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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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rasing lovering indices of 3- vectors?

Now, let space tmie metric is $$\eta_{\mu\nu}=\text{diag}(+,-,-,-)$$ now $$x_{\mu}=(x^0,-\mathbf{x})$$ and $$x^{\mu}=(x^0,\mathbf{x})$$ and $$x^{\mu}=\eta^{\mu\nu}x_{\nu}$$ also $$\partial_\mu=(\...
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26 views

Baryon number conservation

Can someone explain me why the Hamiltonian for the nucleon field (derived from the corresponding Lagrangian) $$H_N=\int d^3xN^\dagger(\textbf{x})\Big(-\frac{\nabla^2}{2M_0}+M_0\Big)N(\textbf{x})$$ ...
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15 views

Vector current conservation in vertex correction

Recently, I was calculating this observable: $\langle p s|\bar\psi(0)\gamma^{\mu}\psi(0)|ps\rangle$ Where we only consider the QED case. $\psi$ corresponds to massless Dirac fermion field, p is the ...
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21 views

When do the solutions of combinatorial Dyson-Schwinger equations generate a Hopf subalgebra?

Say I have a set of combinatorial Dyson-Schwinger equations of the form $$\begin{align} X_1 &= \mathbb{1} + \alpha B_+^a (f_1(X_1,...X_N)) \\ & ... \tag{1} \\ X_N &= \mathbb{1} + \alpha ...
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39 views

Finite conformal transformations of fields from infinitesimal

I know that in conformal field theories conformal group acts not by pushforwards but (e.g. for scalar field $\phi$ with conformal dimension $\Delta$) $$ \phi(x) \mapsto \phi'(x') = \left| \frac{\...
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Scalar electrodynamics “seagull” vertex factor

By expanding the covariant derivative of the Scalar QED lagrangian one gets the following term, sometimes called "seagull" vertex. $$\mathcal{L}_{seagull} = -q^2A_\mu A ^\mu \phi^\dagger \phi$$ Most ...
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1answer
41 views

Klein-Gordon Inner Product from Greiner's book doubt

I was working on free field theory from Greiner's book "Field Quantization" In chapter 4, he introduces these phase functions: $$ u_{p}(\boldsymbol{x}, t)=N_{p} \mathrm{e}^{-\mathrm{i} p \cdot x}=\...
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2answers
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Gauge fixing, invertibility and Green's functional

consider the photon in QED and the corresponding EOM of its Green's functional in k-space: $$(k^\mu k^\nu-k^2g^{\mu\nu})\Delta_{\nu\rho}(k)=i\delta^\mu_\rho.$$ Now, I understand that $U^{\mu\nu}(k):=...
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58 views

Are there more than 3 dynamical pictures of quantum mechanics?

There are 3 well known dynamical pictures of quantum mechanics: the Schrödinger picture, the Heisenberg picture and the interaction picture. In above wikipedia article, their connection is nicely ...
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1answer
68 views

Does Quantum Mechanics claim that dynamical fields have quantum properties?

While reading some of the non-technical articles on quantum gravity, I have come across to a message several times. Consider the following quote taken from the articles form "Approaches to Quantum ...
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1answer
57 views

Renormalization constants

I would like to understand how to extract renormalization constants of vacuum polarization diagram in pseudoscalar Yukawa theory with interaction $ig\bar{\psi}\gamma^5\psi$. This diagram is ...
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29 views

Self Study in QFT question - Srednicki to Weinberg [on hold]

I’ve seen the questions on the forum on books to learn QFT from, but this question is more specific to my situation. Ultimately I want to work through Weinberg. I’ve been using Srednicki as a ...
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1answer
65 views

How to obtain this formula for 2+1 dimensional boosts

In this paper on anyons, a formula for boost transformations in 2+1 dimensional spacetime is given (equations 2.7--2.10). The boost transformation here is defined as: $$\displaystyle B(p) \hat{p} = p$$...
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How everyone can benefit from learning physics? [on hold]

What would be benefits of learning physics in a relatively rigorous way (meaning to take a quick look even at the topics that are more advanced, like quantum field theory) for people who don't aspire ...
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3answers
129 views

How inflation creates a universe from nothing?

