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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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Black hole horizon states in standard derivations of Hawking Radiation

In all standard derivations of Hawking radiation given e.g. by Hawking, Parker and Wald, one has the so-called horizon states. The point is that when one is quantizing a scalar field on a black hole ...
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EW theory vertices

I'm trying to undertand the following vertex: Initial state of up and anti-down quarks with finalk state made of $W^+$ boson. Does it go with left or right projector? I think that from Lagrangian it ...
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Peskin & Schroeder eq. 9.26 and functional methods

I have been reading chapter 9 in Peskin & Schroeder's QFT book and has been stuck in transition from equation 9.26 to 9.27. Equation 9.26 reads: $$\frac{1}{V^2} \Sigma_{m,l} \exp{[-i(k_m.x_1+k_l ....
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Two-point correlation function of a scalar field $\langle 0 | \phi(x) \phi(0)| 0 \rangle$

I'm trying to find the two point correlation function for a massless scalar field obeying $\square \phi = 0$. I can write $$\langle 0 | \phi(x) \phi(0)| 0 \rangle = \int \frac{d^dk}{(2\pi)^d} \delta(...
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How does one find the parity trasformation matrix of spinors for non-free field theory?

In many QFT textbook, for example, the book of Srednicki, they use free field theory to derive the transformation matrix of the Spinors: $$P^{-1}\Psi(x)P=D(P)\Psi(P^{-1}x)$$ Then we have a relation: ...
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In Hamiltonian lattice QFT, does low energy imply low momentum?

In relativistic quantum field theory (QFT), the spectrum of the total energy and total momentum operators is supposed to be restricted to the forward light-cone (the relativistic spectrum condition), ...
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Arbitrary function on the Faddev-Kulish dressing

On this paper the authors review the Faddev-Kulish dressing in QED which is a solution to the IR divergence problem. Given one electron momentum $\mathbf{p}$, They define the soft factor by $$F_\ell(...
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Can you apply product rule to arg of a bra-ket?

I found the following expression in a paper: $$ \frac{d}{dt}\arg\langle\phi_+|\dot{\phi_-}\rangle $$ where the $\arg$ term is the argument of the complex number given by inner product between two ...
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How can I prove this relationship between the S-matrix and the Gamma matrices?

For an infinitesimal Lorentz transformation: $$ S(\Lambda)=1+i\epsilon_{\rho\sigma}s^{\rho\sigma} $$ $$ S(\Lambda)^{-1}=1-i\epsilon_{\rho\sigma}s^{\rho\sigma} $$ and apparently if we just plug that ...
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Is every classical field theory with dimensionless couplings conformally invariant?

I'm trying to learn conformal field theory and getting rather frustrated, because I can't find any source that gives decent examples or straightforward logic. In most sources I have found, conformal ...
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Connected components of conformal group $ {\rm Conf}(p,q)$ containing $P$, $T$ and conformal inversion are same or different?

As we known (see this post), the global conformal group for $\mathbb{R}^{p,q}$ is $$ {\rm Conf}(p,q)~\cong~O(p\!+\!1,q\!+\!1)/\{\pm {\bf 1} \}$$ The global conformal group ${\rm Conf}(p,q)$ has 4 ...
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Normal ordered products of operators and inverses

I have been reading this paper ("Operator ordering in quantum optics theory and the development of Dirac’s symbolic method" by Hong-yi Fan), and on page 3 (right-hand column) the author writes that $:...
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Wilsonian RGE: Problem 23.7 in the textbook, M.D. Schwartz's ''QFT and Standard Model'' [closed]

Can anyone give me some hints or directions to work out the solution to the following problem? This problem is from chapter 23 of the textbook written by Professor Schwartz. I can't figure out ...
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Initial values of creation/annihilation operators

I have a question about creation/annihilation operators. For example, if I have an evolution equation for annihilation operator of photon $$ \frac{da_k}{dt} = -i \omega_k a_k$$ I obviously obtain $$...
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Non-eq QFT: functional formalism

I am looking for references (papers, books etc.) where I can find pedagogical introduction to non-eq QFT without hamiltonian approach. I mean that an author start from writing down the generating ...
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1answer
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Can our universe be a true vacuum bubble?

