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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If subatomic particles pop into existence all the time, why don't I gain weight?

Watching Discovery's first episode of the first season of Curiosity (entitled "Did God Create the Universe?" by Stephen Hawking), I heard this information: [...] you enter a world where conjuring ...
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383 views

Are majorana masses technically natural?

I understand that Dirac masses for fermions are "technically natural" (in the 't Hooft sense of technical naturalness) because they break chiral symmetry. In limit where the Dirac mass goes to zero, ...
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482 views

Open strings from closed strings

This issue comes up in Shiraz's lecture here on 29th October 2008. I understand that he is saying that one can think of closed string theory as having two minima and that the ground state in the non-...
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241 views

When are the OPE relevant?

I've seen OPEs commonly used in 2d CFT, it's quite apparent to me that, in that case, it dresses a bridge between the algebraic and the operator formalism especially when combined with radial ordering ...
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655 views

Why no fundamental force from the Higgs? [duplicate]

I wish to ask whether I understand the following correctly. This universe seems to have six fundamental elementary bosons namely photon $(\gamma),\ W$-bosons$(W^+,W^-),$ gluon$(g),\ Z$-boson $(Z)$, ...
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199 views

Fermion annihilation amplitude

Is there a physical reason why annihilation of 2 identical fermions with mass m to 2 scalars amplitude for $s=4m^2$ (fermions at rest) is zero? For example we can have 2 scalars annihilating in 2 ...
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930 views

What's wrong with this QFT thought experiment?

In quantum field theory, the propagator $D(x-y)$ doesn't vanish for space-like separation. In Zee's book, he claims that this means a particle can leak out of the light-cone. Feynman also gives this ...
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680 views

Born rule for photons: it works, but it shouldn't?

We can observe double-slit diffraction with photons, with light of such low intensity that only one photon is ever in flight at one time. On a sensitive CCD, each photon is observed at exactly one ...
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155 views

Interaction of an electromagnetic wave with a two level system in the domain of quantum field theory

Suppose I shine an electromagnetic wave on a two-level system. I need to describe how the system evolves in context of quantum field theory i.e. using a quantized EM field in the problem. The first ...
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265 views

Integrating out high momentum modes in $\phi^4$ theory

I'm trying to follow section 12.1 of Peskin & Schroeder, which describes how integrating out the high momentum modes of the field in $\phi^4$ theory transforms the Lagrangian both by changing the ...
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141 views

Usefulness of SUSY models when it cannot exist at any non-zero temperature

Unlike other symmetries (like electroweak symmetry), SUSY is spontaneously broken at any non-zero temperature due to some variation of the fact that the boundary conditions on bosons and fermions in ...
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$\mathrm{i}\epsilon$ prescription makes a function analytical?

I've seen this everywhere where they say "Analytic continuation is obtained by the usual $\mathrm{i}\epsilon$ prescription..." but how is that? How do you analytically continue (say) $\ln x$ with ...
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97 views

Emergence of $SU(2)\times SU(2)$ at the self-dual point in bosonic string theory

I want to understand the derivation of the equations 8.3.11 in Polchinski Vol 1. I can understand that at the self-dual point the Kaluza-Klein momentum index $n$, the winding number $w$, and the ...
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358 views

Proof of Spin-statistics theorem [closed]

Is this proof of spin-statistics theorem correct? http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf This proof is probably a simplified version of Weinberg's proof. What is ...
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898 views

Anomalous dimension for bare actions with a standard kinetic term

In this paper on p42, it is explained that when starting with a bare action that contains a standard kinetic term, this kinetic term attains a correction in the course of the RG flow which can be ...
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Helicity dependence in loop diagrams

I am trying to evaluate a diagram that looks like The middle of the diagram is a fermion loop. I know that the coupling between the $Z^0$ and fermions depends on the fermions' helicities, so it ...
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130 views

Path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $

How do I calculate path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $ where $t_i<t_1<t_f$? I am doing this by discretizing, the time intervals and adding a complete set of $...
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382 views

Deriving Feynman Rules (with the presence of a gluon field strength tensor)

If I have a Lagrangian of the form: $$ \mathcal{L} = k \bar{\psi} \varepsilon^{\mu \nu} \lambda^a \phi G^a_{\mu \nu} + h.c. $$ [where $\phi, \psi$ are fermions, $\lambda^a$ are Gellmann matrices, $\...
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Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson $\psi(p_1)\psi(p_2)\rightarrow\psi(p_1')\psi(...
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236 views

What if EM or QCD was spontaneously broken?

Suppose that Standard Model Higgs mechanism broke electromagnetism, by e.g. veving the charged component of the doublet, so that the photon was massive with $m_\gamma\sim v$. Could such a Universe ...
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277 views

How (why!?) does one introduce an UV cut-off in dimensional regularization?

This question is in reference to the confusing equation 3.7 (page 14) of this paper. One sees the 1-loop answers in their theory as given in their A.7 and A.8 on page 20. Each of the terms is a ...
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237 views

Quantum master equation in the Batalin-Vilkovisky formalism

I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have $$ \begin{split} \delta Z&=i\int[d\chi]\...
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Why do single particle states furnish a rep. of the inhomogeneous Lorentz group?