I have a basic, mostly purely conceptual understanding of Quantum Field Theory, and after lots of Youtube (thanks PBS Spacetime!) I have an idea of how inflation works to turn the vacuum into a ...
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45 views

Is the Standard Model UV complete? If not, why? [duplicate]

Below is my understanding of why QED is not UV complete. Please correct me if I am wrong. As a necessary condition, a UV complete quantum field theory must be renormalizable. But a renormalizable ...
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30 views

Four-Divergence of a massive vector field in the interaction term

In an exercise is given the following Lagrangian $$\mathcal{L} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} + \frac{1}{2}MA^\mu A_\mu + \bar\psi(i\gamma^\mu\partial_\mu - m)\psi + \mathcal{L}_{int}$$ with the ...
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How $W^{\pm}$ bosons get their electric charge $\pm 1$ as opposed to $Z_0$ that have neutral electric charge?

In the 'Standard Model' book by Y. Grossman and Y. Nir, in chapter 7 (the leptonic standard model) on page 93 after defining the charge of the broken symmetry generator, i.e $Q=T_3+Y$ they say that ...
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3answers
63 views

Which particle mediates the Aharonov-Bohm effect?

BACKGROUND The Aharonov-Bohm (AB) effect induces phase shifts between the two paths that an electron could take around an enclosed magnetic field. In radial coordinates, assume that the magnetic ...
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1answer
37 views

Creation and Annnihilator Operators: generality and meaning

I am studying my fisrst course in quantum mechanichs where we treated the example of the Harmonic Oscillator through the Weyl Heisenberg Spectrum Generating Algebra Method. In that context we ...
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1answer
75 views

Doubt about mathematical construction underlying physical systems

Consider the first and second videos of this playlist $[1]$. It seems the professor tried to discuss some heuristic approach between number theory abstract algebra and physics; Classical Physics is ...
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48 views

Existence of interacting scalar field theory

I saw a comment in Schwartz's introductory text on Quantum Field Theory (cf. Section 14.5) that it is known that $\phi^4$ theory in five dimensions does not exist. In four dimensions it is not known, ...
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1answer
60 views

Reference for proof of renormalizability

I have been trying to truly understand the renormalizability of quantum (i.e., without anomalies) gauge theories (after which I will focus on the case with spontaneous symmetry breaking). The problem ...
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1answer
50 views

Harmonic oscillator path integral: regularizing the functional determinant

From Polchinski's Vol. 1 Appendix A, we can reduce the Euclidean path integral for the 1D harmonic oscillator to computing $(\det\frac{\Delta}{2\pi})^{-1/2}$ where $$\Delta = -\partial_u^2 + \omega^2.$...
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16 views

Transformation of fermionic creation and annihilation operators

How do the creation and annihilation operators of Dirac fermions transform under a Lorentz transformation whose axis is not parallel with the axis of spin quantization?
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17 views

From the general decomposition of electric field to one polarized along $\hat{\textbf{x}}$

In the gauge $A^0=\nabla\cdot\textbf{A}=0$, starting from the Fourier decomposition of $\textbf{A}(\textbf{x},t)$, the electric field $\textbf{E}(\textbf{x},t)$ is obtained as $$\textbf{E}(\textbf{x},...
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Implications of Instanton Corrections (to Degenerate Vacuua) for Spontaneous Symmetry Breaking

We consider that if the classical vacuua of a theory are degenerate then each of them can be non-invariant under one or more of the symmetries of the Lagrangian. We can choose one of the vacuua and ...
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89 views

Proper time for a relativistic particle in quantum mechanics?

It is an often cited fact that a muon falling through the atmosphere at great speed has a decay time longer than the one we would observe in the same particle at rest due to relativistic effects, and ...
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20 views

Computation of the self-energy term of the exact propagator for $\varphi^3$ theory in Srednicki

In M. Srednicki "Quantum field theory", Section 14 -Loop corrections to the propagator-, the exact propagator $\mathbf {\tilde \Delta} (k^2)$ is stated as $$\frac{1}{i} \mathbf {\tilde \Delta} (k^2)...
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1answer
61 views

Feynman diagrams, Feynman rules and corresponding integrals

I would like some basic examples of Feynman diagrams: in particular I would like to understand how a Feynman diagram produces an integral: before I start let me made some remarks in the form of a ...
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35 views

Expection values of the hamiltonian of Klein-Gordon field

The hamiltonian of the quantized Klein-Gordon field $\phi(\textbf{x},t)$ can be writting using the creation and annihilation operators: $$\hat{H} = \frac{1}{2} \int d^{3}\textbf{p} \ \omega_{p} (\hat{...
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27 views

Why is field action not a pseduo-scalar in 4D?

