# 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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### 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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### 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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### 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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### 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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### 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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### 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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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 $$\int d^4x\ \mathscr{L}_{\mathrm{... 2answers 42 views ### Averaging over spin phase-space for a cross section In Peskin and Schroeder the Dirac equation is solved in the rest frame for solutions with positive frequency:$$\psi(x) = u(p) e^{-ip\cdot x}u(p_0) = \sqrt{m} \begin{pmatrix} \xi \\ \xi \end{...
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}\...
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 ...