Questions tagged [quantum-field-theory]
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 this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.
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Quantum Entanglement Field Theory by Ammar Hafeez [closed]
Is it possible for entanglement to be a dynamic field, suggesting that particles become entangled through their interaction with this field, as opposed to viewing entanglement as a direct, passive ...
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Canonical quantization of abelian vector field in $R_\xi$ gauge
I am trying to do the canonical quantization of an abelian vector field $A_\mu(x)$ in the $R_\xi$ gauge. So the gauge-fixing Lagrangian is given by $$ \mathscr{L}_{gf} = -\frac{1}{2\xi} (\partial_\mu ...
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Relationship of space-time to energy and momentum [closed]
After reading Noether's theoram and many other examples like objects tendency to follow its geodesics in spacetime makes conserved quantities like momentum etc meaningful so , are energy and momentum ...
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Trying to understand Reeh-Schlieder
In an attempt to understand the Reeh-Schlieder theorem, I am currently studying this paper, in which Witten provides a discussion using the formalism of quantum field theory. It is quite ...
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Mathematical rigor behind renormalization [closed]
I struggle to understand how theories that are based on renormalization can be considered mathematically rigorous. I understand how renormalization works for non-abelian theories, through loop ...
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Cross section normalization in $2 \to 2$ scattering
Consider Compton scattering $$p_1 + p_2 \to p_3 + p_4$$ in the laboratory frame. According to Quantum Field Theory and the Standard Model by Schwartz, the relation between the differential cross ...
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Gauge dependent mass definition in perturbation theory
Let's say we describe an unstable particle using perturbation theory. Then we have a non-zero decay width, which we say $\Gamma$. Now, if we define mass to be the pole of the propagator, we get
$$
\mu^...
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About Cutkosky cutting rule
I am working on a problem about Cutkosky’s cutting rule in Matt D. Schwartz’s Quantum Field Theory and the Standard Model. The problem asks us to show that the imaginary part of the amplitude is given ...
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Interpretation of real scalar field, its propagator and causality [duplicate]
It seems this has been discussed here previously (e.g this and this post), but I still feel uneasy. Essentially, I think it all boils down to the popular interpretation of the scalar field operator in ...
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Why do interpretations of quantum phenomena focus on QM rather than QFT? [closed]
UPDATE for Mods: Currently travelling; aiming for edited version over weekend 30 Nov.
After reading a number of posts here in the last few years I'm left wondering why most questions about the ...
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Expressing Feynman Integrals Using Schwinger Parameterization
I am trying to practice the techniques given in the book "Feynman Integrals: A Comprehensive for Students and Researchers," by Stefan Weinzierl (preprint). I am getting stuck on one point ...
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Where do experiments enter the renormalization procedure? [duplicate]
I'm studying the renormalization of scalar quantum field theories ($\lambda\phi^4$ in particular). I'm considering renormalization by counterterms with the old non-Wilsonian interpretation of ...
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Structure of Higgs potential
The Higgs potential is written as
$V(\phi) = -\mu^2 |\phi|^2 + \lambda^2 |\phi|^4$,
where $|\phi|^2 = \phi^\dagger \phi $ and $ \phi $ is a complex scalar doublet.
My question is: why do we not ...
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What is the point of the "Polarization Insertion" in many-body theory?
In Fetter and Walecka's Quantum Theory of Many-Particle Systems, after a discussion of Dyson's equation for the single particle Green's function in spacetime ($x$) and momentum/frequency ($k$; for ...
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Dyson series expression for the two-point Green function
On Chapter 7 of Fetter & Walecka, the authors prove Dyson formula for the (imaginary time) propagator $U(t,t_{0}) = e^{H_{0}t_{0}}e^{-H(t_{0}-t)}e^{-H_{0}t}$, where I am ommitting the $\hbar$'s. ...
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Sign in the PCAC relation and consistency with the GMOR relation
In Peskin & Schroeder (Eq.~(19.88)), the PCAC matrix element is written as
$\langle 0| j^{\mu 5 a}(x) | \pi^b(p) \rangle
= -\, i\, p^\mu f_\pi\, \delta^{ab}\, e^{-ip\cdot x}.$
Q1. Where does this ...
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Is angular momentum generator a tensor in the Poincare group?
