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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Renormalizing QED with on-shell fermions

When renormalizing QED, we calculate the 1 loop correction to the fermion-fermion-photon vertex using the diagram, $\hskip2in$ When doing the calculation we typically let the photon go off-shell ...
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128 views

Can $\langle\Omega|f|\Omega \rangle$ always be reduced to $\langle0|f|0\rangle$?

I've not come across any expression involving $\langle\Omega|f|\Omega\rangle$ in Srednicki's QFT book (please correct me if these exist there). On the other hand, they are abound in Chapter 7 of ...
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1answer
494 views

Lorentz transformation of the vacuum state

In general, the Hamiltonian $H$ has non-zero vacuum expectation value (VEV): $$ H \left.| \Omega \right> = E_0 \left.|\Omega \right>, $$ where $\left.|\Omega\right>$ is the vacuum state. The ...
9
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1answer
475 views

Sign in the photon propagator

The Klein Gordon propagator is given (I use Peskin and Schroeder's conventions, if it matters...), \begin{equation} \frac{ i }{ p ^2 - m ^2 + i \epsilon } \end{equation} The photon propagator (...
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208 views

Vertex for quartic interaction of complex scalar multiplet

Since I'm new to QFT and I tend to do a lot of errors during calculations, I would like you to tell me if I got the four-point vertex of the quartic interaction with a multiplet of complex scalar ...
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1answer
166 views

A question about the Bosonization of the Thirring model

Is there a way or sense in which one can Bosonize this kind of a Lagrangian, $L = \bar{\psi}\gamma^\mu \partial _\mu \psi + f(x) \bar{\psi}\psi$ for $f(x)$ being some function on space-time. ...
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462 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
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173 views

Does $\langle\Omega|\mathrm{e}^{\mathrm{i}Px}=\langle\Omega|\mathrm{e}^{\mathrm{i}0x}$? $(\langle\Omega| =$ ground state of the interacting theory)

Let $\langle\Omega|$ be the ground state of an interacting theory, just as Peskin & Schroeder(PS) describes on page 82 and page 213. On page 213 PS do the following $$\tag{1}\langle\Omega|\phi(x)...
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277 views

About the gauge formalism in statistical quantum field theory

I would like to understand a bit more the aspects of the gauge theory in statistical field theory. In particular, I would like to understand how the replacement $\tau \rightarrow it/\hbar$ is ...
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104 views

Klein Gordon eq. expressed with Killing fields

I have a question on the reformulation of the Klein Gordon equation in terms of Killing fields. Suppose we have a static spacetime with timelike Killingfield $\xi^{\mu}$ (e.g. Schwarzschild). Then ...
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113 views

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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366 views

Rotation Group and Lorentz Group

It is often stated that rotations in the 3 spatial dimensions are examples of Lorentz transformations. But Lorentz transformations form a group named the Lorentz Group, $O(1,3)$ which is a group a $...
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222 views

Gossip in Physics [closed]

Given, $M_4 = \Sigma \times C$, How do you get an effective theory by studying maps $\Sigma \rightarrow M_4$ . Technically, the physics in one manifold is supposed to gossip about the ...
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1answer
973 views

What is the conclusion from Aharonov-Bohm Effect?

What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum ...
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1answer
91 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
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331 views

Chronological and normal ordering

I've realized I'm little bit confused when I want to treat elements like this $$\left<\phi_0|T\{a_p(t)a_p^+(t')V(t_1)V(t_2)\}|\phi_0\right>$$ with $$V(t)=\dfrac12 \dfrac{1}{(2\pi \hbar)^9}\...
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418 views

Tadpole symmetry factor

Can someone help me with symmetry factor of one-loop tadpole diagram (one loop correction to one point Green function in phi-3 theory)?
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545 views

$(\frac{1}{2},\frac{1}{2})$ representation of $SU(2)\otimes SU(2)$

The representation $(\frac{1}{2},\frac{1}{2})$ of the Lorentz group correspond to a four- vector or a spin-one object. Right? Does it imply that any four-vector is identical to a spin-one object or ...
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592 views

Can dimensional regularization solve the fine-tuning problem?

I have recently read that the dimensional regularization scheme is "special" because power law divergences are absent. It was argued that power law divergences were unphysical and that there was no ...
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298 views

Wick's theorem for calculating OPE

I am trying to understand a calculation using Wick's theorem. Let $T(z)$ be the analytic part of a stress-energy tensor, and $\phi(z)$ a free boson field. Now, $$T(z)\partial_{w}\phi(w)=-2\pi:\...
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1answer
284 views

A question about the implication of UV divergence in QFT

I have a basic question about the logic of renormalization in quantum field theory (QFT). We met the ultraviolet (UV) divergence in loop corrections. The standard argument is, our current field theory ...
3
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1answer
207 views

Quick-and-dirty way to integrate out heavy fields

I understand the roughly understand the process of integrating out heavy degrees of freedom of a Lagrangian, namely, taking the action and performing the path integral over the high momentum modes. ...
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1answer
907 views

Boosts are non-unitary!

The boost transformations are not unitary unlike rotations, the boost generators are not Hermitian. When this induces transformations in the Hilbert space, will those transformation be unitary? I ...
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1answer
648 views

Scalar field transformation and generators

When we do a transformation (norm preserving one) for a given quantity, from what I have understood it seems like there is a representation of the group element for each quantity depending how they ...
2
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1answer
110 views

Angular momenta of photon

$A^\mu$ can have multipole expansions in classical electrodynamics. This gives rise to dipole photon, quadrupole photon etc. For dipole photon $j=1$ (In electrodynamics books they write it as $l=1$). ...
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1answer
149 views

Has QFT successfully mediated between QM and Special Relativity?