Following up on this question: Weinberg says In general, it may be possible by using suitable linear combinations of the $\psi_{p,\sigma}$ to choose the $\sigma$ labels in such a way that $C_{\...
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287 views

Physical Interpretation of Lorentz-transformed Single Particle states being linear

As in this question, let $\psi_{p,\sigma}$ be a single-particle 4-momentum eigenstate, with $\sigma$ being a discrete label of other degrees of freedom. Weinberg discusses the effect of a homogenous ...
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Why are non-momentum DoFs of single-particle states discretely labeled?

Following the treatment of Weinberg, chapter 2, we consider $\psi_{p,\sigma}$ as single-particle eigenstates of the 4-momentum. Weinberg says that $\sigma$ labels all other degrees of freedom and we ...
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What is energy in $z \neq 1 $ theories?

In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
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What goes wrong when one tries to quantize a scalar field with Fermi statistics?

At the end of section 9 on page 49 of Dirac's 1966 "Lectures on Quantum Field Theory" he says that if we quantize a real scalar field according to Fermi statistics [i.e., if we impose Canonical ...
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278 views

Anti-particle problem for Dirac sea

According to the Dirac hole theory we know that Dirac sea is completely filled with negative energy, called vacuum. We will need $2mc^2$ or greater to get electron and a positron by incident photon. ...
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Unitary quantum field theory

What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
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588 views

What is the reason why anyons escape spin-statistic theorem?

I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem. I've read somewhere (the wikipedia page is ...
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176 views

Alternative interpretation of Off-shell internal QFT propagators?

In Quantum Field Theory in a (1, D - 1) space-time, to calculate transition amplitudes, we are using Feynman diagrams, where internal lines (internal propagators) corresponds to momenta which are said ...
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298 views

Complex masses for Dirac and Weyl spinors

I'm trying understand how to rotate Dirac fields to absorb complex phases in masses. I have a few related questions: With Weyl spinors, I understand, $$ \mathcal{L} = \text{kinetic} + |M|e^{i\...
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Gauge fields and strings: Loop equations

I am trying to derive Eq. (7.25) (p. 117) of Polyakov's book: $$ \delta \Psi (C) ~=~ \int_{0}^{2\pi} {\rm P} \left(F_{\mu\nu}(x(s)) \exp \oint_C A_\mu dx^\mu \right)\dot{x}_\nu \delta x_\mu(x) \, {\...
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Relevant operators in two dimensional O(n) models

The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written: $$ H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 +\...
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295 views

Quantum field theory quote

I have read this in scientific American: According to quantum field theory, all particles spend a little time as combinations of all other particles" Is this right? How long? And how can they be a ...
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1answer
595 views

Quantum Field Theory and Hilbert space dimensionality

Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis. How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
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837 views

Can one define a “particle” as space-localized object in quantum field theory?

In Peskin and Schroeder, while discussing creation and annihilation operators for a Klein-Gordon field (p.22), the authors say, as we all know the creation operator $a_p^{\dagger}$ acts on vacuum to ...
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768 views

How to directly calculate the infinitesimal generator of SU(2)

We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial U}{\...
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1answer
174 views

Lie algebra of lorentz group

I'm stuck in following calcualtion from sredniki's QFT book.(Its actually in the solution manual) How can i get from $$\delta\omega_{\rho\sigma}(g^{\sigma\mu}M^{\rho\nu} - g^{\rho\nu}M^{\mu\sigma}) $...
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161 views

Categorizing solutions to Hierarchy problem

We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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1answer
247 views

What is the reason that relativistic corrections for hydrogen atom work?

Here I cite part from Sidney Coleman's lectures on Quantum Field Theory: It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
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1answer
603 views

Gradient involved commutator in $\phi^4$ theory

In a phi fourth theory, the Hamiltonian density is: $$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$ Now I impose the usual equal time ...
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2answers
530 views

Calculating the the kernel using path integrals for quadratic lagrangians

I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is $K(b,a)=e^{\...
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374 views

Imaginary time in QFT

I'm reading chapter 4 of Introduction to Quantum Field Theory by Peskin & Schroeder. In the $\phi^4$ theory, the authors state that the ground state of the interaction theory $|\Omega\rangle$ can ...
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Scalar-fermion bound state

Is it possible to have a bound state between a scalar and a fermion? For example, a squark--anti-squark bound state, provided that the decay width is sufficiently small compared to the binding energy?
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1answer
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Derivation of Dirac equation using the Lagrangian density for Dirac field

How can I derive the Dirac equation from the Lagrangian density for the Dirac field?
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310 views

Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?

Suppose we have an integral $$\int \mathrm{d}^4k \,\ f(k)$$ we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$. Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ \...
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1answer
364 views

de Sitter versus Minkowski QFT and cosmological constant

WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the ...
7
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2answers
410 views

Mass gap for photons

I am puzzled by the answers to the question: What is a mass gap? There, Ron Maimon's answer gives a clear-cut definition, which I suppose applies to any quantum field theory with Hamiltonian $H$, ...
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Intuition behind the notion of reflection positivity

I came across Yuji's question. I'm finding it difficult to parse the meaning behind what's said on Wikipedia. Could someone give an explanation of the concept involved? I would also appreciate ...