According to Weinberg' QFT vol I, (2.4.8), the generator of angular momentum $J^{\rho\sigma}$ transform as
$$U(\Lambda, a) J^{\rho \sigma} U^{-1}(\Lambda,a) =\Lambda_\mu^{\,\,\rho} \Lambda_\nu^{\,\,\...
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Why do these first-order diagrams represent "direct" and "exchange" interactions?
In Quantum Theory of Many Particle Systems by Fetter and Walecka, they perturbatively expand the fermionic interacting single particle Green's function $iG_{\alpha\beta}(x, y)$ (where $\alpha$, $\beta$...
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Time ordering vs symmetry transformation in Euclidean correlation functions
In a QFT with Euclidean signature, the correlation functions can only be well-defined in a time-ordered manner (This is Claim 1 on Page 2 of Simmons-Duffin's lecture note). For example, a scalar 2pt ...
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Scattering probability distribution for $2 \rightarrow 2$ scattering
Consider a 2-to-2 particles scattering process (treated in second quantization) of particles with the following $4$-momenta:
$$p_1 + p_2 \rightarrow p_3 + p_4.$$
The probability measure associated ...
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Understanding how second quantization recovers full $N$-body correlations from classical Schrödinger fields
I'm trying to understand a conceptual point in many-body quantum mechanics and quantum field theory.
Starting point: Consider a classical Schrödinger field $\psi(\mathbf r, t)$ with interactions, ...
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Why does QED use spinors but Classical Electrodynamics doesn't?
I am curious as to why we find Dirac spinors in QED but when working in CED we can formulate systems using complex scalar fields. For instance, the typical Lagrangian density for a charged particle ...
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Why do we need two Hamiltonians — the Kohn–Sham Hamiltonian and the second-quantized many-body Hamiltonian — in condensed matter field theory?
Dear members of the condensed matter community,
There are two things in the non-relativistic quantum field theory of solids that I cannot quite reconcile:
(1) We start from the full crystal ...
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Reeh-Schlieder violates Poincare invariance?
In Why particles only make sense in flat spacetime? user Chiral Anomaly says
the Reeh-Schlieder thereom implies that the vacuum state (the lowest-energy state of the global Hamiltonian $H$) cannot be ...
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Do the canonical twisting bundles play a role in quantum physics?
$\Bbb {CP}^1$ the Riemann sphere appears in quantum physics as the Bloch sphere, and is the natural home for two-dimensional phenomena such as spin. It is sometimes said that bundle theory is relevant ...
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Proof for scalar field VEV solving classical equations of motion to lowest order [duplicate]
Page 370 (start of section 11.4) of Peskin and Schroeder claims that the VEV of a scalar field in the presence of an external source,
$$\phi_\text{cl} \equiv \langle 0_J|\phi(x)|0_J\rangle,\tag{11.46}$...
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On the interpretation of spontaneous symmetry breaking (SSB) and fields
I am a math student taking a course in fundamental interactions and I have two questions about the interpretation of the spontaneous symmetry breaking (SSB). For contest we started with a classical ...
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QFT Path Integrals: How to define a precise initial state if vacuum fluctuations can alter it?
I'm trying to solidify my understanding of the path integral formalism in Quantum Field Theory, and I've run into a conceptual paradox regarding the definition of initial states. I would be grateful ...
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Potential and Radiation gravitons scaling
I am studying the Effective Field Theory for extended objects proposed by Goldberger and Rothstein. This theory studies a binary system in inspiral phase. By means of the virial theorem we get a ...
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How can Different neutrino flavours have different masses?
I've heard about neutrino oscillation, where can neutrino can change between each flavour. I've also heard that the neutrino flavours are not guaranteed to have the same mass. If this is the case how ...
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What is Talagrand's "massive Weyl spinor"?
In the book What is a Quantum Field Theory by Michel Talagrand, he introduces (in §10.15) a "massive Weyl spinor."* In physics, common wisdom says there is no such thing. A quick internet ...
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In what sense is "momentum" flowing in Feynman diagrams?
Given a Lagrangian $\mathcal{L} = \mathcal{L}_0 + \mathcal{L}_I$, we can construct the Feynman diagrams for some process by writing out the Taylor series for our interaction term and judiciously ...
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Energy-dependent width of a Breit-Wigner for $\ell=0$?
