Let $I = \int \frac{d^4k}{(2\pi)^4} \frac{(p+k)\cdot\gamma}{(p+k)^2-m^2+i\epsilon} \frac{1}{k^2+i\epsilon}$ I would like to do two operations on the integral, namely Feynman parametrization and $\...
-1
votes
1answer
64 views

Such a huge mass for Higgs boson? And how can it, as a quantum, decay?

With a mass of 126GeV/c2 Higgs boson would have a mass slightly greater than a caesium atom. Isn't it too much? Wouldn't be in this way the ubiquitous Higgs field so dense to cause problems for the ...
2
votes
2answers
101 views

Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
2
votes
2answers
55 views

Does QFT modifies Quantum Mechanics? [duplicate]

The basis of Quantum Mechanics is contained in the postulates which tell us how to describe quantum systems (below I disconsider possibly degenerate spectra just for simplicity): To describe a ...
5
votes
1answer
54 views

How to define the distance between two points in a conformal transformed space?

Consider a particular conformal transformation $x^\mu\rightarrow x'^\mu$, and the metric of a flat space transforms in the following way, $$\eta_{\mu\nu}\rightarrow g'_{\mu\nu}=\Lambda^2(x)\eta_{\mu\...
1
vote
0answers
38 views

Is it possible in this Universe to communicate a bit of information with energy that scales sub-linearly with distance?

If we look at all the ways that people do communicate information, they all seem to have a cost "at least linear in distance." For example, communicating over a wire has attenutation, so the energy ...
4
votes
1answer
87 views

Is the usage of the Fock space a postulate in QFT?

In this question, when I write Fock space, I mean "the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H", as it is described by Wikipedia. ...
3
votes
1answer
41 views

Experimental observation of non-perturbative effects

Many quantum field theories come with non-perturbative objects such as solitons and instantons, and non-perturbative effects such as the Schwinger effect. However, it is hard to find any review on ...
1
vote
1answer
110 views

A question from A. Zee's book

On page 463, it writes in eq. (3) $$4H=\Sigma_\alpha(Q_\alpha Q^\dagger_\alpha+Q^\dagger_\alpha Q_\alpha).\tag 3$$ And then it writes that this is followed by eq.(4) as $$\langle S| H|S\rangle=\frac{...
2
votes
0answers
18 views