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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Could the divergences in loop Feynman diagrams be resolved by applying an exponentially decreasing probability eg fluctuation theorem?

Since the divergence originates from having to integrate over an infinite range of intermediate energies, surely the bigger the temporary energy delta, the less likely it will be, and the shorter the ...
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Traveling at the speed of light [closed]

Assume that we can travel at speed of light. Does it mean time will stop? How would the passenger of this space ship feel? Could they live the normal life in the space craft or they frizzed up?
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Could a free conformal field theory be solved by second quantization?

I'm a beginner in CFT and I'm trying to understand whether or not standard tools in quantum field theory--more specifically second quantization--can be used to solve a conformal field theory. To begin,...
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What does the Pontryagin index do in BPST instanton (solution to Yang-Mills theory)?

$$ \mathcal L = -\frac12\mathrm{Tr}\ F_{\mu\nu}F^{\mu\nu}+i\bar\psi\gamma^\mu D_\mu\psi $$ We take this Lagrangian for QCD, after this I need to calculate BPST instanton with topological Pontryagin ...
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Two-particle operators in QFT and the factor 1/2

I am learning about QFT through the book Quantum Field Theory for the Gifted Amateur and I am having trouble understanding the factor 1/2 in the definition of two particle field operators. In the book ...
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3answers
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A strange requirement on projective representation

I am reading the QFT book by Weinberg. The first volume. On page 82, he discussed projective representation. $$ U(T_2) U(T_1) = \exp(i \phi(T_2, T_1)) U(T_2 T_1 ) .\tag{2.7.1} $$ Here $\phi(T_2, T_1 )$...
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Wick contraction for fermions of different types

When we have an interaction hamiltonian with fermion field of two different types ($\Psi_a$ $\overline{\Psi_b}$) and a scalar field $\Phi_c$. How does one do the wick contraction? eg. Leptoquark decay ...
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1answer
46 views

How to perform Fourier transform of this Hamiltonian?

I am reading this article (arXiv:1505.01908 ) in which author is calculating linear response of a perturbation. The perturbation Hamiltonian is $H$ (Eq. 2 of article) given as $$ H = \frac{JS}{a^3}\...
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Matsubara sum of thermal Green's function

I need to retrieve a Matsubara sum representation of the thermal Green's function $$G_{ij}(\tau)=-\frac{1}{Z}\int \mathcal{D}(\overline{\psi},\psi)\psi_i(\tau)\overline{\psi}_j(0)\exp(-\sum_k\int_0^\...
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What is the relation between the partition function from Stat. Mech. And the Path Integral? [duplicate]

Beside the fact that they look identical when you take imaginary time in the path integral formulation. I understand we doing statistics and we are just integrating over all states with a relative ...
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What does the term "condense" mean in the physics literature

When reading the physics literature, we often see the term "condensate". Some examples: in the string net model (Wen, Levin), one will say the string "condensate". in QCD, people ...
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What are linking diagrams in string theory like $SO(6)$?

https://youtu.be/5rB1YKjEwco (51:33) A toy model is presented but I want to know the name of this toy model as well as $\phi^4$ in QFT what is that called? What is it doing with the $SO(6)$ group?
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The residual gauge symmetry of Yang-Mills theory after Wick rotation

I am a bit puzzled by a statement in this question here. In particular, the claim that the residual gauge symmetry in Yang-Mills theory disappears upon Wick rotation to the Euclidean theory. For ...
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1answer
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Rotation of plane wave spinor versus plane wave spinor with rotated momentum

Suppose I have a massless fermion with momentum $p^\mu = (E,\, E\cos\theta,\, 0,\, E\sin\theta)$. There are two ways to write the plane wave spinor $u(p)$ with respect to the spin $\xi$, and I seem to ...
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What does mathematical consistency in QFT mean?

