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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Momentum eigenstate definition in Eq (2.5.5) of Weinberg Vol. 1 clairification

This is question is related to one asked here: Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT. In Eq (2.5.5) of Weinberg's "The Quantum ...
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60 views

Why group elements associated with gauge transformations of finite action field configurations in QCD don't depend in $r$?

I am reading the chapter on instantons in Coleman's Aspects of Symmetry. I am puzzled by an argument i don't quite follow. In section 3.2, Coleman considers configurations of the gauge field with ...
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50 views

Expansion operator for quantum mechanics

As a counterpart to the quantum mechanical translation operator (see for example this post) is there a unitary operator which describes the stretching of a line. That is consider I have a chain of ...
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121 views

time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in the second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
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51 views

How to construct effective interaction vertex?

In literatures, I often come across interactions like the $D^*D\gamma$ vertex: $$\mathcal{L}_{D^*D\gamma}(x)=\frac{e}{4} \epsilon^{\mu \nu \alpha \beta} F_{\mu \nu}(x)\left({g_1} D^{*-}_{\alpha ...
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Yukawa interaction and four fundamental forces [closed]

What is the difference(or relation) between Yukawa interaction($\mu\bar{\psi}\phi\psi$) and the other four fundamental interactions(e.m., weak, strong and gravity)? Does it fall anywhere on the ...
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2answers
206 views

In quantum field theory, how can Compton scattering change the frequency of light?

Classically, when light scatters off matter, the frequency of the light must stay the same. This follows directly from a continuity argument: if you put in $f$ field oscillations per second, you'd ...
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1answer
52 views

Simple feynman parameters question

I have the following integral $$\int d^D l \frac{1}{p^2 (p-l)^2 l^2}$$ which I want to rexpress using feynman parameters. I can write as a first step, $$2 \int_0^1 dx \int_o^{1-x} dy \int d^D l ...
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90 views

Why does a Heisenberg magnet break the O(3) symmetry in stead of SU(2)?

As stated in the question, why does a Heisenberg magnet break the $O(3)$ symmetry while degrees of freedom of the underlying spins are $SU(2)$?
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1answer
116 views

On shell and off shell simultaneously?

I am considering the following one loop virtual correction in the DIS process: where I have a quark of momentum $p$ coming in, emitting a gluon before interacting with a photon of momentum $q$ to ...
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48 views

Single-particle operator in second quantization

I am new to second quantization and I am still rather uncomfortable with the bra-ket notation. I feel like I am slowly getting the hang of it but when it comes to shifting bra's and ket's around, I ...
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1answer
53 views

Is a system of free spinless fermions always critical?

Consider a system of free spinless fermions, whose Hamiltonian can be written as $$ H = \sum_{i,j}h_{ij}a_i^\dagger a_j-\lambda\sum_i a^\dagger_i a_i $$ with $h_{ij}=h_{ji}^*$ scalars and ...
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32 views

Derivation of Functional Renormalization Group Equation in non-zero spin particles

I know the functional renormalization group equation(also known as Wetterich Equation) is $\partial_k \Gamma_k = \frac{1}{2} \text{STr} \, \partial_k R_k \, (\Gamma^{(2)}_k + R_k)^{-1},$ and ...
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86 views

TQFT's as effective theories of the groundstate subspace

I often hear: "The degenerate groundstate subspace of a QFT is often a TQFT". I'm trying to work out an example of this for, say, superconductors: In the context of condensed matter physics, the ...
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2answers
90 views

Is QFT time symmetric, and how is it implemented?

In electromagnetism, while the Maxwell equations are time symmetric, there is a choice to restrict solutions specifically to retarded potentials, imposing a time direction on the equations. And in ...
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23 views

Nonequilibrium Green's functions weakly interacting two-component Bose gas

I am planing to describe time evolution of two-component BEC. I was thinking about non-equilibrium Green's functions, but I don't if the method can be applied to the problem describe below. I know ...
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51 views

$i\epsilon$ in CFT correlation functions

M. Luescher in his talk on p.6 writes that the 2-point correlation function of a Hermitian local field $O_k$ of scaling dimension $d=3-k$ looks like $$ \langle 0| O_k(x) O_k(y) |0\rangle = A_k (x-y-i ...
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1answer
51 views

Would the existence of more than 16 quark flavors make QCD deconfinning?

