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
49 views

A special path integral

May be $f(\vec{x}), \vec{g}(\vec{x})$ an arbitrary functions dependent on the coordinates $\vec{x}=(x,y,z)^T$. Defining the following function dependent on a 3-dimensional curve $\vec{\gamma(t)}$ ...
0
votes
1answer
79 views

Photons acting as carriers of both attractive and repulsive forces

I understand, in basic terms, how a photon, whilst not being electrically charged itself, is viewed as creating electrical repulsion by means of positive momomentum transfer between two negatively ...
2
votes
0answers
26 views

Parker-Taylor formula in the $n=4$ simple case

I am trying to do ex. 2.23 of http://arxiv.org/pdf/1308.1697v2.pdf. I have chosen as reference spinors $q_1,q_2 = p_3$ and $q_3,q_4 = p_1$. Therefore if I compute $A^4[1^- 2^- 3^+ 4^+]$ the ...
0
votes
0answers
19 views

complex scalar field as a sum of scalar and pseudoscalar fields

Let's consider theory of a complex scalar field $$\phi = \frac{1}{\sqrt{2}}(s+\imath p)$$ Is it true that under CPT transformations $s$ is a scalar field and $p$ is a pseudoscalar field?
2
votes
0answers
27 views

How do I arrive at the perturbative expansion of a proper n-vertex from the Effective Action without resorting to Feynman Diagrams?

I am especially interested in the expansion of a 4-vertex which is the sum of 1PI diagrams in the expansion of the 4-point connected correlation function.
4
votes
1answer
98 views

Which cardinality of infinities are subtracted in the renormalisation of quantum field theory?

In quantum field theory, e.g. in quantum electrodynamics, renormalisation is used to make sense of an infinite number of virtual particles. This, crudely, involves the subtraction of infinities. But ...
3
votes
3answers
211 views

Are electrons held together by vacuum energy?

If one models the electron as a hollow spherical conductor with charge $e$ and radius $a$ then its electrostatic energy is given by: $$E_{em}=\frac{1}{2}\frac{e^2}{4\pi\epsilon_0a}$$ However if one ...
3
votes
1answer
78 views

About $SU(2)_L \times U(1)_L = U(2)_L $

In the many textbook of standard model, i encounter the relation \begin{align} SU(2)_L \times U(1)_L ~=~ U(2)_L. \end{align} Here $L$ means the left-handness. (It is a physical ...
1
vote
1answer
106 views

Why are right hand neutrinos unaffected by all forces except gravity

I'm curious as to something I read on Berkeley's website. Does anyone happen to know why, according to this model,right hand neutrinos are unaffected by all forces except gravity? (Model taken from ...
3
votes
0answers
48 views

Are the following terms, related to scale invariance and renormalization in QFT, equivalent?

Which of the following terms are equivalent? and in what cases/limits do the non-equivalent terms become equivalent? A) a scale invariant quantum field theory. B) a conformal quantum field theory. ...
2
votes
0answers
42 views

Asymptotic behavior of Euclidean correlators in QCD

I am reading an old review paper (http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.65.1). In the beginning it makes the following statement (I copy with slightly different notation). If we ...
4
votes
0answers
37 views

Recommendation about higher derivative theory

Are there some textbook or review about following parts of higher derivative Lagrangian? How to figure out the degrees of freedom of higher derivative theory? How to analyse the stability of a ...
2
votes
1answer
52 views

Pion decay into electron and anti-neutrino

In Peskin and Schroeder Books Chapter 5 subsubection Bound State equation (5.43) $\mathcal{M}(\uparrow \uparrow \rightarrow B)=\sqrt{2M}\int ...
2
votes
1answer
80 views

Why don't virtual particles violate conservation of mass/energy?

If virtual particles sometimes add more mass/energy to a system then was inputed or comes out in the output, how do they not violate conservation of mass/energy.
1
vote
1answer
49 views

What are the quantum numbers of Majorana neutrinos?