If the Lagrangian density is a scalar and the 4-volume is a pseudo-scalar (w.r. to proper orthochronous LT), how is then action not a pseudo-scalar? If it is a pseudo-scalar (i.e. the above reasoning ...
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Parity transformation on annihilation operator for the Dirac field $U(p)^{+} c_{r}(\vec k)U(p)=i c_{r}(- \vec k)$

I want to verify the discrete parity transformation action on annihilation operator for the Dirac field. Given the dirac field: $$ \psi(x) = \frac{1}{(2\pi)^{\frac{3}{2}}} \int \frac{d^3k}{\sqrt{2\...
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2answers
86 views

Why can't two real photon, gluon, graviton, and $W$ and $Z$ fields interact by means of their virtual counterparts (the mediators of the process)?

It is a fact that two real (massless) photons, gluons, or gravitons can't react by means of their virtual counterparts (for example, two external photons that interact via one of these massless ...
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1answer
96 views

What's the meaning of “inequivalent quantizations”?

The notion "inequivalent quantizations" is regularly used when topological terms are discussed. From what I've gathered so far, "inequivalent quantizations" means that there are different quantum ...
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27 views

What happens to large gauge transformations in gauges different from the temporal gauge?

There are already several questions regarding the meaning and definition of large gauge transformations. Discussions of large gauge transformations typically only happen in the context of the ...
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30 views

Are negative values in quantum fields the basis of anti-particles? [closed]

Perhaps I'm asking a question which I am not even qualified to ask, but in researching Quantum Field Theory I've seen reference to negative values in the field. If one understandings the existence of ...
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16 views

Implications of momenta sign conventions in QCD Feynman rules

In QCD, the Feynman rules for the vertices are usually presented with all momenta pointing inward. For the total amplitude of a given process, does this also affect the signs of the momenta taken in ...
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1answer
58 views

Interpretation of field operators

In the book Field Quantization of Greiner, in section 3.2 he introduces the field operators (for bosons), that are postuleted to satisfy the commutation relations $$[\hat{\psi}(\textbf{x},t), \hat{\...
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1answer
229 views

Why aren't all particles virtual? [duplicate]

It is my understanding that virtual particles are those that are internal to a particular interaction. They do not fulfill the requirements of a freely-travelling particle (ie a plane wave) and as ...
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1answer
42 views

Anomalies in Global Symmetries (Srednicki ch 76)

In chapter 76 of Srednicki's QFT book, he defines $C^{\mu\nu\rho}(p,q,r)$ via (76.21) \begin{equation} (2\pi)^{4}\delta^{4}(p+q+r)C^{\mu\nu\rho}(p,q,r)\equiv \int d^{4}xd^{4}yd^{4}z e^{-i(px+qy+rz)}\...
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1answer
174 views

Conservation of angular momentum in pair annihilation in scalar QED

Suppose we have the usual scalar QED for a massive charged field $\phi$ , $$\mathcal L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D_\mu\phi)^\dagger(D^\mu\phi)-m^2\phi^\dagger\phi$$ with $g^{\mu\nu}=\text{...
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3answers
64 views

Bound on fermions in a finite volume?

The Pauli Exclusion Principle says that two or more identical fermions cannot occupy the same quantum state within a quantum system simultaneously. However, I'm wondering if we could potentially pack ...
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20 views

How to put the terms in correct order when deriving amplitudes in QED from the S-Matrix?

I am trying to derive the amplitude for the Møller scattering process $e^-+e^-\rightarrow e^-+e^-$ from "first principles", that is, by working out the calculation with the relevant S-matrix terms ...
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2answers
87 views

Interpretation of the propagator

In quantum mechanics, it is clear that $\langle x|y\rangle = 0$ for $x\ne y$, where $|x\rangle$ is the state with the particle at position $x$. (Notice that this $|x\rangle$ is different from the ...
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1answer
36 views

What's the relation between Euclidean and Minkowski entities in lattice field theory?

To my understanding, lattice QFT basically continues the time $t$ (and fields depend on it) in Minkowski space action to imaginary time $\tau\equiv it$. But normally when we do calculations in lattice ...
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1answer
39 views

Solutions of relativistic wave equations compared to classical wave functions

In classical quantum mechanics, absolute square of the wave function (i.e. $|\psi|²$) means probability density of particle's location, so when we integrate this over certain volume we get the ...
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0answers
28 views

Is the Casimir force a conservative or a non-conservative forces?

If the Casimir force is a non conservative forces, how can this affect the polarized vacuum theory in the universe's evolution?
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78 views

The very first phase of our universe, are we missing something? [closed]

We have no really secure information from the very first phase of our universe, because we can neither observe nor generate the corresponding energies experimentally. Therefore, all these initial ...
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1answer
20 views

Does density of states at Fermi level reduce or increase for decreasing the diameter of a nanowire?

As we decrease the diameter of a nano wire /quantum wire, does the density of the states at Fermi level increase or decrease?. If it does then, Why?