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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Multiplying propagators

The amplitude for a particle going from $x$ to $y$ is $G(x,y)$. So why isn't the amplitude for going $x$ to $y$ to $z$ $$ G(x,z) \neq \int G(x,y)G(y,z) dy^4 $$ but instead $$ G(x,z) = \int ...
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29 views

How should we deal with diagrams which do not conserve particle number in a non-relativistic field theory?

In the last 10 years there has been more and more crossover of techniques from high energy physics being used in AMO and condensed matter scenarios, in particular diagrammatic techniques and related ...
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2answers
69 views

Self-teaching Green's function approach to quantum many-body systems

My question is where can I find a good book, review, online course, or all of them for self-teaching Green's function in quantum many-body problems (if it has problems with solutions for ...
2
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0answers
38 views

Bound state of $\mu^- \mu^+$ . Why non-relativistic muon states?

Peskin & Schroeber page 148 discuss the creation of a $ \mu^+ \mu^-$ resonance state . Equation (5.44) describes the creation of a Spin Up bound $ \mu^+ \mu^-$: $$ \mathcal{M} = \sqrt{2M} \int ...
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1answer
31 views

Regarding different representations of the Lorentz Group & its defining properties

Take $\Lambda$ to be a Lorentz matrix, it satisfying $\Lambda^T \eta \Lambda=\eta$. By writing $\Lambda=\exp[-\frac{i}{2}\omega_{\mu\nu}\mathcal J^{\mu\nu}]$, we find that the generators satisfy $$ ...
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19 views

Is one of the matrix elements in the optical theorem complex conjugated or not?

The standard form of the optical theorem for amplitudes (Edit: in D-dimensional space-time) looks like this: \begin{align*} -i& (\mathcal{M}(in \rightarrow out)-\mathcal{M}^*(out\rightarrow in))\\ ...
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2answers
43 views

Time-ordering and Dyson series

In Dyson series we use a time-ordered exponential by arguing that a Hamiltonian at two different instants of time does not commute. Why is it that so? Can anyone explain with example why should the ...
2
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1answer
55 views

Is microcausality a statement about locality?

As far as I understand it locality is the rejection of action-at-a-distance. By this I mean that in a given frame of reference at a given instant of time (in that reference frame), two physical ...
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43 views

Do quantum fluctuation particles have any trend regarding their average velocity and direction? If so does that infer and inherent reference frame?

In a vacuum particles appear from no where due to quantum fluctuations. In various reference frames would the overall mass of all these particles be moving in a direction? Could I find a reference ...
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35 views

Normalising a massive propagator?

If you take a propagator Greens function for a massless photon from the origin as $$G(0,x) = \frac{1}{x^2-t^2 +i \varepsilon}$$ then the normalisation factor at time t is: $$ N = \int |G(0,x)|^2 ...
2
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1answer
84 views

Is there a reason why a relativistic quantum theory of a single fermion exists, but of a single scalar not?

When we try to construct the relativistic generalization of non-relativistic time dependent Schroedinger equation, there are at least two possible completions - Klein-Gordon equation and Dirac ...
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1answer
46 views

Issues with the chain rule in derivatives in chiral perturbation theory [duplicate]

I realize that this is a purely math question, which however has arisen in a physics computation. The reason to post it here is that I want a fast dirty answer. Not something cluttered with ...
4
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1answer
92 views

Anomaly cancellation in the standard model (calculating the symmetrized trace of generators)

The Problem We can show that the condition for the Standard Model to be anomaly-free is that the symmetrized trace over the generators of the gauge group vanishes: \begin{align} \text{tr} ...
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24 views

Experimental sensitivity to variance of the fine-structure constant

If some of the fundamental parameters of the Standard Model had quantum uncertainties, they should manifest mainly as a minimum width in the experimental sensitivity of measurement of some of them, ...
3
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2answers
157 views

Weinberg QFT (2.5.5)

I'm slightly confused about something in volume 1 of Weinberg. He says $U(\Lambda)\Psi_{p,\sigma}=\sum_{\sigma'}C_{\sigma'\sigma}(\Lambda,p)\Psi_{\Lambda p,\sigma'}$. Then, "In general, it may be ...
2
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1answer
90 views

Feynman diagrams vs Feynman integrals?

