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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Looking for self-contained introductory books on Quantum Field Theory and QM [closed]

Like the title says, I am looking for introductory books on QM and QFT that is self-contained (has all the mathematics and physics required). Any help with me much appreciated. Self-containment is ...
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Luttinger Liquid Parameter - Attractive or Repulsive

For 1+1D systems at long wavelength, it is known that the (Tomonaga)-Luttinger Liquid can be rewritten in terms of bosonic parameters, where the Hamiltonian densities can be written \begin{align*} H =&...
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Is a field a physical object?

I read in various sources that fields in physics are some distribution of quantities at different points in space. For example, an electric field is the distribution of the value of the electric ...
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Particle fields and field theory

All particles have their own fields. More precisely, I've learned that an electron is just a bundle-up packet of energy from an 'electron field'. So as in this sense, all particles (from the standard ...
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1answer
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Question on how to actually use momentum space Feynman rules in $\phi^4$-theory

The momentum space Feynman rules state that we "integrate over all undetermined momenta" and "impose momentum conservation at each vertex". This is given for example on page 95 of ...
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Photon - Neutrino interaction

Suppose we have a laser source, that means a coherent laser beam formed by 'in phase' photons. Is it possible to calculate how many photons can change their wavelength in neutrino - photon interaction ...
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Particle representation and Field representation

This question might be too trivial/dumb but I wanted to be more specific about how one can distinguish between Particle representation and Field representation by looking at the underlying mathematics ...
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Mathematics for general gauge structure?

I am currently studying field-antifield (BV) quantization formulation from the review - arXiv:hep-th/9412228. This review gives a nice and quite involved treatment of general gauge structure and how ...
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1answer
89 views

What is the idea behind the quantization of fields?

I'm trying to learn the basics of quantum field theory and I must say it has been quite difficult to me. After some deep thinking, it occurred to me that one of my main difficulties here is that I don'...
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58 views

What does negative $\mu$ physically means?

I have recently heard the following statement: A negative chemical potential means absence of particles. However, I cannot make this consistent with e.g. a system of free bosons for which $\mu$ must ...
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1answer
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Do negative energies exist in the Standard Model?

As far as I understand, the Hamiltonian of QED and QCD are positive definite. The QED Hamiltonian in Coulomb Gauge is given by the following (credits David Tong QFT Notes): $$ H=\int d^{3} x\left[\...
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1answer
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QFT/QM on loop space

I am reading "Gauging What's Real" by Richard Healey and the author argues for formulating electrodynamics/QED on loop space/the holonomy group, so that the real objects described by the ...
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How do we find Noether currents for quantum fields, given that they are operators?

I am reading Quantum Field Theory for The Gifted Amateur by Lancaster and Blundell. In the book, it states that quantum fields transform under spacetime translations according to the rule $$\hat U(a_{\...
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Dimensional analysis and more: Order of divergences in the $\phi^4$ theory

On page 324 of his book on qft, Peskin analyzes the superficial degree of divergence of the 1-loop self-energy correction of the $\phi^4$ scalar theory. Realizing that $D=2$, he concludes that the ...
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Transition amplitude, $\langle f|i\rangle$ or $\langle f|S|i\rangle$?

I have seen the transition amplitude was written in different ways, but I don't understand. For example, in Mark Srednicki's textbook section $10,11$, it is written as $\langle f|i\rangle$. But in ...
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Multi-mode Fock states

I would like to ask if this expression makes sense. $$|Ψ⟩ = \frac{1}{\sqrt{7}}(|1000000⟩+|0100000⟩+|0010000⟩+|0001000⟩+|0000100⟩+|0000010⟩+|0000001⟩)$$ For example, $|1000000⟩$ represents one particle ...
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Spinor satisfying Dirac's equation with $M\neq 0$, how one should start evaluating Pauli-Lubanski scalar on it

I have been provided that Spinor $\psi(x)$ satisfying Dirac's equation with $M\neq 0$, how one should start evaluating Pauli-Lubanski scalar on it, I mean how to evaluate $W^{\mu}W_{\mu}\psi(x)?$ ...
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An exercise for axion from Mark Srednicki's QFT book