I am doing calculations with a resonance with the invariant mass $W$, which can decay to $a + b$ with masses $m_a$ and $m_b$. Since I treat all particles as scalar, I calculate with $\ell=0$. The ...
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Eliashberg theory
I’m a physics major working on magnon–phonon mediated superconductivity. I have a solid foundation in many-body theory and field theory, but I’m looking for good reading material or notes on ...
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Is particle number a monotonic function of chemical potential when fixing self-energy?
I am performing numerical calculations using quantum many-body theory, and I would like to fix the particle number, either for fermions or bosons. The particle number can be expressed in terms of the ...
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Microcausality in Fermions
We can show that for the Dirac field, the anti-commutator between the field and its adjoint vanishes for space-like separated points. However, for causality we need to show that the commutator instead ...
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How can we read Feynman rules from the equations of motion?
Reading Feynman rules from a Lagrangian is a quite standard procedure. However I have seen papers (for example Appendix A of arXiv:2412.14858) where this is done from the Equations of Motion instead ...
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Can photon be emitted if it will never be absorbed, going to infinity? (in CPT perspective no emission)
Photon in QFT is e.g. a coupling between two electrons using below Feynman diagram - requires both emitter and absorber, they are switched in perspective of CPT symmetry.
So can photon be emitted if ...
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How does the Berezin integral for fermions represent a "sum over all configurations"?
In quantum field theory, the path integral for a bosonic field has a very intuitive interpretation as a "sum over all possible field configurations."
To make this concrete, let's consider a ...
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Effective interactions and screening from Feynman diagrams in condensed matter and interpretations
recently I was revisiting the path integral formalism to approach condensed matter systems, and there is a question I've always had which is not yet clear to me.
In physics, there are many ways to ...
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How to calculus the corresponding operators of bosonic beta-gamma ghost systems? [closed]
In Polchinski's book, it states that the corresponding operators of $|1\rangle, |-1\rangle$ are $\delta(\beta),\delta(\gamma)$, and suggests that it can be shown by path integral. I'm a little ...
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Reweighting method for Metropolis algorithm
I read the Wiki page about the reweighting procedure as a way to use Monte Carlo methods with the sign problem, but I'd like to know more about how this could be implemented in the Metropolis ...
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Additional conserved currents and charges of the free scalar QFT
I'm following notations/conventions of Srednicki, chapter 3. My question relates to some conserved currents and charges of the free real scalar field, that arise in addition to the translation and ...
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Why do we only look for representations of dynamical symmetries and not other transformations?
There are plenty of discussions on this site about why particles correspond to representations (reps) of the Poincaré group $\mathcal P$. My question (perhaps quite naive) is why we consider $\mathcal ...
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Is the commutator of field operators in an interacting theory always a $c$-number?
I understand that the commutator of field operators in a free field theory is always a $c$-number. Now I want to see whether a generalization to interacting fields is also possible?
In the interacting ...
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Under what conditions do functional renormalization group (FRG) limit cycles occur in asymptotically safe gravity? [closed]
In the functional-renormalization-group (FRG) formulation of quantum gravity, the effective average action Γₖ evolves with the RG scale k according to the Wetterich equation
$$\partial_k \Gamma_k = \...
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Is there any difference between the left and right local minimum of the real-valued Higgs field's double well?
The real-valued Higgs field potential is usually described as a double well, where below a certain temperature the ball has to roll in one direction and go to a local minimum. There are two local ...
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Adiabatic evolution of the free vacuum in QFT
In the context of the pertubative expansion of Green's functions in Quantum Field Theory, it is a pretty standard trick to assume the free and interacting Hamiltonian are conected via adiabatic ...
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Partial waves in QFT: Why only $l=0$ modes contribute for $\varphi^n$ like interactions, and for derivative interactions we also have $l \ne 0$?
Some context
In these notes on AdS/CFT by Jared Kaplan (section 8.1) on pg. 70-71, he tries to derive anomalous dimensions from basic quantum mechanics and the idea is simple: We are doing ...
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Formal definition of $d$-dimensional integral for complex dimension $d\in\mathbb{C}$
This question concerns the definition of dimensional regularization in quantum field theory, specifically as presented in this Wilson paper (see free version here).
This operation must fulfill three ...
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