If one assumes that a neighborhood of the point may have any number of quanta then to get classical spaces one needs renormalization procedures similar to renormalization in quantum ﬁelds theory.
Gibbs and Quantum Discrete Spaces
Since Γ[u] deﬁnes the renormalized 1PI vertices, its zero momentum limit deﬁnes the renormalized disorder.
Functional renormalization group at large N for random manifolds
In this limit d ≪ δ , the contribution of the layer to the dissipation, QI , corresponds to the δ−type renormalization of the viscosity in the effective boundary condition of Section III with renormalization parameter β = ǫ2 h2ℓ1 + √2Λℓ2 i .
Surface Roughness and Effective Stick-Slip Motion
Since H 2 = L, the renormalization of H will enable us to renormalize L.
Random Vibrational Networks and Renormalization Group
This leading correction emerges when the renormalized coupling u is not exactly equal u∗ since the renormalization ﬂow has not arrived at its ﬁxed point yet.
Corrections to Scaling in Random Resistor Networks and Diluted Continuous Spin Models near the Percolation Threshold
Due to the mixing, a proper renormalization requires an entire renormalization matrix Z .
Corrections to Scaling in Random Resistor Networks and Diluted Continuous Spin Models near the Percolation Threshold
The ﬁeld σ has vanishing anomalous dimension due to the normalization of the Lagrangian (2.3). A wavefunction renormalization of σ cannot be balanced by a coupling-constant renormalization since the coefﬁcient of the σ interaction term is ﬁxed to 1.
String Theory and the Vacuum Structure of Confining Gauge Theories
Finally, we solve the renormalization group equation and give the analytic expressions for the low-energy Wilson coeﬃcients relevant for non-leptonic B meson decays beyond next-to-leading order in both renormalization schemes.
Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
This scheme dependence arises because the requirement that all UV divergences are removed by a suitable renormalization of parameters, ﬁelds as well as operators, does not ﬁx the ﬁnite parts of the associated renormalization constants.
Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
Indeed, these constants can be deﬁned in different ways corresponding to distinct renormalization schemes, which are always related by a ﬁnite renormalization.
Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
In the following we will give only the relevant entries of the necessary renormalization constant matrices, denoting elements that do not affect the ﬁnal results for the residual ﬁnite renormalizations introduced in Eq. (85) with a star.
Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
R contains the divergences which are eliminated by the renormalization procedure, so that relations (5.36) and (5.37) are important for renormalization.
An Axiomatic Approach to Semiclassical Field Perturbation Theory
The pure problem can be solved easily by a Real space renormalization approach where one needs only the renormalization of the Boltzmann factor y = exp(v/T ).
Directed polymers and Randomness
Another route to deal with the Gutzwiller pro jection is to use a renormalized mean-ﬁeld (MF) theory 24 in which the kinetic and superexchange energies are renormalized by different doping-dependent factors gt and gJ respectively.
Bond-order modulated staggered flux phase for the $t{-}J$ model on the square lattice
The renormalization constants Zi = Zi (ε, y , g , w) capture the divergences at ε, y → 0, so that the correlation functions of the renormalized model (11) have ﬁnite limits for ε, y = 0 (when expressed in renormalized parameters u, w , τ and µ).
Effects of mixing and stirring on the critical behavior
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