I understand that QFT is the theoretical framework for combining QM and Special Relativity, but as I understand it, though even without proof or experimental confirmations; has QFT managed to "behind ...
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1answer
426 views

Why do we assume local conformal transformations are symmetries in 2D CFT

The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional. However, when ...
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1answer
164 views

Definition of vacuum in field theory; Connection between the classical definition and the connection to QFT

I am a bit confused by what is defined to be a vacuum in field theory. Classically a vaccum state is defined to be the state where the field sits at some minima of the potential $\frac{\partial V}{\...
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44 views

Coupling constraint in massless Thirring Model in (1+1) Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (Link to the PRD paper http://prd.aps.org/abstract/PRD/v11/i8/p2088_1), he pointed out that the massless Thirring Model ...
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189 views

what is 't Hooft up to? [closed]

apart of the 't Hooft diagrams that you all love (and find all sort of dualities starting with them) one of the venues 't Hooft works nowadays is apparently some sort of "deterministic representation ...
5
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1answer
229 views

Does This Really “Prove” Spin-statistics Theorem?

In quantization of scalar field theory we impose commutation relation between the field operators by hand and similarly we impose anti-commutation relation between Dirac field operators by hand. As a ...
2
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1answer
166 views

Where did $\mathcal{M}^\mu(k) = \int \mathrm{d^4}x \; \exp(\mathrm{i}k \cdot x)\langle f | j^\mu(x) | i\rangle$, in Peskin and Schroeder, come from?

On page 160 Peskin & Schroeder, they say: Therefore we expect $\mathcal{M}^\mu(k)$ to be given by a matrix element of the Heisenberg field $j^\mu$: $$\mathcal{M}^\mu(k) = \int \mathrm{d^4}x \;...
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229 views

Evaluate $1$-loop contribution to the $4$-point Green's function

I am trying to evaluate the following integral \begin{equation} I = \int \frac{d^d p_\text{E}}{(2 \pi)^d} \frac{1}{(p_\text{E}^2+m^2)((q_\text{E}-p_\text{E})^2 + m^2)} \tag{1} \end{equation} where $p_\...
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1answer
116 views

Would it be consistent with QED to have leptons of different charges?

A recent question, Equality of electric charges of all leptons, made me wonder about a specific aspect of why exactly the charges of the different (free) fundamental particles are all the same. ...
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79 views

Equality of electric charges of all leptons

What does it precisely mean the often repeated statement that the electric charges of all leptons are the same. Let's consider QED with two leptons: electron and muon. The interaction part of the ...
3
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1answer
133 views

Massless Thirring Model in 1+1 Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (link to Phys Rev D article), he pointed out that the massless Thirring Model is exactly scale invariant. More over, ...
3
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2answers
563 views

Derive Schwinger-Dyson equations in Srednicki

On page 135 in Srednicki he defines the functional integral $$Z(J) = \int\mathcal{D}\phi\,\exp\Big[\mathrm{i}\big(S+\int\mathrm{d^4}y \,J_a\phi_a\big)\Big], \tag{A}$$ where $S$ and $J_a$ are the ...
4
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1answer
199 views

localized field quanta?

In the quantization of the Klein-Gordon field (for example) we interpret the quanta of the fields with definite momentum and energy as particles but are they also localized in space? Shouldn't a ...
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1answer
1k views

Source Theory - Alternative to QFT

I am a graduate physics student. I have started learning QFT. As a project my professor has asked me to take up and learn Source Theory, seems an alternative to regular QFT. How exactly is this ...
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1answer
108 views

Resources for QCD colour factors

I'm looking for resources on the computation of (I think) very simple Feynman diagrams for QCD processes. The processes are q'qbar' -> qqbar and gg->qqbar (only at tree level, no loops involved) and ...
6
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1answer
540 views

Does the concept of both helicity and chirality make sense for a massive Dirac spinor?

Does the concept of both helicity and chirality make sense for a massive Dirac spinor? A massive electron in the chiral basis is written as a column made up of $\psi_L$ and $\psi_R$. What is the ...
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1answer
1k views

Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
6
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2answers
302 views

Feynman Diagrams in 2 component notation

When using two component notation people often prefer to refrain from using arrows in Feynman diagrams to denote charge flow as is done in four-component notation. Instead, if understand correctly, ...
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1answer
1k views

Superficial Degree of Divergence for Feynman Diagrams

The superficial degree of divergence for a diagram is defined as the power of $k$ in the nominator minus the power of $k$ in the denominator. It is written to be equal to $4\times$ (...
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1answer
326 views

What is the difference between QFT and elementary particle physics?

I'm a little unclear as to how QFT differs from Elementary particle physics. They both use pictorials of Feynman graphs, is it that Elementary particle physics assumes the point particle perspective, ...
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1answer
520 views

Is the second derivative of the effective potential always the mass square of the particle?

In quantum field theory, we can calculate the effective potential of a scalar field. My question is whether the second derivative of the effective potential always represents the mass square of the ...
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1answer
360 views

Conceptual difficulty in understanding Continuous Vector Space

I have an extremely ridiculous doubt that has been bothering me, since I started learning quantum mechanics. If we consider the finite dimensional vector space for the spin$\frac{1}{2}$ particles, ...
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108 views

Some questions about the large-N Gross-Neveu-Yukawa model

Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$, $S = \int d^dx \{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu \...
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1answer
1k views

Green's function in path integral approach (QFT)

After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with. I have the ...
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1answer
119 views

QCD string breaking and glueballs

When one tries to pull two quarks appart, a flux tube is created. The tube eventually breaks, creating quark anti-quark pairs and eventually hadrons. Can there also be creation of gluons to form ...