My question is more naive than Is QFT mathematically self-consistent? Just when people talk about the mathematical consistency of QFT, what does consistency mean? Do people want to fit QFT into ZFC? ...
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Relative signs in interaction terms of the Standard Model Lagrangian

I'm trying to understand how to decide if a minus sign is to be put in front of a vertex of interaction when dealing with Feynman diagrams at lowest order. At first I thought that you just take the ...
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1answer
68 views

Changing the basis of a wavefunction [closed]

Usually wavefunctions are given in problems of quantum mechanics. I have the following question in which we want to find thee wavefunction: The state of a system is given by the wavefunction $\psi(x)=...
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32 views

Discrepancy between the two different equations of the momentum operator

i am doing a thesis on the quantization of a real scalar field in a gravitational wave background. I am doing this in lightcone coordinates, so $u$ is $z-t$. I start with an action and define a ...
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Local scale invariance without conformal anomaly

I need to know if conformal symmetry can be localized in the same manner that global symmetries like $SU(2)$ is localized and gauge bosons pop up?(I assume the trace anomaly doesn't violate the scale ...
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Expectation values in path integral formalism

In quantum field theory, it is often assumed that the expectation value $\langle A\rangle$ of an operator $A$ can be written in the path integral formalism in the following way: $$ \langle A\rangle = \...
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1answer
71 views

Conditions on the covariance operator in Gaussian Path Integrals

In field theory, one typically encounters integrals of the form: $$ \mathcal{Z}[J] = \int \mathcal{D}[\phi] \exp \left( - \frac{1}{2} \int d^Dx d^Dx' \ \phi(x)A(x,x')\phi(x')+ \int d^Dx \phi(x) J(x)\...
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1answer
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QFT and divergences: what makes the finite part be regularization-independent?

It seems that the "finite part" of divergent loop integrals are the same, irrelevant of the regularization scheme used to regulate the integrals - why is this? Consider the following ...
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Please solve the integral . OR You can solve the below path integral [closed]

The integral arises during calculation of commutator of two bosonic fields for a spacelike interval.The answer will come in terms of spherical bessel functions and hankel function.The answer you will ...
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48 views

Does choice of renormalisation scheme affect the consequences of Haag's theorem?

So Haag's theorem means that the interaction and Hamiltonian picture are not equivalent. The reason seems to be that renormalization mixes interactions and free particles (ie self energy of a free ...
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Does the electron sources its energy from vacuum space? [closed]

An electron conserves its rest mass all times. (except the case of an electron-positron annihilation). Since the electron does work all the time, in order to conserve its rest mass its energy must be ...
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1-loop diagrams in Scalar Yang-Mills

Disclaimer: I've been calculating the renormalization constants $Z_i$ for the ScalarQED seen as the abelian limit of the Scalar Yang-Mills, and I know that I've made some mistakes because I find the ...
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1answer
56 views

Fokker-Planck equation from Langevin equation in stochastic inflation

I'm reading this paper by Starobinsky and Yokoyama where they give the coarse-grained equation of motion, $$ \dot{\bar{\phi}}({\bf x},t ) = -\frac{1}{3H}V'(\bar{\phi}) + f({\bf x},t) $$ where $f({\bf ...
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1answer
58 views

Does the Slavnov-Taylor identity still hold for scalar Yang-Mills?

I want to renormalize the minimally-coupled scalar Yang-Mills theory: $$\mathcal{L}_{YM\phi}=(D_\mu\phi)^\dagger(D^\mu\phi)-\frac{1}{4}F_{\mu\nu}^a{F^{\mu\nu}}^a-\frac{1}{2\xi}(\partial_\mu {A^\mu}^a)^...
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1answer
75 views

Density, density operator, and number operator in quantum mechanics

Density is the number of particles per unit volume. But in quantum mechanics, the density operator is defined as $$ \hat{\rho}(r) =\Psi^\dagger(r) \Psi(r) $$ here $\Psi(r)$ is the field operator. The ...
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How to prove the helicity operator is a Casimir operator for massless particles?

I am reading the classification of irreducible unitary Poincaré group representations. It seems that for massless particles, the momentum operator and the Pauli-Lubanski operator get aligned so the ...
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3answers
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Why do we care about chirality?

I'm trying to figure out what's the importance of chirality in QFT. To me it seems just something mathematical (the eigenvalue of the $\gamma^{5}$ operator ) without any physical insight in it. So my ...
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1answer
45 views

Superposition of Fock states

Fock states form the most convenient basis of a Fock space. Does it mean that any state of a quantum field (any element of Fock space) can be expressed as a superposition of Fock states? Does this ...
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1answer
186 views

Infinite-dimensional representation of Lorentz algebra

In QFT, we need to use infinite-dimensional representations of the Lorentz algebra, because all the non-trivial finite-dimension al representations are not unitary, and we need unitary ...
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Special Orthogonal Group in Euclidian and Minkowski spacetimes

I apologize if my question seems a little half-baked. I was wondering if while working with a QFT, one can make transitions from imaginary time to real time and thereby changing the underlying ...
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1answer
67 views

1-loop renormalization of general scalar in general dimension

I'm interested in studying the theory $$S=\int d^dx\left(\frac{1}{2}(\partial\phi)^2-\frac{g}{(2k)!}\phi^{2k}\right)$$ in $d=2, 3, 4$ and for $k=2, 3, 4\dots$ and I'm having trouble with the the 1-...
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1answer
107 views

Could Matter Go Backwards in Time?

