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 [tag:particle-physics]. Don’t combine with [tag:quantum-mechanics].

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Interference in “Frustrated Two photon Creation”

In this paper it is explained how an SPDC source can have its emission inhibited by destructive interference with emission from a previous time. I have had a (maybe incorrect?) general intuition ...
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Is there a first-order formulation of CP-violating QCD?

In QCD without a CP violating $\theta$ term, (I believe) we can express the gauge kinetic Lagrangian in a first-order form with the field strength $F_{\mu\nu}$ taken to be Lagrange multipliers. Up to ...
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Momentum in complex scalar field

Consider a complex scalar field $\psi(x)$ with Lagrangian density $$ \mathcal{L} = \partial_\mu\psi^* \partial^\mu\psi - M^2\psi^*\psi. $$ Expand the complex field operator as a sum $$ \psi = \int \...
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Commutation relations for creation, annihilator operators $a_\mathbf{p}^\dagger, a_\mathbf{p}$

Write the field $\phi$ and momentum $\pi$ in terms of creation and annihilation operators $a_\mathbf{p}^\dagger, a_\mathbf{p}$ $$ \phi(\mathbf{x}) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_\...
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First-order Contribution to the Self-energy Operator

In Altand and Simons' book 'Condensed Matter Field Theory,' on page 225 they claim that the first-order contribution to the self-energy (effective mass) operator reads $$[\Sigma_{\vec{p}}^{(1)}]^{ab} =...
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What is an vacuum in QFT in curved spacetime?

Sometimes in some public lectures about General Relativity (GR) and Quantum Mechanics, in college, the professors dealt with the vacuum concept, precisely in the context of Quantum Field Theory (QFT), ...
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Quantum Non-Demolition of entangled superposition using an electron with infinite spin

Disclaimer: I have no idea what I am talking about, as I just started college and barely understand quantum physics. If an electron can have a linear velocity of the speed of light, theoretically ...
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Off-shell angular momentum conservation

In QFT, when the scattering process occur, the mass does not conserved in off-shell. What I'm curious about is whether the angular momentum is conserved or not in off-shell. Thank you for answering ...
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Can we derive $\vec{S}=\frac{1}{2}\vec{\Sigma}$ in a representation independent way in terms $\vec{\alpha},\vec{\beta}$?

For the Hamiltonian $H=(\vec{\alpha}\cdot \vec{p}+\vec{\beta}m)$ of the Dirac equation $i\frac{\partial \psi}{\partial t}=H\psi$, it can be shown that $[H,\vec{L}]=-i(\vec{\alpha}\times\vec{p})$. Now, ...
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Entropy in the SYK model

Reading about the SYK model I encounter a trick that should help to calculate the thermal entropy of the system. I am not able to understand what they are doing though. Particularly the part from eq....
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What macroscopic, classical fields exist?

Two example are certainly the electromagnetic field and the gravitational field. The Higgs field, weak fields, and strong fields are too short ranged to operate on macroscopic scales. Moreover, the ...
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Question about operator spreading in QFT

It is a well-known effect that generic localized operators spread out under evolution by lattice Hamiltonians. For example , $e^{iHt} \sigma^x _j e^{-iHt}$ will in general not be supported only at ...
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Is my understanding of physics/ my theory possible? If not, why? [on hold]

WARNING: LONG POST, PLEASE READ ONLY IF YOU HAVE TIME I was never a fan of particles and Einstein’s time dilation. It just does not seem right to me that forces have speeds and mass - attributes ...
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Collective, emergent motion, solitons etc. in multiparticle system described by second quantization?

Multiparticle systems are described by vectors of creation and annihilation operators $a_i^\dagger$, $a_i$ for each particle $I_i$. The atate is described by $b_1 b_2\dots b_n$ applied to the ground ...
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Which temperature transformation does QFT allow?

Background Taken from here Is temperature a Lorentz invariant in relativity?: Einstein himself, in a 1907 review (available in translation as Am. J. Phys. 45, 512 (1977), e.g. here), and ...
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Chiral anomaly: gauge covariance and regularization

I am looking at the treatment of the chiral anomaly in Fujikawa and Suzuki's "Path Integrals and Quantum Anomalies." To illustrate the quantum breaking of chiral symmetry (section 4.3), they start ...
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Why doesn't accelerating reference frames in QFT lead to horrible paradoxes?