In Mark's QFT book, exercise 94.2(d) says In eq.(94.10), we should replace $\theta$ by $\theta+a/f...$. eq.(94.10) is just the mass term \begin{equation} M=Diag\{m_{u},m_d\}e^{-i\theta/2}, \end{...
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Spontaneous symmetry breaking, massless bosons and the equations of motion

I am currently studying spontaneous symmetry breaking, and I don't entirely understand the implications of what we are doing at certain places. Consider the standard complex scalar field with the $\...
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Classical field theory correlation function

I'm studying QFT from Schwartz's "Quantum Field Theory and the Standard Model", and in chapter 7 he derives the Schwinger-Dyson equations for the correlation functions in a scalar field ...
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1answer
59 views

LSZ reduction formula for free fields

I'm reading the section on the LSZ reduction formula in Schwartz's QFT book and he talks about the action of free fields in the formula. Specifically he says (sec. 6.1.1, p. 73): The LSZ reduction ...
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1answer
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On the normal ordering of Fermi fields

From my understanding, the normal ordering of Klein-Gordon fields in QFT is valid because of the ambiguity that comes with quantizing a classical theory, in the sense that the conmutator of fields is ...
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Why do we not observe a greater Casimir force than we do?

I am very new to quantum field theory, so forgive me if this question is a bit silly. The Casimir force is usually explained by the zero point energy of the field. You assume that the frequencies of ...
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Does a photon have an amplitude of motion at a speed less than the speed of light?

In the book QED: The Strange Theory of Light and Matter, Richard Feynman writes that for a photon there are nonzero amplitudes of motion with a speed that is greater or less than the speed of light. ...
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Question about the position of electron and it mass [duplicate]

In order to measure the location of an electron you may use a photon, so the photon would hit the electron exactly where the electron, according to QFT. But wouldn't the mass of the electron create a ...
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How is the interaction time distributed in quantum mechanics? [closed]

In quantum mechanics, the time of the beginning of the interaction and the time of the end of the interaction of particles are precisely defined, or are they "smeared" over the entire time ...
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What are these symbols /feynman diagrams physically [closed]

Well the symbols are as follows These are the images from the diagrams, I wanted to know what physical meaning of them, if it has.
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How to understand the action in path integral formulism of field theory?

In Quantum Field Theory for superconductors (see e.g., P292 of Condensed Matter Field Theory by Altland and Simons), there was a action given by: $$S[\theta] = \nu\sum_{m,q}\omega_m^2\theta_{m,q}\...
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Does the structure constant of Yang-Mills field change sign under time reversal?

The time reversal of Abelian (electromagnetic) field strength is pretty straight forward. The electric field $F_{0i}$ is even under time reversion. The magnetic field $F_{ij}$ is odd under time ...
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Diagonalizing the linearized optomechanical Hamiltonian

I am trying to diagonalize the Hamiltonian in equation (2) in the paper "Nonlinear Interaction Effects in a Strongly Driven Optomechanical Cavity", by the means of a Bogoliubov ...
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Possible errata in Weinberg volume 3 (SUSY calculation)

I am wondering if I have spotted an errata in Weinberg volume 3, equation 26.1.3. Here is my derivation. Let $Q_b$ be supersymmetric symmetry generators and $\zeta_a$ spinor fields given in terms of ...
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How to understand this formula in quantum field theory?

In Condensed Matter Field Theory (page 288) by Altland and Simons, there is one mathematical formula: \begin{equation} \sum_\mathbf{p} \left(\mathbf{p}\boldsymbol{\cdot}\mathbf{v}\right)\left(\mathbf{...
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Wick rotation on Ward identities

I'm having trouble performing a Wick rotation back to Minkowski spacetime ($\eta_{\mu\nu}=(-1,1,1,\dots)$), following page 19 in the lecture notes here. I have this expression (equation 53 from the ...
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Is the contribution of diagrams without vertices taken into account in calculating the process amplitude?

