# Questions tagged [field-theory]

For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.

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### Representation of The Poincare Group

I am currently trying to understand the representations of the conformal group. I am following the script by J.D Qualls. At page 29, the author finds the effect of $L_{\mu\nu}$ by "studying the ...
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### Asymptotic form of a Coulomb-like integral

I need to evaluate or work out the asymptotic scaling of the following integral: \begin{equation} I~=~\int_{\mathbb{R}^3} dq d^2p \frac{e^{i\vec{p}\cdot \vec{r}}e^{iq z}}{p^2 + \frac{1}{g^2}q^4} \end{...
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### Coulomb matrix element in Quasi-2D bilayer system

In the paper "Electron-hole pairing of Fermi-arc surface states in a Weyl semimetal bilayer" (arxiv) the authors derive an interlayer Coulomb matrix element as (Appendix A). \begin{align} V_{...
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### Doubt in the definition of the stress-energy tensor in Peskin and Schroeder's QFT book

We can describe the infinitesimal translation $$x^{\mu} \to x^{\mu}-a^{\mu}$$ alternatively as a transformation of the field configuration $$\phi(x) \to \phi(x+a) = \phi(x) + a^{\mu} \phi(x).$$ ...
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### Deriving the Generalized Fierz Transformation from Schroeder's Textbook

I am self studying QFT from the textbook An Introduction of Quantum Field Theory and the corresponding solutions from Zhong-Zhi Xianyu. The generalized Fierz Transformation is derived in problem 3.6. ...
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### Gauge theoretic formulation of a classical particle in an electromagnetic field

In gauge theory, we can view the electromagnetic potential as connection on the principal bundle. Wave functions are sections of the associated bundle and we can derive i.e. the Klein-Gordon equation ...
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### QM is Feynman path ensemble - can QFT be viewed as Feynman field ensemble?

While classical mechanics uses single action optimizing trajectory, QM can be formulated as Feynman ensemble of trajectories. As in derivation of Brownian motion, mathematically it is convenient to ...
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### Klein Gordon equation from its classical Hamiltonian

I don't have much experience in classical field theory and have been trying to study it for the past week. However, I don't know if my understanding of the equations of motion for the fields are ...
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### Peskin Schroeder 2.44 application [duplicate]

After 2.44, the book calculates the commutators of $\phi$ and $\pi$ with the Hamiltonian. But in the first expression the Hamiltonian has a different form than in the second. The first one matches ...
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### Is $\phi^4$ theory unstable?

I tried to write a simulation of a $\phi^4$ theory for 2+1 dimensions. But whatever values I gave for the coupling constant it always seems to blow up. i.e. a wave-like equation with a mass and ...
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### Help with a supersymmetry problem 3.5b in Peskin and Schroeder

I am self studying Quantum Field Theory and I am using the book Introduction to Quantum Field Theory by Peskin and Schroeder along with the solution manual by Zhong Zhi Xianyu. I am currently working ...
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### What is the role of the dilaton in Jackiw-Teitelboim 2D gravity?

I read that the Einstein Hilbert action is topological in 2 dimensions. (What does that mean?). To write down a non-trivial action one introduces the dilaton field in JT gravity. Does this field have ...
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### Why do we study symmetries only via Noether conserved currents?

In general, we say a transformation is a symmetry of a theory if it leaves the action invariant, i.e. if $$S \to S' = S,$$ up to, perhaps, a boundary term (b.t.). However, it is known (see e.g. this ...
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### Is there a symmetry one can impose to forbid a four point interaction term?

If I have this lagrangian of a real scalar field $S$: $$\mathcal{L}=\frac{1}{2}\partial_\mu S\partial^\mu S-\frac{\mu^2}{2}S^2-\frac{\lambda}{4!} S^4$$ does there exist a symmetry one can impose to ...
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### How to write lattice $\phi^4$ hamiltonian in terms of Pauli matrices?

I want to decompose lattice~$\phi^4$ hamiltonian in terms of Pauli matrices. Particularly, how can I decompose  H_\text{Lattice}=a^d\sum_{{n}\in{Z}}\left[\frac{1}{2}\Pi_{n}^2+\frac{1}{2}\left(\...