Background So I remember that in Special Relativity while one can define acceleration things can go horribly wrong has happened historically (I'm sure there many other paradoxes). The real reason of ...
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Bosonization and gauge symmetry

The bosonization map relates the fermionic current $\bar{\psi}\gamma\psi$ to the bosonic current $\partial\phi$, and also the components of $\psi$ to $e^{i\sqrt{\pi}\left(\phi\pm\bar\phi\right)}$. ...
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Self-energy series expression in terms of unperturbed Green function for exited states

I would like to understand how to arrive at the series in equation (36) in this paper https://arxiv.org/abs/cond-mat/0506438, specifically $$\Sigma(E) = V+VG'_0(E)V+VG'_0(E)VG'_0(E)V$$ where $G'_0(E)$ ...
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Feynman diagram literature for antiproton production via proton-proton collisions

I'm looking for literature, or anywhere I can find a Feynman diagram, which describes the proton-proton collision where antiprotons are produced in the following reaction: $$\rm{p} + \rm{p} \...
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Ward identity prohibits mass of photon

On wikipedia one can read the following statement: The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of ...
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Wick Rotation and sign of the integrand in Weinberg's book

I'm studying from Weinberg's QFT volume 1, chapter 11. I have a problem with equation $(11.2.7)$. Starting from eq. $(11.2.5)$ $$ \begin{align} \Pi^{\rho\sigma} (q) = \frac{-ie^2}{(2\pi)^4} \int_0^...
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In what way do non-rigorous arguments make sense? [on hold]

I specifically have in mind arguments made in QFT textbooks in mind. There are no rigorous foundations for QFT, at least not any that can reproduce the predictions of the Standard Model. In fact, ...
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Symmetry factor of gluon self-energy

In Peskin & Schroeder, p.523, they give the diagram contributing to the gluon self-energy that arises from the 3-gluon vertex, and they claim that the $1/2$ factor is a symmetry factor: How can ...
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How is “the collapse postulate is also present in QFT, only hidden inside the LSZ formula?”

Background So I am reading the following here (Blog: Not Even Wrong, Blog post: Not So Spooky Action at a Distance, Commenter: vmarko) "The collapse postulate is also present in QFT, only hidden ...
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Equivalence Principle holding in Special Relativity? (let alone QFT)

Motivation I am pretty confused of why people are hopeful to find a version of the equivalence principle ("the complete physical equivalence of a gravitational field and a corresponding acceleration ...
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Local fields vs particles

I have heard it said that Richard Feynman was a proponent of a particle approach to QFT while Julian Schwinger preferred a local fields description. What is meant by “local fields”? Surely when one ...
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Does the vacuum energy density of quantum fields violate conservation of energy?

The vacuum energy density, or the zero point energy, of fields are said to be constant as space expands. Doesn't this mean that as space expands, more and more energy is being created? Don't particles ...
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Does the delayed choice quantum eraser demonstrate the state of the entangled particles are set before they even start moving?

This would mean unobserved quantum waves do not use spacetime and their lives (the states they will ever be) from point A to B are instantaneous. i.e. they are not using time from spacetime when ...
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Feynman rules for scalar field with second order derivatives in the interaction term

Given the interaction term with $N$ scalars $\phi_i$, each massless, what would be the Feynman rules for an interaction term in the action as $$ \int d^dx (\partial^2 \phi^i)\phi_i(\partial_\mu \phi^...
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Field strength renormalization and the energy-momentum tensor

This question is about the connection between the energy-momentum tensor, dilation transformations, and field renormalization. From a Wilsonian perspective on renormalization we start out with a ...
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What are current major things going on in the field of Quantum Spin Liquids? [closed]

I have recently started reading about quantum spin liquids (QSL). I have read a few articles, everyone is talking about high-temp superconductivity -- first proposed by Anderson in 1973, and Quantum ...
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Feynman rules of $\mathcal{N}=4$ supersymmetric Yang-Mills in Euclidean space

I am trying to derive the Feynman rules for $\mathcal{N}=4$ supersymmetric Yang-Mills. The (Euclidean) action that I start with comes from this paper (Wilson Loops in $\mathcal{N}=4$ Supersymmetric ...
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Why propagator in three time intervals can be connected together in the Green function?