Consider the QCD beta function. Its expansion in powers of the coupling is $$\beta(\mu)=-(\beta_0a(\mu)+\beta_1a^2(\mu)+\ldots)$$ where $a=\alpha/4\pi$. For simplicity let's neglect everything but ...
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IBP application in feynman box diagram

I'm trying to calculate the box diagram also mentioned in this question, but with the Integration by Parts (IBP) identities. At first, if I neglect all the external momenta for a moment, I get $$\int ...
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1answer
59 views

Computing the pole mass from a given $\overline{MS}$ mass?

Given a Yukawa coupling as a function of scale $\mu$ and a vev, therefore $m_R(μ)=Y(μ)⟨ϕ⟩$, how can I compute the corresponding pole mass $m_p$? Relations I was able to find are (page 39) ...
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54 views

How to get anti-commuting rule from the view of field?

I was reading the 1951 Lectures on Advanced Quantum Mechanics and I found something really disturbing. That's the anti-commuting rule mentioned on Page 40 at last. Though it was named as Quantum ...
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37 views

Why does the cup stay on the table? [duplicate]

The question is in the title. It is a very simple question and I am asking myself if this is only the reason of electron repulsion and the Pauli principle or what else comes into play to answer this ...
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54 views

Particle creation through a time dependent Hamiltonian

We know that a time dependent Hamiltonian can create particles. We know this for instance from field theory in curved spacetime, where for instance in an expanding or contracting universe creation and ...
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1answer
90 views

Vacuum has both zero four-momentum and nonzero vacuum energy?

I have heard that in QFT, the vacuum has zero four-momentum: $$P^\mu |\Omega \rangle = 0.$$ However, I also know that the vacuum has vacuum energy, i.e. $$ \langle \Omega | H | \Omega \rangle = E_0 ...
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49 views

Solving non scalar integrals in loop calculations

Consider the following integral that comes out of a loop calculation along with some fermionic propagators (e.g virtual one loop correction to a $p \gamma^* \rightarrow p'$ process such as in DIS): $$ ...
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36 views

Gauge invariance of quantum scalar field coupled to classical electromagnetic potential

I would like to quantize a scalar field that is coupled to a classical electromagnetic field $A_\mu$. More precisely, I start with the action (signature -+++) $$ S=\int ...
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1answer
84 views

Renormalisation group equation for Green's functions

The renormalization group equations for the $n$-point Green’s function $$\Gamma(n) = \langle \psi_{x_1} \dots \psi_{x_n}\rangle $$ in a four-dimensional massless field theory are $$\mu \frac{d}{d ...
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36 views

Decay rate and differential cross-section

If I have a $pp-$beam producing an on-shell particle $A$, which then decays into particle $B+C$, then I can find the total cross-section $pp \to A \to B+C+Y$ ($Y$ being inclusive particle which should ...
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40 views

Symmetries of a Lagrangian density

Given some Lagrangian density as this how in general can one finds it's symmetries that give conserved currents? For example in this case U(1) is ok, but are there others? Do you know some book ...
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32 views

Charge conjugation and the conserved charge for the Dirac field

So, while reading Peskin & Schroeder's chapter on the Dirac field, they claim that the charge conjugation operator has the following properties: $$ \mathcal{C}\psi(x) \mathcal{C} = -i \gamma^2 ...
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2answers
110 views

Question about source terms in scalar quantum field theory

I'm having a bit of a mental block when trying to interpret the inhomogeneous Klein-Gordon equation $$(\Box +m^{2})\phi(x,t)=j(x,t)$$ In particular, how does one interpret the term on the right-hand ...
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50 views

Mass of an imaginative stable top quark at low energies? [duplicate]

Masses are not fixed quantities, but change with energy because of the renormalization group running. These can be calculated in a given renormalization scheme, for example, the MS scheme: Imagine ...
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40 views

Where did Schwinger term come from?

