Renormalization scheme dependence and the renormalization group beta function

Renormalization Scheme Dependence

The running couplings such as λ(E) depend not only on the energy scale E but also on the specific rules we use to fix the finite parts of δλ(E) and other counterterms. If we change those rules — collectively known as the renormalization scheme — then for the same energy scale E we would get a slightly different running coupling λ(E) 6= λ(E). The difference is due to quantum corrections which us...

Renormalization Scheme Dependence

The running couplings such as λ(E) depend not only on the energy scale E, but also on the specific rules we use to fix the finite parts of the δλ(E) and other counterterms. If we change those rules — collectively known as the renormalization scheme — then for the same energy scale E we would get a slightly different running coupling λ(E) 6= λ(E). The difference is due to quantum corrections whi...

On scheme dependence of gravitational dressing of renormalization group functions

It is shown that for 2D field theories only the first order coefficient of the gravitationally dressed RG β-function is scheme independent. This is valid even for matter theories with one dimensionless coupling, where the first two coefficients of the original β-function are scheme independent.

Renormalization Group Renormalization Group

Time-Dependent Real-Space Renormalization Group Method

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...