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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Coset construction of Tricritical Ising CFT

In http://iopscience.iop.org/1742-5468/2008/03/P03010 the authors state that the Tricritical Ising Model (TIM) CFT can be obtained from a Wess Zumino Witten construction based in the coset ...
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219 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 ...
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131 views

What is the difference between the Higgs Boson particle and an electron moving through the Higgs field?

I am watching a lecture by Sean Caroll titled "Particles, Fields, and the Future of Physics". I am not a physicist by any means but enjoy the subject in my spare time hoping to understand it. This ...
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427 views

Hawking Radiation: how does a particle ever cross the event horizon?

The heuristic argument for Hawking Radiation is, that a virtual pair-production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation. ...
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106 views

Why does the electric field escape a black hole? [duplicate]

An (unlikely) charged black hole can be described with the mass, angular momentum, charge and the thermal radiation. The reasoning behind the thermal radiation rests on the particle creation outside ...
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267 views

How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
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76 views

Clarification: Why the gauge symmetry of pure Yang-Mills is $PU(n)$ and not $SU(n)$? [closed]

I am quoting the following from the Wikipedia article on the projective unitary group: In the pure Yang–Mills $SU(n)$ gauge theory, which is a gauge theory with only gluons and no fundamental ...
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73 views

Connection of “spin” to conformal dimension

I have read The spin and weight of a primary field in CFT but it does not answer my question, short of a restatement of the question itself. So I hope this post does not risk being removed.. In ...
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644 views

the causality and the anti-particles

How can I quantitatively and qualitatively understand the fact that there is a relevence between the existence of anti-particles and the causality?
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1answer
171 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 ...
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38 views

Can quantum fluctuation happen outside space-time? [duplicate]

So far I know, quantum fluctuations happen inside the vacuum which resides in the space-time. So, can it happen outside space-time? Because, one proposition suggest, big-bang was result of some kind ...
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Renormalization group and minimum substraction

I have several questions about renormalization group and minimum substraction scheme in particular. My first question is: 1) Why is the beta function typically just a function of coupling? In other ...
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655 views

Wick rotation and spinors

I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; ...
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69 views

Expressing the Schrödinger equation in terms of spinors

I appreciate that the Dirac equation can be thought of in terms of spinors, as it directly implies the presence of spin, in addition to initiating the concept of treating fields as operators. From ...
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131 views

Can the Higgs condensate be described in terms of creation operators?

In superconductivity, the BCS condensate can be described in terms of 2 creation operators (the 2 electrons of the pair) acting on the vacuum. I'm wondering whether a similar description can be given ...
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1answer
191 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
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51 views

Green's Functions from Gell-Mann and Low Theorem

What I want to do: $\newcommand{\ket}[1]{\left|#1\right\rangle}$ $\newcommand{\bra}[1]{\left\langle#1\right|}$ $\newcommand{\braket}[1]{\left\langle#1\right\rangle}$ The Gell-Mann Low Theorem tells ...
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42 views

W boson one loop electroweak contribution to muon g-2

I want to calculate the one loop W boson contribution (triple gauge boson vertex WW-Photon) to the muon anomalous magnetic moment g-2 with the help of Dimensional Regularization. Diagram given below: ...
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464 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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761 views

Is Maxwell's field the wave function of the photon?

In his ArXiv paper What is Quantum Field Theory, and What Did We Think It Is? Weinberg states on page 2: In fact, it was quite soon after the Born–Heisenberg–Jordan paper of 1926 that the idea ...
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How does the electric field operator change inside an optical cavity

In the free field, transverse electric field operator is given by the below expression; $$d^{\bot}(R)=i \sum_{p,\lambda}\Big( \frac{\hbar cq}{2V\epsilon_{0}}\Big)^{1/2} ...
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Is a “third quantization” possible?

Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
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Differential geometry of Lie groups

In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they ...
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Writing down many particle Hamiltonian

We are given that \begin{align}\mathrm{tr} e^{-\frac{i}{\hbar}\hat{H}t}&= \int D[a_1,\dots,a_n]\times\\&\qquad\exp\left[\int_0^t dt' \left(\frac{1}{2}\sum_j ...
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60 views

Most general separable solution of free Dirac equation

In relativistic quantum mechanics, the solution of the free Dirac equation is assumed to be $$\Psi(\textbf{r},t)=u(\textbf{p})e^{i(\textbf{p}\cdot \textbf{r}-Et)}$$ How do I know that this is the most ...
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102 views

Photon polarization sum prescription in $e^-e^+\to{}2\gamma$

In calculating the amplitude for the process $e^-\gamma\to{}e^-\gamma$ the substitution $\sum\epsilon_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$ is useful to sum over photon polarizations. If we ...
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How do you simulate chiral gauge theories on a computer?

David Tong and Lubos Motl have argued that our universe can't possibly be a digital computer simulation because chiral gauge theories can't be discretized, and the Standard Model is a chiral gauge ...
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Invariance under charge conjugation… Or not?

I have read some paper which says that the electroweak Lagrangian includes these terms like $\bar{\psi} \gamma_a\gamma_5\psi$ and $\bar{\psi} \gamma_a \psi$. They violate charge conjugation symmetry. ...
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40 views

How many photons are absorbed during Rabi oscillations?

In my understanding, Rabi oscillations are derived using the classical approximation for the electromagnetic field. I don't get how this picture fits with a quantized EM field though. Say you excite a ...
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4answers
649 views

Dirac equation as Hamiltonian system

Let us consider Dirac equation $$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$ as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
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489 views

Theory that gets rid of dark matter/energy

Is there any physics theory that either groups together gravity and dark energy/dark matter or eliminates dark energy/dark matter by modifying standard understanding of gravity or any force? If so, ...
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65 views

Why photon propagator has metric tensor additionally?

Klein Gordon propagator is (Peskin p-30) $$ D_F(x-y)=\frac{i}{p^2-m^2} $$ which is actually Green function of KG field. But photon has $g_{\mu\nu}$ additionally in the numerator. I would expect its' ...
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Range Of An Interaction

Why is the Compton wavelength $\lambda_c=\frac{\hbar}{mc}$ used as a sensible measure for the range of an interaction, where $m$ is the mass of the corresponding mediator?
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What is the Meaning of the equation $\frac{d\sigma}{d\Omega}=\left|f(\theta,\phi)\right|^2$

In the "Preface for Students" of the book "Quantum Field Theory" by Mark Srednicki is a set of equations. Quoting from the author: "In order to be prepared to undertake the study of quantum field ...
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QFT and violation of Heisenberg uncertainty principle

In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time: $$\Delta t<\dfrac{\hbar}{2\Delta E}$$ ...
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105 views

Perspectives of QFT [closed]

From the answer to this question Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, I have discovered that there is two perspectives to QFT. I am doing a course which is unfortunately a summary of QFT and ...
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Why are $SU(N)$ gauge theories easier to handle for $N\rightarrow \infty$?

I was wondering if there was a intuitive/heuristic argument to understand why generalizing the QCD gauge group $SU(3)$ to $SU(N)$ and taking $N\rightarrow \infty$ simplifies the analysis of the ...
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Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

I suppose there was a discussion already on speed-of-gravity-and-speed-of-light. But I silly wonder whether all the massless mediators of four fundamental forces, i.e. Graviton: $g_{\mu\nu}$ ...
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86 views

Is there any theory in physics that might support the existence of tachyons?

According to Einstein, we all know that light is the fastest thing and it's impossible to beat it's speed. But isn't there a way to go around this? I read somewhere that tachyons gain speed per the ...
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177 views

Why isn't the path integral rigorous?

I've recently been reading Path Integrals and Quantum Processes by Mark Swanson; it's an excellent and pedagogical introduction to the Path Integral formulation. He derives the path integral and shows ...
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51 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 $\vec{\gamma(t)}$ ...
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1answer
81 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 ...
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546 views

Why are only logarithmic divergence relevant for the Callan-Symanzik equation? Intuitive understanding?

I may be wrong, but it seems that only logarithmic divergences need to be retained when using the Callan-Symanzik equation, finding running couplings, etc. Why is this the case? Is there some simple ...
3
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3answers
216 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 ...
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1answer
94 views

Can we measure the electron spin independently of its magnetic moment?

What experimental evidence do we have for the intrinsic angular momentum of the electron (its spin)? I am specifically interested in whether we have a value for this that is independent of the ...
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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 ...
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1answer
82 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 ...
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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?
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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...