# Tagged Questions

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### What is a nonlinear field?

I have read two possible definitions. A nonlinear field is A field taking values on a manifold. A field whose equation is nonlinear. What do you understand by a nonlinear field or a nonlinear ...
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### Permutation symmetry - a continuous symmetry?

From quantum mechanics it is known that permutation between identical particles does not change the Hamiltonian. Assuming that the quantum system consists of a very high number of particles such that ...
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### 2D square lattice, nearest neighbor and next-nearest connected by springs

For my field theory class I am trying to build the Lagrangian for the following system. Consider a 2D square lattice where the nearest and next-nearest neighbor interactions are modeled by springs ...
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### Maxwell's Inspiration to think about fields

I was looking at a Wikipedia article which had the following statement Atomists, notably James Clerk Maxwell and Ludwig Boltzmann, applied [...]. In modern literature Maxwell is often thought ...
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### Scalar operators In Quantum Field Theory

I am trying to learn Quantum Field Theory and I am stuck in a basic point. What is the definition of a scalar operator in QFT? That is, how does it transform under a Poincare transformation? Why do ...
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### Massless Thirring Model in 1+1 Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (link to Phys Rev D article), he pointed out that the massless Thirring Model is exactly scale invariant. More over, ...
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### Is the force between solitons with same charge always repulsive?

I know the one-dimensional case in which the force is proportional to $e^{-R}$ and the force is attractive for solitons with opposite charge and repulsive for solitons with same charge. I was ...
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### How do force carrying particles “give” force? [duplicate]

So, I am not taking physics in school, but I do have an interest in it, and I was wondering, in the standard model, all of the force carrying particles (photons, Z Bosons, W Bosons, gluons, and (...
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### Running coupling, effective potential and the stability of vacuum

Consider the potential $$V(\phi)=\frac{1}{2}\mu^2\phi^2+\lambda\phi^4$$ where $\phi=\phi(t,\textbf{x})$ is a real scalar field. Let, $\mu^2<0$ and $\lambda>0$ then the potential is bounded from ...
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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 is stat mech involved in mean field theory?

Mean field theory involves approximating an interacting system by a non-interacting one, by replacing some operators with their expectation value. However, to my surprise, free energy is involved in ...
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### What is a field? [duplicate]

What is a field? Lengthy texts about fields have been published but none ever answer the simple question "What do you mean when you say the world field."
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### Charge not conserved in scalar QED? [duplicate]

Since conservation of charge seems to be a well known concept, I am hoping that I am missing something and that the conclusion is incorrect. However, I have been unable to disprove this. Let me ...
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### What is the reason for chiral anomalies in condensed matter systems?

If you consider a massless relativistic fermion theory and you perform a chiral transformation, then you realize that while the classical action remains invariant under this transformation the ...
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### Field Lagrangian <--> Particle Lagrangian

The action-functionals describing the motion $\mathbf{x}:[a,b]\to \mathbb{R}^3$ of a free particle of mass $m$ and the evolution $\varphi:[a,b]\times \Omega\to \mathbb{R}$ of a free scalar field of ...
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### Moduli space for $CP^N$ and $T^{*} CP^N$ in $\mathcal{N}=2$ SUSY

For complex $\phi$ in $U(1)$ gauge theory, \begin{align} |\phi_1|^2 + |\phi_2|^2 +\cdots |\phi_N|^2 =r \end{align} This equation $|\phi|^2=r$, describes sphere $S^{2N-1}$. Dividing the space of this ...
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### Path integral measure and symmetry

For a generic field theory the path integral measure is defined as, $$\mathcal{D}\Phi = \prod_i d\Phi(x_i),$$ where $\Phi$ is a generic field (i.e. it may be scalar, ...
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### The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
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### Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?

Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
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### Space orientation of light waves

Recently I've started to be really intrigued with the electromagnetic spectrum and bumped into this problem: According to the wave theory of light (or any electromagnetic wave, really), the magnetic ...
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### Poincare invariant Lagrangians

The Lagrangian density of a Poincare invariant theory should not depend explicitly on the space-time coordinates. Does this mean $$\partial_\mu \mathcal{L}=0~?$$ If this is the case doesn't the ...
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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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### How to tell local and non-local in QFT?

I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?
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### Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
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### Inverse square law in 2+1 dimensional universe from a Yukawa coupling?

There is a nice result that in 3+1 space time, a Yukawa coupling leads to an inverse square law force as the mass of the scalar field goes to zero. I was wondering what the corresponding force in a 2+...
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### General form for functional derivatives

Working on the hamiltonian formalism applied to canonical field theory, how do I deduce the general form for the functional derivatives $\frac{\delta}{\delta \pi}$ and $\frac{\delta}{\delta \phi}$ (...
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### How to explain the upgrade from Particles to Fields between Relativistic QM->QFT?

It is strange that all books I walked through, non of them explains or motivates how physicists realised that we need to deal with fields instead of particles. Maybe the closest thing I found is the ...
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Suppose I have an Lagrangian $$\mathcal{L} = \frac{1}{2}g_{ab} \bar{\psi}^a \Gamma^k \partial_k \psi^b$$ and I want to show it's invariance under the infinitesimal Lorentz transformations $$\delta \... 1answer 134 views ### Hamiltonian field equations constraints Let's consider the Lagrangian$$\mathcal{L}~=~-\frac{1}{2}(\partial_\mu\phi^\nu)^2+\frac{1}{2}(\partial_\mu\phi^\mu)^2+\frac{1}{2}m^2\phi_\mu \phi^\mu,$$with Minkowski metric \eta_{\mu\nu}={\rm ... 1answer 137 views ### How to derive the conserved current of the Klein Gordon equation? Similarly to the probability current in non-relativistic quantum mechanics, there is a conserved current for the Klein Gordon equation, however a different one. I'm trying to calculate that. The KG ... 1answer 132 views ### How is domain wall formation related to spontaneous symmetry breaking? It is said that domain wall formation is the signature of in spontaneous symmetry breaking but not explicit symmetry breaking. Why is this so? 1answer 827 views ### Tracelessness of energy-momentum tensor and massless photons I have read the statement that the tracelessness of the energy-momentum tensor is demanded by the condition of photons being massless. I see how this comes about starting from the canonical energy-... 1answer 151 views ### Crushing a magnetic field What would happen if you crushed a magnetic field to an ever decreasing size? Thanks. EDIT: How small could the field possibly go? Is there a limit on how small it could get? Is there a maximum ... 1answer 47 views ### 4-Gradient Lorentz Transformation I am currently studying the behavior of a scalar field \phi under a Lorentz transformation \Lambda. However I am having trouble understanding why the following holds true:$$\partial_{\mu}\left(\...
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 $$|k_1k_2...k_n\rangle$$ ...
Peskin and Schroeder, equation 3.28, states that the Klein-Gordon equation $$(\partial^2+m^2)\psi=0 \tag{3.28}$$ is a valid choice of equation for a Dirac spinor field. Their explanation makes sense (...