I have a question about majorana neutrinos. Majorana particles are particles that are their own antiparticle. From this I would argue that they need to have all quantum numbers equal to zero. My ...
5
votes
0answers
60 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 ...
5
votes
0answers
66 views

Intuition for Homological Mirror Symmetry

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 ...
0
votes
0answers
47 views

General solution of the four-vector with each component satisfying the wave-equation

Maybe this is more appropriate for Math stackexchange, but this question regards the solution we use in order to find representation for massive / massless spin-1 particle. When $$(\Box + m^2)A_\mu = ...
1
vote
0answers
52 views

How to find creation and annihilation operators? [duplicate]

I get confused when trying to find this. Please describe it as simply as possible, but keep in mind I have no budget whatsoever to pay for textbooks, so here goes: How do you find the creation and ...
3
votes
1answer
72 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
106 views

Writing scalar quantum field as mode expansion form for interacting theory

We know that for Klein-Gordon Equation, quantum field can be written in the form $$\phi(\mathbf{x},t) = \int \frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}[a_p e^{-ipx} + a^\dagger_p e^{ipx}]$$ It ...
1
vote
0answers
33 views

The meaning of keeping the bare parameters fixed

So, this question concerns two different kinds of renormalization group equations. I would like some clarifications, if possible. The usual RG equations taught in QFT courses, like the ...
0
votes
2answers
51 views

Why are the charge operator $Q$ and the baryon number operator $B$ unbounded?

A friend recommended me to read PCT, Spin and Statistics, and All That written by R. F. Streater and A. S. Wightman. In page 5 to 6, here's what the authors of this book have to say: [...] In ...
2
votes
0answers
40 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and then ...
1
vote
0answers
29 views

How to parametrize off-shellness?

The energy of a massive on-shell particle of mass $m$ and three-momentum $\vec{p}$ satisfies $$E_\vec{p} = \sqrt{\vec{p}^2+m^2}. $$ What would be the analogous expression for an off-shell particle? ...
0
votes
1answer
56 views

Why 5D gauge theory is non-renormalizable?

My question is following "Why 5D gauge theory is non-renormalizable?" Here I treat $5D$ supersymmetric gauge theories. Also I heard Non-renormalizablity of $5D$ gauge theories implies the ...
0
votes
1answer
48 views

Neutrino mass and the Majorana equation

I can't seem find this on the Internet. What does the Majorana equation predict neutrino masses to be (if they were their own antiparticle), and how? (I have little understanding of spinors, btw...) ...
4
votes
3answers
104 views

What is the relationship between vibration of the field and quantum fluctuation?

Consider a free field like the KG equation. I see that why $$\tilde \phi(\mathbf{p},t)$$ a momentum-dependent quantity, is an oscillator, vibrating at a frequency because when we apply the Fourier ...
0
votes
1answer
64 views

Time-dependence of ladder operators in quantized EM fields

My Question Are the operators for the $A$, $E$ and $B$ field to be treated as operators in a Heisenberg description or is their time dependence explicit when performing a textbook EM quantization as ...
3
votes
1answer
53 views

Quantization of a free field: Klein-Gordon case

I am a beginner and reading this course text on QFT. The author first introduces the KG equation: $$\partial_\mu\partial^{\mu}\phi+m^2\phi=0$$ [with Minkowski signature $(+,-,-,-)$]. Then the ...
3
votes
0answers
51 views

Feynman Propagator in Position Space through Schwinger Parameter

So I am aware of a thread at Propagator of a scalar in position space but it does not answer my question, which is more about poles in position space. Starting from $$D_F(x_1-x_2) = \int \frac{d^4 ...
1
vote
0answers
43 views

Shifting the integration variable in loop integrals

We know that, in four dimensions, shifting the integration variables is valid only for convergent and logarithmically divergent integrals. If we employ a hard cutoff $\Lambda$, is it permissible to ...
-1
votes
1answer
64 views

Why renormalizable theory is useful?

Why renormalizable theory is useful? I want to know detail reason for above question. At a glance, I know following things. In quantum field theory, $i.e$ computing self-energy(or self-interaction) ...
0
votes
0answers
32 views

The limited Computing Capabilities of Space, Increased quantized info leads to time-dilation?

Are there any approaches to Special and General Relativity using space as a computing medium? With space having a maximum computing capability and time dilation as lag? Could this idea describe the ...
4
votes
3answers
465 views

Does the need for renormalization in QFT vanish once you use a more fundamental theory (e.g., string theory)?

