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Results tagged with field-theory
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user 36793
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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quantum fluctuations and the virtual particles
In the introduction of chapter-12 of “An Introduction to Quantum Field Theory” by Peskin and Schroeder I encountered this line: “The quantum fluctuatuations at arbitrarily short distances appear in Fe …
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Meaning of kinetic part in the Lagrangian density?
What is the physical meaning of the kinetic term in the classical scalar field Lagrangian $$\mathcal{L}_{kin}~=~\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi)~?$$ It gives how does the field change f …
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What is the physical intuition of Noether current?
In case of translational symmetries of spacetime, the Noether charges $\int T^{00}d^3x$ and $T^{0i}d^3x$ represent the Hamiltonian and the components of the momentum of the field, respectively. Here, …
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How can I derive the most general scalar field Lagrangian from locality?
My understanding of the principle of locality in a field theory demands that field degrees of freedom interact locally. For example, $\phi(x)$ at the spacetime point $\phi(x+\delta x)$ can interact wh …
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Does $[P_j,B_k]=i(Mc^2)\delta_{jk}$ imply particle number conservation?
From reading Weinberg's Quantum Theory of Fields, Vol. 1, I learnt that for the Galilean group $[P_j,B_k]=i(Mc^2)\delta_{jk}$, and for the Poincare group $[P_j,B_k]=iH\delta_{jk}$ where $P_j$ and $B_k …
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Why is inflation described by a scalar field?
Textbooks on cosmology describe the phenomenon of cosmic inflation in terms of the existence of a scalar field (or many scalar fields, as the answer and comments pointed out), called inflaton. Such as …
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Attempt to define a momentum space wavefunction for a superposition of of 1-particle states
Consider an arbitrary state in the Fock space constructed by superposing 1-particle states: $$|\psi\rangle=\mathbb{1}|\psi\rangle=\int\frac{d^3\textbf{p}}{(2\pi)^32E_p}|p\rangle\langle p|\psi\rangle$$ …
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Form of $SU(N)$ gauge transformations in $SU(N)$ Yang-Mills theory
For $SU(N)$ Yang-Mills theory, instantons correspond to finite action solutions $A_\mu(x)$ of the Euclidean equation of motion. The requirement of finite action demands that $A_\mu(x)$ is a pure gauge …
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What is a 'potential' in the context of physics and gauge symmetry?
The non-derivative terms of a field $\phi$ in the Lagrangian are often (not always) collectively called its "potential" $V(\phi)$. This is because in field theory, the field $\phi$ is the analog of co …
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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?
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Lagrangian density with explicit $x_\mu$ dependence
In the Quantum Field Theory book, by Ryder, he says that a Lagrangian density of a field can also be an explicit function of $x_\mu$ if the field interacts with external sources. Can someone give an e …
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Determination of the ground state of a field theory
Consider the Spontaneous symmetry breaking in the theory
$$\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{\mu^2}{2}\phi^2+\frac{\lambda}{4!}\phi^4.$$
By the ground state of a classica …
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Why is it that the interacting fields cannot be decomposed into Fourier modes like free fields?
In quantum field theory, a free scalar field can be decomposed into Fourier modes. But why is that, an interacting field cannot have Fourier decomposition? Can we not decompose any arbitrary reasonabl …
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Relation between Wilsonian renormalization and Counterterm Renormalization
Wilsonian renormalization The answer by Heider in this link points out that when we integrate out high momentum Fourier modes, we end up with Wilsonian effective action (not the 1PI action). This is t …
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Can a four-divergence be added pure Yang-Mills Lagrangian to alter the action? [duplicate]
A four-divergence term $\partial_\mu K^\mu$ when added to a Lagrangian, the action changes as $$S\to S^\prime=S+\int_R d^4x \partial_\mu K^\mu\tag{1}$$ where $R$ is a region of spacetime. Using Gauss' …
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