In the real world, it seems that traveling backwards in time is impossible, but do we have a theorem in physics that would imply this fact? Some people (including Feynman) describe antiparticles as ...
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32 views

About the generating functional in non-abelian Yang-Mills Theory [closed]

Lately I have been trying to calculate the Feynman rules for some vertex involving gluons in QCD in the path integral approach. When looking for the generating functional for the free field theory, I ...
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1answer
74 views

The $D_{00}$ component of the photon propagator in the Feynman and Coulomb gauges

I am trying to understand some derivations involving the photon propagator, and I am having a lot of trouble with expressions in different gauges and also with terminology in general. Here is what I ...
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56 views

Difference between theoretical vacuum and experimental vacuum?

As is well known, the vacuum in QFT is defined by the lowest energy state of the total Hamiltonian, and particles are understood as elementary excitations above that vacuum. On the other hand, the ...
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2answers
101 views

Why are only positive frequency mode functions allowed in Quantum field theory? How is this consistent with anti particles having negative energy?

In quantum field theory, one can redefine the particle creation and annihilation operators using Bogoliobov transformations, which can give rise to a different vacuum state, using a new set of ...
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1answer
97 views

Why do we use two ways to write the kinetic term in a Lagrangian?

I have just started reading Schwartz's book on QFT and I see from the first few chapters that he writes the kinetic part of the Lagrangian in a way I find strange. As an example, for the massless ...
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Deriving a squeezing Hamiltonian in the context of second-quantization

I intend to rederive the Hamiltonian of a two-mode system which describes squeezing/amplification. This is given as (see Gerry, Knight Eq. 7.187) $$ H = \hbar\omega_{s}a_{s}^{\dagger}a_{s}+\hbar\...
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1answer
57 views

Order and Disorder Operators in QFT

On the wikipedia page, the 't Hooft loop operator is called a "disorder parameter," in contrast to the Wilson loop operator, which is an "order parameter." From my limited ...
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1answer
24 views

What is the relation between joint measurability and common refinement (pure state decomposition) of density operators?

Here page 13, the author states "...just as two quantum observables are often not jointly measurable, two decompositions of mixed states often have no common refinement (Actually, in the ...
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Effective Field Theory approach: Radiated Power from Multipole Moments

Recently I have been reading Andrea Ross' paper "Multipole Expansione at level of the Action" (https://arxiv.org/abs/1202.4750). The second chapter focuses on the case of a scalar field and ...
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1answer
39 views

Is is possible to extract an effective Hamiltonian from a Boltzmann equation (or any other kinetic theories)? [closed]

I got kind of confused when reading Xiaogang Wen's famous textbook Quantum Field Theory of Many-body Systems. In Section 5.3.3 the book claims that From a kinetic theory of Fermi liquid (a Boltzmann ...
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1answer
50 views

For real scalars $\phi$ and $\partial_t \phi = \pi$, why can't the Hamiltonian have terms of the form $\phi\pi$?

Suppose one has a real scalar field $\phi$ and its conjugate momentum field $\pi := \partial_t \phi$. If the scalar is free and using metric $(-+++)$, the action is $$ \int d^4x\ \mathscr{L}_{\mathrm{...
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2answers
42 views

Averaging over spin phase-space for a cross section

In Peskin and Schroeder the Dirac equation is solved in the rest frame for solutions with positive frequency: $$\psi(x) = u(p) e^{-ip\cdot x}$$ $$u(p_0) = \sqrt{m} \begin{pmatrix} \xi \\ \xi \end{...
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1answer
32 views

Parity transformation on the adjoint spinor

In eq. (3.128) of page 66 of "An Introduction to QFT", by Peskin & Schroeder, a step involves: $$P\,\overline{\psi}\left(t,\textbf{x}\right)P^{-1}=P\,\psi^{\dagger}\left(t,\textbf{x}\...
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1answer
71 views

Meaning of Scattering Amplitude in QFT

I've been reading a textbook on QFT, and learned that we can calculate the probability amplitude that a system in state $|i\rangle$ will "collapse" into state $|f\rangle$ after some amount ...

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