Questions tagged [effective-field-theory]
An effective field theory is a systematic approximation for an underlying quantum field theory or a statistical model that includes the appropriate degrees of freedom of phenomena occurring at a chosen length scale (or energy scale), while ignoring substructure and degrees of freedom at shorter distances (or higher energies), summarizing those in its parameters.
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Time dependent mass terms in field theory
In my research on Q-balls (a certain type of non-topological soliton) in cosmological backgrounds, I have obtained an equation that is nearly usable, except for one caveat. It would require me to ...
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What does it mean to "resum" the large logarithms?
I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
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How do I obtain the low energy supergravity actions from the 5 superstring theories?
In Domain-Walls and Gauged Supergravities by T.C. de Witt, there is a small table giving the 5 string theories and each of their effective sugras. I am looking for detailed reviews of how these sugras ...
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Weyl variation of a generic action
In this paper https://arxiv.org/abs/hep-th/9906127 (see eq. 15)
The following identity appears
$$ \delta_{W} \int d^d x \sqrt{-\gamma} \tilde{\mathcal{L}}^{(n)} = \int d^d x \sqrt{-\gamma} \sigma\left(...
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Uniqueness of Maxwell Lagrangian: Why does it not include the term $c_3 (\partial_\mu j_\nu)F^{\mu \nu}$?
In the textbook Condensed Matter Field Theory by Altland and Simons, it is said that the Maxwell Lagrangian $\mathcal{L}$ coupled to a four-current $j^\mu$ satisfying $\partial_\mu j^\mu = 0$ is the ...
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Why does integrating out microscopic degrees of freedom lead to the effective free energy rather than the effective energy?
In David Tong's lecture notes on statistical field theory, he considers the partition function of the Ising model and computes the effective free energy by integrating out the microscopic details of ...
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Fermi theory cutoff from unitarity bound
Tree-level cross sections for processes described by Fermi theory behave like $\sigma $ $\sim$ $G_{F}^2 \cdot s$, where $G_{F}$ is the Fermi constant and $\sqrt s$ is the energy entering in the ...
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The origin of the Hierarchy Problem
In the answer to this question on the origin of the hierarchy problem, it is stated that:
The low-energy parameters such as the LHC-measured Higgs mass 125 GeV are complicated functions of the more ...
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Loops and UV divergences
I read when asked whether a force could only exist at a certain phase transition or high energy:
"I am not aware of a coupling that only exists at high energies or in a phase transition -- in ...
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Why the coupling constant in context of different approaches has different energy dependence?
I know that in the language of renormalization group, the coupling constant in the Hamiltonian is dependent of energy, for example in condensed matter physics, of band width. So, we can do a 'poor man'...
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3-Particle Kinematics and Parity of Operators
Recall that if the momentum of scattering amplitudes is taken to be complex and from little group scaling that the 3-particle interaction for massless particles of any spin is given as
\begin{equation}...
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Chern-Simons (K matrix) theory and ${\rm Spin}^{\mathbb C}$ connections
If I understand correctly (e.g. from this paper), an Abelian bosonic Chern-Simons theory defined on $T^2\times \mathbb R$ is specified by a $K$ matrix via e.g. $S \sim \int_M K_{IJ}A^I \wedge dA^J$. ...
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Invert operator to integrate heavy fields
We have a Lagrangian $$\mathcal{L}=\frac{1}{2} \partial_\mu \Phi \partial^\mu \Phi - \frac{1}{2} M^2 \Phi^2- \frac{\lambda}{4}\phi^2 \Phi^2 - \frac{g}{2} \Phi \phi^2+\cdots $$ where $\Phi$ denotes a ...
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Why do we rescale momenta after integrating out high momenta in Wilsonian renormalization?
In Section 12.1 of Peskin & Schroeder they motivate Wilson's approach to renormalization by asking how a quantum field theory changes after changing the momentum scale. To answer this they start ...
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Derivative interactions in the Wilsonian renormalisation Group
I am currently working through some basic renormalisation group problems, and have come to one about derivative interactions. It has been a while since I have studied QFT formally so bear with me ...
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