It is well-known how one can translate a (physical) Feynman diagram into integrals of kind: $$I(p_1, \dots, p_n) = \idotsint \prod_{l=1}^{L} \frac{d^D k_l}{(2\pi)^D} \frac{\text{scalar ...
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0answers
61 views

Taking squares or square roots of differential forms?

Reading the recent paper Loop Integrands from the Riemann Sphere by Yvonne Geyer, Lionel Mason, Ricardo Monteiro and Piotr Tourkine I noticed that the authors occasionally seem to take squares and ...
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62 views

Anomaly polynomial of Hitchin system $\mathcal{N}=2$ 4d SQFT

I would like to ask about mathematical background of this object. So, I am trying to puzzle out with 4d $\mathcal{N}=2$ SQFT. As far as I can gather this theory can be described in terms of ...
4
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96 views

The classification of particles or fields in general spacetime- Is it still meaningful to say spin-0, 1/2 ,1 field in general spacetime? [closed]

In 3+1 dim Minkovski spacetime, the classification of particle or field, that is spin-0, 1/2 , 1..., depends on the representation of the universal covering group of $SO(1,3)$, that is $SL(2,C)$. When ...
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1answer
63 views

Convert Grassmann numbers to real numbers [closed]

We know Grassmann numbers are complex numbers. Hence Grassmann integrals are also complex. How can we convert a Grassmann integral into real one, ie is there any transformation of converting complex ...
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0answers
26 views

Antiparticles, charge conjugation and chirality

(Why/how) are antiparticles and charge-conjugates different things? I am trying to understand the effect of discrete symmetries on spinor fields (neutrinos in particular). In the article, Dirac, ...
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0answers
15 views

Cosmological constant in General Relativity [duplicate]

According to my GR notes the cosmological constant can be thought of as a vacuum energy much in the same way as the ground state of the harmonic oscillator. The notes claim that the regularised energy ...
1
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1answer
40 views

Is it possible to have spontaneous symmetry breaking without scalars?

I have never seen spontaneous symmetry breaking with a fermion filed, or a gauge field. Always scalars. So is it possible to have spontaneous symmetry breaking without scalars, and why?
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0answers
19 views

CP odd Higgs coupling to bosons

It is stated that CP-odd Higgs does no couple to vector bosons at tree level. Terms like $A V_\mu V^\mu$ (where V is W or Z) can only appear through loop diagrams (and if they appear at tree-level, ...
4
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1answer
53 views

Non-hermiticity of Dirac Lagrangian: null momentum?

The usual Dirac Lagrangian is $L(\psi,\bar\psi)=\bar\psi(i\not\partial-m)\psi$. The canonical momenta are $$ \pi=\frac{\partial L}{\partial \psi_{,0}}=i\psi^\dagger \\ \bar \pi=\frac{\partial ...
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59 views

Why does Landau theory not fail when dealing with a first order phase transition?

Here is a problem where I can do the calculation, but I am not understanding the philosophy behind it. It is about Landau theory: The Landau theory of phase transitions is based on the idea that the ...
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0answers
19 views

How to interpret “smooth momentum space slicing” in renormalization group analysis?

Ref: [John B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please refer to Page 703 within the section of renormalization group ...
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50 views

What is fermion anomaly?

In the proposal of single electron source (PRL 97,116403 (2006)), the author mentioned that "a large momentum transfer $2n\hbar k_F$ associated with an excitation which is slow on the scale of Fermi ...
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1answer
26 views

How can we calculate pion decay constant in Chiral Perturbation Theory ?

Above diagram is an one-loop contribution to the Pion decay constant $f_\pi$. For example in this paper (Eq.7) they have written down the pion decay constant to one loop, but the calculation is not ...
3
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1answer
79 views

Representations of Lorentz group in interacting QFT

In QFT, we obtain a representation of the Lorentz group by defining a set of unitary operators whose action on (spinless) free particle states is given by \begin{equation} U(\Lambda) |k \rangle = ...
3
votes
1answer
414 views

Casimir effect for spinning Casimir plates

I recently thought of the following experiment. Let's say I have two plates in vacuum facing each other. Now, due to the Casimir effect, there will be some internal attraction between the plates. Now ...
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33 views

Why topological strings have to be closed or infinite?