It is often explained that renormalization arises in QFT because QFT is a low-energy effective theory that needs to be replaced by a more fundamental theory at higher energies/smaller distances. While ...
6
votes
2answers
524 views

How is a blackbody spectrum formed in the Sun?

Sunlight can be treated as BB radiation. Why is it a continuous spectrum while the sun contains only a few elements and the radiation from the jumps between atomic levels are discrete? How does the ...
0
votes
2answers
50 views

Incorrect proof that all gauge theories are abelian

Consider a gauge field $W_\mu = W_\mu^{a} \tau_a$ where $\tau_a$ are the generators of the Lie algebra and $W_\mu^{a}$ just numbers. Then: $$ W^2 = W_\mu W^\mu = W_\mu^a\tau_a W^{\mu b} \tau_b = ...
1
vote
1answer
57 views

vanishing of $\Pi^0$ and non-existence of propagator

We know that if we try to quantize the free electromagnetic field without a gauge fixing term added to the Lagrangian, then one of the conjugate momentum density $\Pi^0$ vanishes. We also find that ...
1
vote
1answer
70 views

How could the effective electric dipole interaction be derived

In some papers (e.g. Bernreuther equation (1.4), The electric dipole moment of the electron) you can find the electric dipole interaction defined as $$L_I=-\frac i2 ...
0
votes
0answers
28 views

How to calculate explicitly the *external leg correction* diagram

I tried to calculate the Amplitude of the external leg correction of figure 6.1 in Peskin&Schroeder. I focus on the diagram with one incomming charged fermion $f^-$ (with momentum $p'$), then a ...
2
votes
1answer
52 views

How does a laser emit light in a coherent state?

Lasers work by stimulated emission of atomic transitions. Stimulated emission produces two photons which, because the particle number is well-defined, projects the field into a Fock state. However, it ...
5
votes
0answers
204 views

Quantum fields from cluster-decomposition principle

I would like help proving Weinberg's claim (I've quoted him below) that quantum fields are an unavoidable consequence of merging particle-based quantum mechanics with both Lorentz invariance and the ...
0
votes
0answers
53 views

Is the elementary charge really a constant of nature? - Accuracy of QED

There are a couple of natural constants; examples are Planck's constant or the Speed of light in vacuum. The elementary Charge is the coupling factor to all Kind of electromagnetic interactions; this ...
1
vote
0answers
26 views

Defining a gauge field for an anisotropic material under strain

I have a Hamiltonian for a system which is somewhat analogous to graphene but with additional degrees of freedom. The Hamiltonian is $H=\sum_q \Psi^\dagger \mathcal{H}\Psi$ where ...
4
votes
1answer
148 views

Does magnetic monopole violate $U(1)$ gauge symmetry?

Does a magnetic monopole violate $U(1)$ gauge symmetry? In what sense and why? Insofar as I know, there are at least two types of magnetic monopoles. One is the Dirac monopole while the other is the ...
3
votes
1answer
106 views

Missing a factor of $\sqrt{\frac{\hbar}{m}}$ in a QFT Practice Problem. Can someone explain why?

I am doing problem 2.3 on page 27 of Quantum Field Theory for the Gifted Amateur. Use eqns 2.46 and 2.62 to show that \begin{equation} \hat{x}_j = \frac{1}{\sqrt{N}} ...
0
votes
0answers
43 views

Physical meaning of the coupling matrix in Fermi golden rule

I am calculating the energy transfer rate using Fermi golden rule where the coupling matrix $M$ is obtained using second order pertubation method. $$ \Gamma_{tran}=\frac{2\pi}{\hslash}|M|^{2}\rho$$ ...
1
vote
0answers
36 views

Running of the Higgs mu term (or: running of individual mass terms in a complicated mass matrix)

I am wondering how to calculate the (one-loop) beta function for an individual mass term that appears in combination with a number of other mass terms in the coefficients of a number of fields. What ...
3
votes
1answer
100 views

Tadpole diagrams in $\phi^3$ theory

In "Quantum Field Theory" by Mark Srednicki, Chapter 9 page 67, after he proves that $\langle 0|\phi(x)|0 \rangle$ vanishes (meaning sum of all connected diagrams with a single source is zero), he ...
11
votes
0answers
287 views

Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...