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Marco D'Attanasio

Publications and source records attributed to Marco D'Attanasio.

5 recordsLinked to original sources
arXiv1997

Large N and the renormalization group

In the large N limit, we show that the Local Potential Approximation to the flow equation for the Legendre effective action, is in effect no longer an approximation, but exact - in a sense, and under conditions, that we determine precisely. We explain why the same is not true for the Polchinski or Wilson flow equations and, by deriving an exact relation between the Polchinski and Legendre effective potentials (that holds for all N), we find the correct large N limit of these flow equations. We also show that all forms (and all parts) of the renormalization group are exactly soluble in the large N limit, choosing as an example, D dimensional O(N) invariant N-component scalar field theory.

hep-th↗
arXiv1996

Wilson Renormalization Group formulation of Real Time thermal field theories

We apply Renormalization Group techniques to the Real Time formulation of thermal field theory. Due to the separation between the $T=0$ and the $T\neq 0$ parts of the propagator in this formalism, one can derive exact evolution equations for the Green functions describing the effect of integrating out thermal fluctuations of increasing wavelengths, the initial conditions being the renormalized Green functions of the $T=0$ theory. As a first application, we study the phase transition for the real scalar theory, computing the order of the transition, the critical temperature, and critical exponents, in different approximations to the evolution equations for the scalar potential.

hep-ph↗
arXiv1996

Gauge Invariance, the Quantum Action Principle, and the Renormalization Group

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We show that an effective Quantum Action Principle can be formulated in perturbation theory which enables the effective Ward identities to be solved order by order, even if the theory requires non-vanishing subtraction points. The difficulties encountered with non-perturbative approximations are briefly discussed.

hep-th↗