Let's assume spontaneously broken global $U(1)$ group. During phase transition global topological strings are formed. Why they have to be infinite or closed (there doesn't exist finite strings)?
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68 views

In QFT do we always use normal-ordered Hamiltonian? [duplicate]

In quantization of the Dirac field I learned that we use normal ordering to get rid of negative energy vacuum state. From this point is there any reason we would use original Hamiltonian?
0
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1answer
110 views

Asymmetry of relativistically treated EM force between atoms

There are two neutral atoms set separated at a long distance $R$ and let's consider them phenomenologically through Bohr model. Let's also assume that the nuclei (charged $+q$) of the atoms are fixed ...
2
votes
1answer
101 views

Regarding a small step in the derivation of the LSZ formula

I'd like to prove the LSZ formula, but there is a specific step that is bugging me a lot. I know there are many subtleties in its derivation, but I'm not worrying about this right now: I'm trying to ...
0
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1answer
71 views

Number conservation in imaginary time evolution

It is clear that if we perform dynamics of the system with hamiltonian commuting with total particle number, this quantity will be an integral of a motion. Is it the case for imaginary time evolution? ...
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0answers
17 views

What is the reason behind restriction imposed by no-cloning theroem on (k,n) quantum threshold scheme (QTS)?

A $(k,n)$ quantum threshold scheme (QTS) is a method to split up an unknown secret quantum state $\lvert S\rangle$ into $n$ pieces (shares) with the restriction that $k > n / 2$ (for if this ...
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22 views

Does RF have any non-orthagonal properties?

Quantum Key Exchange takes advantage of the fact that observing a photons polarization will alter it's polarization. This, along with some tricky back and forth, allows two people to exchange data ...
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0answers
61 views

Any textbook about non-renormalizability of gravity?

I have learned general relativity in a graduate-level. My knowledge about QFT is very rudimentary. But, I need to learn about non-renormalizability of gravity. I have these questions. Is there any ...
1
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2answers
163 views

What determines the probability of creating a particular particle in a collision?

When discussing events at the quantum level, we deal in probabilities and not absolutes. Articles I've read on particle physics state that a particle has a probability of being created in a collision. ...
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0answers
46 views

Plane wave solutions of Dirac equation

I'm reading chapter 3 in Peskin on the Dirac equation. First of all, they say since Dirac satisfies Klein Gordon it can be written as a linear combination of plane waves. This is fine. So a general ...
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3answers
79 views

Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
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29 views

What is the explicit decay width formula for a four body decay?

I'm trying to calculate the decay width for a theory with one particle having a decay mode into 4 particles. Does anyone know the explicit formula for this (not the generalized decay formula).
2
votes
1answer
40 views

Lorentz-invariant phase space of a three-body decay process

I am not following the use of delta function in the 3-body decay process. In $\gamma^* \to gq\bar{q}$ process, with $\gamma^*$ being a virtual photon, we have a phase space factor $$d^9R_3 = ...
2
votes
1answer
98 views

Solving the Klein-Gordon equation via Fourier transform

I have been writing a personal set of notes on QFT and I'm currently writing up a section on solving the Klein-Gordon (K-G) equation. I many texts that I've read, the author starts by expressing the ...
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1answer
33 views

Complex scalar theory: annihilation and creation operators give wrong commutators with Hamiltonian

The theory of a real (hermitian) scalar field can be found in many books and everywhere online. On the other hand, if we take the field non-hermitian, then I can only find notes on path integrals. I ...
2
votes
1answer
121 views

How was this one probability amplitude derived by Mattuck?

I'm reading A Guide to Feynman Diagrams in the Many-Body Problem by Richard D. Mattuck (2nd edition). You can look at the relevant pages here. On page 45, he presents a formula for $D_t c_p(t)$. ...
3
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1answer
97 views

One-particle scattering: LSZ vs Feynman

This question is about Klein-Gordon theory (the field is hermitian). If I calculate the amplitude for the process $\phi\to\phi$, I get two different results depending on whether I use Feynman rules ...
5
votes
1answer
116 views

Georgi-Glashow model and the VEV of the scalar field

Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is $$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} ...
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3answers
134 views

How is this possible that photons are absorbed?

From the lessons on QM, I got impression that there are some discrete orbitals that emit light when electron drops from one to another. Specific molecules emit light in very narrow bands, therefore. ...