It seems I have finally decided on the question. When expanding the interaction process in a perturbation theory series, it is also necessary to take into account the contribution of the diagrams in ...
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How to distinguish first-order Feynman diagrams from the rest? [duplicate]

On what basis is it determined to what order the given Feynman diagram belongs? Does it depend on the number of interaction vertices? For example, two vertices are first order, four vertices are ...
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Confusion about spontaneous symmetry breaking rod example

I was reading a book on QFT and the example he uses to make an analogy of spontaneous symmetry breaking in QFT is that of the rod where a compressive force is applied on the top surface of the rod ...
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The neutrinoless double beta decay can only occur if $\dots$

In Wikipedia https://en.wikipedia.org/wiki/Neutrinoless_double_beta_decay#Overview it says that The neutrinoless double beta decay can only occur if (1) the neutrino particle is Majorana, and (2) ...
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1answer
66 views

Particle interpretation for Fields and (non) vanishing VEV

I have some questions about the first part of the answer by Arnold Neumaier dealing with the interpretation of VEV (vacuum expectation value). Let me quote the parts I would like to understand better: ...
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Spontaneous Symmetry Breaking vs Addition of 'Mass terms' by hand [duplicate]

Let consider an $SU(2)$ doublet of bosons $\Phi =(\phi_A, \phi_B)$ which is described by the Lagrangian $$L = (\partial_{\mu}\Phi)^{\dagger}(\partial_{\mu}\Phi) +a^2 V(\Phi^{\dagger} \Phi) -\frac{\...
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Third-order Feynman diagrams of 2-point function in $\phi^4$-theory

$\newcommand{\Braket}[1]{\left<\Omega|#1|\Omega\right>}$ Hello, I am currently studying QFT and have a problem concerning the 2-point correlation function in $\phi^4$-theory. When I draw all the ...
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Why secondary constraints in Quantum Theory?

I am self-studying dynamics of constrained systems and their quantisation from Rothe and Rothe book "classical and quantum dynamics of constrained systems". While using Dirac quantisation, ...
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1answer
55 views

How to correctly represent a quantum field?

How to correctly represent a quantum field? As something single that fills all space (and particles are excitations of the field just like waves are excitations of a single ocean), or as a set of ...
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Example of truncated expectation which gives a disconnected diagram. Where am I wrong?

My notes introduce the truncated expectation in the following way: given $S_0$ a quadratic form, consider a generating function $$e^{W(J)} = \int \prod_x d\varphi_x e^{-S_0+ JO} = \int P(d\varphi) e^{...
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1answer
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Casimir energy in a circle for a scalar field with antiperiodic conditions

Following the section 2.3 of the book "Advances in the Casimir Effect" by M. Bordag, the Casimir energy is given, for a maseless field, by $$E(a) = E_0 (a) - E_{0M} (a)$$ where $E_0 (a)$ is ...
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1PI effective action action for quadratic interaction [closed]

If the interaction given like $-\frac{\lambda}{3!}\phi_1\phi^3_2$. How can I derive the 1PI effective action?
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Real scalar field and its quantum state: why are the diagonal components static here?

Consider a (free and massless) real scalar field $\phi(x)$ with Hamiltonian $$ H := \int d^3\mathbf{x}\; \bigg[ \frac{1}{2} \pi^2(\mathbf{x}) + |\nabla\phi(\mathbf{x})|^2 \bigg] $$ where $\pi(\mathbf{...
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Why should the split property hold in AQFT?

In algebraic quantum field theory, one assigns complex unital $*$-algebras (or von Neumann algebras) $\mathfrak{A}(O)$ to open regions $O$ of Minkowski spacetime. I am reading an article by Chris ...
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41 views

Energy-momentum $T_{00}$ component for a scalar field in 2-dimensional spacetime

I'm reading the book "Advances in the Casimir Effect" by M. Bordag. In section 2.4 it says that the $00$-component of the energy-momentum tensor is given by (eq. 2.59): $$T_{00}(t,x)=\frac{\...
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1answer
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Chiral symmetry breaking and appearance of hadrons (from Schwartz's QFT book)

Matthew Schwartz's QFT book mentions following thing, but I cannot understand the logic Spontaneous symmetry breaking of $SU(2) × SU(2)$ happened 14 billion years ago, when the temperature of the ...
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Proton decays in Pati Salam model or Georgi Glashow model

This Pati-Salam model doesn't predict gauge mediated proton decay, according to Wikipedia. However the Georgi-Glashow model predict gauge mediated proton decay, according to Wikipedia. I thought the ...

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