In the page 91 of Many particle physics by Mahan, why $S(+\infty,t) C(t)S(t,t')C'(t')S(t`,-\infty)$ in the numerator can be written as $C(t)C`(t`)S(\infty,-\infty)$? And why in the first place the ...
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Vacuum decay and Coleman-de Luccia bubbles

Can someone suggest me some good and detailed books (or notes) on the problem of vacuum decay and Coleman-de Luccia bubbles?
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How to properly make sense of the $\mathcal{S}$-matrix as a correlator on a sphere?

In the book "Lectures on the Infrared Structure of Gravity and Gauge Theories" by Andrew Strominger, the author discusses in Chapter 3 the idea of "The $\mathcal{S}$-matrix as a Celestial Correlator". ...
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What is a non-local particle in condensed matter physics?

What exactly is "non-local" in physics? How can a particle be non-local particle? Are non-local particles and collective modes related with each other? Are solitons local or non-local? (I am asking in ...
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Physical Meaning of a Quantum Field

Sorry in advance if this question doesn't make sense. Anyway, I am reading a paper about quantum field theory and the Whitman Axioms (http://users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf), ...
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Questions about mean field theory

I have a question about mean-field theory. Suppose I have a Hamiltonian like: $$H=\sum (a^{\dagger}_{i}a_{i+1}+h.c)+U\sum (a^{\dagger}_{i}a^{\dagger}_{i}a_{i}a_{i}).\tag{1}$$ The part in bracket ...
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Given a positive element, $a$, of a $C$*-algebra, why does there exists a pure state, $p$, on $A$ such that $p(a)=||a||$? [duplicate]

I'm reading secondary literature where they make this claim, however, I cannot see why it holds true. This is a reformulation from a previous question that I didn't specify good enough.
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Generalization of Wick's Theorem

Wick's theorem allow us to write a time-ordering of creation and annihilation operators as a normal-ordering of contractions of these operators. I am studying a system that consists of two kinds of ...
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geodesic equation for electromagnetic field

I am trying to derive geodesic motion for photons from the Lagrangian of electromagnetism coupled to General Relativity. I tried to use the covariant conservation of the Stress energy tensor: $$\...
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What would a Lagrangian without a kinetic term represent?

Imagine we write a Lagrangian without kinetic term, for example something like: $$\mathcal{L} = -\frac{m^2}{2} \phi^2 -\frac{\lambda}{4!} \phi^4. \tag{1}$$ What would that represent? Let's look at ...
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Why is there no gauge-invariant local operator in GR?

I have a hard time understanding why the bulk locality is a question. I know some operator which depends on a particular coordinate $x$, $O(x)$, and its correlation function like $ \langle O(x)O(y) \...
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Irrational Conformal Field Theory v.s. Non-Unitary Conformal Field Theory?

Unitary conformal field theories (CFTs) with irrational (or including the special case of rational) central charge is called irrational conformal field theory (ICFT). Irrational conformal field ...
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Problem during calculation of Pauli-Lubanski vector squared [closed]

I am trying to show that $W^2=-\frac{1}{2}M_{\mu\nu}M^{\mu\nu}P^2+M_{\mu\sigma}M^{\nu\sigma}P^\mu P_\nu$, following the derivation from Ashak Das' Lectures on QFT. Here, $W$ is the Pauli-Lubanski ...
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Field diffeomorphisms preserve the equations of motion

In this paper (Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansion, by Kreimer & Velenich), the authors claim in section 3, page 3, that the field diffeomorphism $F(\phi)$ ...
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Particle hole symmetry in 2nd quantization

In second quantization one the Particle hole trasnformation is defined as \begin{align} \hat{\mathcal{C}} \hat{\psi}_A \hat{\mathcal{C}}^{-1} &= \sum_B U^{*\dagger}_{A,B} \hat{\psi}^{\dagger}_B \\...
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For which values of $n$ and $n'$ are $n \to n'$ particle scattering cross-sections well-defined?

When studying particle interaction events in QFT, we usually consider either (a) $2 \to 2$ particle "scattering" events, whose probabilities are quantified by scattering cross-sections, or (b) $1 \to ...
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Complete proof of Von Neumann's uniqueness theorem

I am looking for a complete detailed proof of Von Neumann's uniqueness theorem. I found two books. The first is a book written by Derezinski and Gerard (Mathematics of quantization and quantum fields) ...