The paper "Spontaneous creation of the universe from nothing" by Dongshan He, Dongfeng Gao and Qing-yu Cai claims that our universe was created by the quantum fluctuations in the metastable false ...
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Intuitive/Physical reason why fields are distributions

I read in Urs Schreiber's notes on mathematical QFT that the infinities in the standard approach to QFT appear because the product between operator-valued field distributions is not always well ...
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Compton wavelength in massive vector field theory

What is the significance of Compton wavelength in massive QEDs? When we expand $A_{\mu}$ in Fourier modes, is there any significance for modes whose wavelength is less than Compton wavelength?
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Time Reversal of electric field in Euclidean signature (Wick Rotation)

This is a follow up to this question: How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)? I am wondering if their (6), using that $E^i_M = F^{0i}_M = i F^{0i}_E = i E^i_E$, ...
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Representations of scalar fields from the expressions of fields

Consider scalar field $\phi(x)$, when we quantize this scalar field we get an expression in terms of creation and annihilation operators as $\phi(x) = \sum c(p)({ae^{ipx} + a^\dagger e^{-ipx}} )$. If ...
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Interacting conformal field theories in spacetime dimensions higher 6?

Are there any papers which directly tackle the question of whether or not there exists interacting CFTs in spacetime dimensions higher than 6? It has been proven that there do not exist any ...
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Ghosts use in the calculus of the scattering matrix

When you perform the calculus of $S$ matrix in, for instance, QCD maybe you need to add ghosts in external legs or internal loops. E.g.: $q\bar{q} \rightarrow gg$ needs 2 ghosts diagrams with ghosts ...
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Quick questions about second quantization?

What were the historical problems that the second quantization solved? My current understanding is that in re-normalisation one splits the result into a finite and a divergent part and only keeps ...
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Can space be considered as a grid of cubes of planck length, or is it continuous? [duplicate]

I don't know how to describe it exactly, please try to understand. The question is if space is continuous or gridded. Consider a particle of planck length (or whatever is the smallest possible ...
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Euler-Maclaurin formula for path integral

Is there a corresponding Euler-Maclaurin formula for path integral when we divide the path integral into discrete lattice? What is the error correction when we divide the space into lattice of length ...
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1answer
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Fourier transform property in Feynman 1986 Dirac Memorial Lecture

In his famous 1986 Dirac Memorial Lecture, Feynman refers to a Fourier transforms theorem holding in case F(w) satisfies "certain properties", while being restricted to positive frequencies only: ...
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Coupled quantum oscillator: Field theory

Consider two masses $m$ connected by a spring with a spring constant $k$. Each mass is also connected to the wall using the same springs. The Hamiltonian is $$ H = \frac{p_1^2 + p_2^2}{2m} + \frac{k}{...
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Could I use this informal explanation for Hawking radiation?

I need to explain Hawking radiation to my classmates for a homework. Could I use this informal explanation? (unfortunately without math). Correct me if I need to change/add something: Quantum ...
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Reality of Dirac kinetic term

The Dirac kinetic term is $$\mathscr{L}_{\text{ferm}}=-i\bar{\psi}\gamma^\mu D_\mu\psi$$ where $\bar{\psi}\equiv \psi^\dagger \gamma^0$. Here I've assumed the mostly plus metric, so $\left(\gamma^0\...
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1answer
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Why can't we superpose two quantum vacuum states?

i read in this paper (Spontaneous Symmetry Breaking as the Mechanism of Quantum Measurement by Michael Grady) that we are not allowed to consider the superposition of two vacuum states. i do not ...
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Dimensional regularization and expansion of gamma function

In my calculations, I used dimensional regularization, i.e. replace $d\rightarrow d-\epsilon$ and calculated the divergent integral. Then, I would like to expand the answer into seriers by $\epsilon$ ...
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How is deSitter group tranformations different from poincare group transformations

In QFT, we have studies Poincare group of massive and massless particles. Is the deSitter group also useful to study such things? What exactly is the main role of this group in QFT? I just know the ...
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Naive question about particles and spinor fields [duplicate]

What is the difference between the "real" particle electron (for instance) and the spinor field of electron? I mean, which means that the electron have been described by a spinor field?My question is ...
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QFT Hilbert space and analysis of quantum black holes

QFT Hilbert space is infinite dimensional and it is known that given a region $A$ and its complement $A^c$ of the spacetime, the QFT Hilbert space $\textbf{does not}$ decompose into $\mathcal{H}_A \...
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Four point function with complex momenta?