Where did Schwinger term in the commutation relation of current density and charge density come from?
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1answer
177 views

Quantization on Minkowski/Schwarzschild spacetimes based on unusual surface

I'm reading the book of Wald "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics", and I'm pondering on this problem: In Minkowski spacetime, we usually quantize our fields with ...
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1answer
174 views

How much QFT do I need to get started on String Theory? [closed]

I want to get started learning String Theory (most likely from David Tong's lecture notes) and I would like to know which topics I need to know from QFT. In particular, if I were to follow Peskin, ...
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Is there an introduction to non-commutative geometry for non-physics and mathematics students?

I am looking for a simple explanation as how spectral triples give rise to definition of distance using Dirac operators?
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1answer
62 views

Green's function in Hamiltonian vs. Path Integral QFT

For a spacetime $M$, the Green's function for the operator $\Delta+m^2$ is the following distribution on $M\times M$: $$G(x,y):=\langle \phi(x)\phi(y)\rangle=\int_{C^\infty(M)}\mathcal ...
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1answer
79 views

I am recently reading Srednick's QFT, and I am a little confused with the counterterm Lagrangian

Srednicki treated􏰍 $$L_{0}=-\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^2\\ L_{1}=\frac{1}{6}Z_{g}g\phi^3+L_{counterterm}\\ ...
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1answer
48 views

Applicability of Cardy's “doubling trick” to the 2D Ising Model

In Section 11.2.2 of the book on Conformal Field Theory by di Francesco, Mathieu, and Senechal (page 417), the two point function on the Upper Half Plane is written as being equal to the four point ...
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4answers
596 views

Why is the Lagrangian approach preferred over the Hamiltonian approach in QFT? [duplicate]

Going from non-relativistic quantum mechanics(QM) to QFT there is a marked change in the approach used. QM almost exclusively uses Hamiltonains. Lagrangian based methods like the path-integrals are ...
2
votes
1answer
115 views

Derivation of Gordon identity from Srednicki [closed]

On srednicki page 240 (print) there is a derivation of the Gordon identity, and it starts with stating that $$ \require{cancel} \gamma^{\mu}\cancel{p} = \frac{1}{2} \big\{\gamma^{\mu},\cancel{p} ...
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1answer
67 views

Betti number of Feynman graph

Let $\mathcal{L}$ be a Lagrangian, which contains polynomials of bosonic fields $\phi$. After Wick's rotation we obtain a perturbation expansion od Green's function. In this expansion there are terms ...
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30 views

What is the name of the basis that uses objects of definite parity?

Currents to which gauge fields couple in four dimensions can be described as follows: $$ \mathcal{L} = -g A_\mu J^\mu. $$ Sometimes it useful to discuss these couplings in the chiral basis, ...
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63 views

Adiabatic turning on of coupling constant in simulation of $\phi^4$ theories in the JLP algorithm

In the Quantum Algorithms for Quantum Field Theories by Jordan, Lee and Preskill they have devised an efficient algorithm to simulate $\phi^4$ theories. Given by the Lagrangian density ...
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199 views

Why doesn't gravity fit into quantum theory?

Before you read, I want to point out that I probably don't know nearly as much as you guys about quantum theory, even though I love learning about it, so I would prefer explanations in relatively ...
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1answer
54 views

Time evolution of the universal wave function

Consider the energy conservation principle, than the total amount of energy in the universe is a fixed value $E$. Let us denote with $| \psi \rangle$ the wave function of the entire universe. Is it ...
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1answer
57 views

Gordon Identity confusion

For the Gordon identity $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ If I plug in $\mu$=5, ...
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1answer
58 views

A question from A.Zee's Nutshell

When discussing topological monopole in Page 309, A.Zee wrote: But I am still not clear how the mass of topological monopole which is related to the mass of intermediate vector boson of the weak ...
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Axiomatic QFT: Time-slice Axiom vs Transformation Properties

I am studying Wightman axioms and Haag–Kastler axioms for QFT from Haag's book "Local Quantum Physics". In both axiomatic frameworks, he introduces the "Time-slice Axiom" (axiom G) as "There should ...