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### Active transformation and passive transformation of a scalar field

For the Lorentz transformation $x \to x'=\Lambda x$, the active transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda^{-1}x)$ and the passive transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda x)$. ...
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### QFT: prove Dirac lagrangian is invariant under C, P, T separately

As it is stated in Peskin, $\mathcal{L}=\bar\Psi(i\gamma_{\mu}\partial^{\mu}-m)\Psi$ is invariant under C,P and T transformation separately. I have some problems to see how the partial derivative is ...
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### What defines the spin of a certain field? (formally)

Update: see the restatement of the question below! I've seen this question over and over through the archive of questions, but so far the closer to an answer was this. But I still don't understand. ...
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### How do I obtain the SUSY Transformations from Poisson Brackets?

In Friedman's and Van Proyen's Supergravity textbook it is explained how one can get the supersymmetry transformations using the conserved currents. Specifically this is in section 6 where we are ...
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### Why Different charges attract while they should repel? [closed]

When I started studying magnetic fields, my teacher was always telling me that strong fields push the bodies to weaker fields, so i tried to apply the same concept to charges in the following picture: ...
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### Field theory on a lattice, what is this?

I only have the training of undergraduate quantum mechanics and solid state physics. For me, field theory is defined on a continuous space. So, what does lattice field theory mean? Is it similar to ...
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### General Relativity as a Special Relativistic Field Theory

In this question, I want to consider only the classical case. I have seen the statement that general relativity can be considered as a spin-2 field living on a Minkowski background. In that case, you ...
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### what the explicit formula magnetic field a electron that moving on the curve path?

,hi,we suppose ,we have a single electron that moving on a curve path,the velocity is v (it is variable),the path moving is a curve not direct path.i saw maxwell equation my question is ,is there a ...
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### How does the choice of a particular vacuum in a field theory problem decide the number of Goldstone bosons?

How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in front)...
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### What's the meaning of a field?

Sorry if the title sounds meta-sciency, allow me to clarify. In physics, our goal is to understand how the universe works. To this end, we construct a theory, which hopefully makes falsifiable ...
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Classically anti-fields are obtained by charge conjugation, right? But sometimes authors label hermitian conjugated fields as anti-particles (or barred fields in Dirac language). But h.c. and charge ...
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### Non-Euclidean mechanics; is it useful?

Special relativity has the following single-particle Lagrangian: $$S = \int_{t_0}^{t_f}\sqrt {\langle \mathrm d\vec{s},\mathrm d\vec{s}\rangle}.$$ Clearly it is based on Euclidean norms; it is in ...
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### Reparametrization invariance in scalar QFT: What does it mean, exactly?

In the Cecotti's book "Supersymmetric Field Theories" he wrote " Physical quantities are independent of the fields we use to parametrize the configuration, that is, observables are invariant under ...
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### Transformation of photons under Lorentz transformation

This question is a continuation of one of my earlier post. In this post,I asked about the transformation of photon fields under rotation. Here I generalize the question to Lorentz transformation, and ...
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### Higher order Lagrangians [duplicate]

Recently I have read some papers in which the authors considered higher order lagrangians. For example, in this paper "A path integral leading to higher-order Lagrangians" by C.Acatrinei the higher ...
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### What is populating a force “field”? [closed]

What "matter" is populating a force "field"? It can't be actually empty?
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### Are there conserved quantities in field theory which don't arise from Noether's Theorem?

In some QFT texts one writes down the number operator $N$ for free theories, such that when acting on an $n$-particle state $|n\rangle$ we have $$N|n\rangle=n|n\rangle$$ In free theories this is a ...
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### Why do some fields have a distance limit and other don't? [closed]

I'm not a mathematician or a physicist but interested in quantum mechanics/gravity/relativity. I'm trying to understand some ideas that are presented for laymen, and a lot of them talk about different ...
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### How is everything a field?

I've heard before that everything in physics can be thought of as either a field, or its excitation. Is there some intuitive explanation of how I can look at gravity, light, electromagnetism, etc as a ...
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### Majorana fermions and the continuum limit of the Ising model

In Paolo Moligini's Analyzing the two dimensional Ising model with conformal field theory lecture notes, it is shown at the end of chapter 3 that the Lagrangian of the continuum limit of the Ising ...
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### What is the difference between the momentum in the Fourier transform of a scalar field and the conjugate momentum of the field?

What is the difference between the momentum $p$ in $e^{i\mathbf{p}\cdot{\mathbf{x}}}$ in the Fourier transform of a scalar field and the corresponding conjugate momenta $\pi(x)$ of the scalar field?
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### Why do $\psi_a$ and $\bar{\psi}_{\dot{\alpha}}$ represent two different degrees of freedom?

I am taking a course in QFT and I've been introduced to the concept of left-handed (undotted) and right-handed spinors (dotted). I know that left-handed spinors are associated with the irreducible ...
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### How to interpret the field configuration in quantum field theory?

We often use the Fock space as the start point for our quantum field theory. In the Fock space we have definite physical meanings for the state. For example, the state $$|k_1k_2...k_n\rangle$$ ...
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### Non-perturbative effects: classical or quantum?

Are non-perturbative effects (solitons) classical or quantum effects (corrections) ? (examples ?) My confusion stems from the fact that, for instance, an instanton is a classical solution of the ...
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### Simple conceptual question conformal field theory

I come up with this conclusion after reading some books and review articles on conformal field theory (CFT). CFT is a subset of FT such that the action is invariant under conformal transformation ...
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### Magnetic field outside the solenoid

I found solution to problem 257 from "300 Creative Physics problems" hard to understand. In that problem we have very long solenoid with coil wounded in one layer. Data such as: density of turns, ...
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### Relation between interaction Lagrangian and interaction Hamiltonian

I work with this interaction Lagrangian density $$\mathcal{L}_{int} = ia\bar{\Psi}\gamma^\mu\Psi Z_\mu +ib(\phi^\dagger\partial_\mu \phi - \partial_\mu\phi^\dagger \phi)Z^\mu,$$ where $Z^\mu$ is an ...
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### What, to a physicist, are instantons and the Donaldson invariants?

I study gauge theory from a mathematical perspective. To me, one of the most fundamental ideas is the notion of an instanton on a 4-manifold. To be precise, I have a Riemannian 4-manifold and a ...
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### Center of mass of a quantum field

In classical field theory the Noether conserved quantities associated to the translation symmetry are the momentum of the field $P^i = \int\! d^3 x\ T^{0i}$, where $T^{\mu \nu}$ is the energy-momentum ...
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### Self Study Textbook Progression from QM to QFT? [duplicate]

Hello Physics StackExchange! I will put the TL;DR in the beginning: I need a self contained, relatively hand-holding sequence of textbooks that covers up from the end of Griffith's Intro to QM to ...
### Why four-point vertex function in $\phi^3$ theory?
So as I understand it the order of $\phi$ in a scalar Quantum field theory is indicative of the number of lines entering a given vertex. For example for $\phi^3$ this leads to vertices like the one ...