It is well known that the four-point function $$\int_{\mathbb{R}^{3,1}}\frac {d^4 q}{((q+p_1)^2-i\epsilon)((q+p_2)^2-i\epsilon)((q+p_3)^2-i\epsilon)((q+p_4)^2-i\epsilon)}$$ can be computed using the ...
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Nonperturbative results for $\phi^3$ theory in dimensions $d>6$?

The theory is nonrenormalizeable in those dimensions, but can you say anything about the theory anyway? Specifically I am wondering about the status of whether the theory is trivial, i.e. a ...
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1answer
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Behavior in renormalization group flow that reaches critical point

First question. Does correlation length in renormalization group flow has to be infinite when it eventually reaches critical point? Second question. Why does renormalization group flow keep partition ...
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Computing correlation functions sandwiched between momentum eigenstates

Suppose I have a free scalar theory, and I want to compute the following correlation function $<p|\phi(\zeta)\phi(0)|p>$ where $|p>$ is a momentum eigenstate in my quantum field theory. My ...
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Can we measure renormalized mass in QFT? [duplicate]

Due to QFT books, we measure pole mass(physical mass) in experiments. From the Lagrangian point of view, renormalized mass is a parameter(in MS bar or some similar renormalization scheme that has an ...
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1answer
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Definition of QFT in Vertex Operator Algebra by Kac

QFT is composed of the following data with some axioms(I omitted them here). (1) Hilbert space $H$. (2) Vacuum belongs to $H$. (3) There is unitary representation of Poincare group. (4) A ...
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Claim of high order electron-electron repulsion

A member of staff at uni once claimed in an interdisciplinary seminar that electron-electron repulsion can be to the 11th power of the reciprocal of displacement. I have tried to find this mentioned ...
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1answer
115 views

Doubt about the probabilistic nature of quantum stuff and the field theory

To the quantum field theory, is it like there's "two layers of reality", one in which things are just probabilities waves that collapses into the quantum fields or is the quantum field and its waves ...
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Feynman diagrams: from QFT to condensed matter

I studied Feynman diagrams in quantum field theories and I'm going to study them in the context of condensed matter physics. In this post Books for Condensed Matter after Ashcroft/Mermin, two books ...
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1answer
113 views

What classifies gaugings?

Gauging a global symmetry $G$ introduces several free parameters to the theory. For example, In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
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Feynman $i\epsilon$-prescription for fermion propagator via path integrals

In Section 9.4 of S. Weinberg's book "The quantum theory of fields" it is shown how to get the Feynman $i\epsilon$-prescription in the propagator of a free scalar field using path integrals and ...
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1answer
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Why this loop diagram is not included in Phi-4 theory of Peskin?

Consider a $2\rightarrow2$ scattering process in $\phi^4$ theory. In the book of Peskin's, he consider the 3 loop corrections in the parenthesis: My question is: Why doesn't he include this diagram? ...
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Are quantum state vectors dependent on coordinate systems or observers?

I'm confused about the two following points of view: In Weinberg's QFT book 1 he claims "if an observer O sees a system represented by a ray R..., then an equivalent observer O' who looks at the same ...
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Heisenberg Uncertainty Principle derivation question [closed]

So I'm rading Shankaar's book and got stuck in this place. $ (\Delta \Omega)^{2}(\Delta \Lambda)^{2} \geq \frac{1}{4}\left\langle\psi\left|[\hat{\Omega}, \widehat{\Lambda}]_{+}\right| \psi\right\...
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1answer
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Eigenvalue counting number in Functional Integral

My question is about the calculation of a functional integral (which looks like a partition function). If we have the operator $A$ having discrete spectrum, and eigenvectors $\phi_{i}$ and ...
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Are there any gapped systems that aren't invertible?

Assume the following definitions: A gapped phase of matter is a collection of (quantum-mechanical) systems with a unique ground state and an energy gap to all excitations in the limit of infinite ...