effective field theory Definition and Topics - 10 Discussions

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies). Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales. Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in particle physics, statistical mechanics, condensed matter physics, general relativity, and hydrodynamics. They simplify calculations, and allow treatment of dissipation and radiation effects.

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  1. E

    A The vertex factors in QCD penguin operators

    Have a look at O5 & O6 in Eqtns(5.4) . Why is there a (V+A) ? (V+A) contains the projection operator which projects out the right Weyl from a Dirac spinor. As per the Feynman rules of electroweak theory, there is a (V-A) assigned to each (Dirac) spinor-W boson vertex because W only couple to...
  2. E

    A Operator Product Expansion as shown in Schwartz

    I have included here the screen shot of the page I am referring to. I am unsure of how this non-local Lagrangian of Eqtn(32.68) has been constructed. Have they just integrated the interaction Lagrangian densities over two different sets of points (x & y) ? If so, then why is there no P_L in...
  3. M

    I How to determine matching coefficient in Effective Field Theory?

    Assume that I have the Lagrangian $$\mathcal{L}_{UV} =\frac{1}{2}\left[\left(\partial_{\mu} \phi\right)^{2}-m_{L}^{2} \phi^{2}+\left(\partial_{\mu} H\right)^{2}-M^{2} H^{2}\right] -\frac{\lambda_{0}}{4 !} \phi^{4}-\frac{\lambda_{2}}{4} \phi^{2} H^{2},$$ where ##\phi## is a light scalar field...
  4. A

    Forbidden beta decay form factors

    My idea was to consider first the structure of the matrix element and to see if there are any possible constraints that we could use for parametrization. If I am not mistaken, we are dealing with the hadronic decay governed by QCD which conserves parity. Since we have a derivative operator...
  5. I

    Operation with tensor quantities in quantum field theory

    I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera. I...
  6. T

    A Quantum Gravity: Renormalization vs. Effective Field Theory

    In quantum gravity, I get 'mixed signals' as regards renormalizability. My state of confusion is being caused, I suspect, by an incomplete understanding of what is covered under t'Hooft's 1972 proof that non-Abelian gauge theories are renormalizable. ( = Nobel Prize 1999). Specifically, some...
  7. S

    A Wilsonian RG and Effective Field Theories

    Years ago after reading Ch. 12 of Peskin and Schroeder (and the analogous discussion in Zee), I thought I fully understood the modern Wilsonian view of renormalization, and how it explains why non-renormalizable field theories still have meaning/predictive power at energies well below the...
  8. Ken Gallock

    Non-relativistic complex scalar field

    This is spontaneous symmetry breaking problem. 1. Homework Statement Temperature is ##T=0##. For one component complex scalar field ##\phi##, non-relativistic Lagrangian can be written as $$ \mathcal{L}_{NR}=\varphi^* \Big( i\partial_t + \dfrac{\nabla^2}{2m} \Big)\varphi -...
  9. B

    A Effective field theory in Srednicki's book

    Hi! I'm currently learning for my QFT exam with the book from srednicki (here as pdf: http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf) and I am trying to understand the chapter "Effective field theory" (p. 185 in the pdf above) He first introduces an ultraviolet cutoff Λ and then computes...
  10. P

    A Trace in QCD lagrangian

    I have a question about the use of trace in QFT in general - more specifically the use of trace in the lagrangian in the effective theory concerning chiral symmetry in QCD. I am slowly trying to get a hang of everything, and most things i am able to calculate, but i still have som very specific...
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