Riccardo Guida

Convergence of Scaled Delta Expansion: Anharmonic Oscillator

Abstract We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency Ω is chosen to scale with the order as Ω = CNγ; 1/3 0 as N → ∞. It converges also for γ = 1/3, if C ≥ αcg1/3, αc ≃ 0.570875, where g is the coupling constant in front of the operator q4/4. The extreme case with γ = 1/3, C = γcg1/3 corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones.

All order I.R. finite expansion for short distance behavior of massless theories perturbed by a relevant operator

Abstract We consider here renormalizable theories without relevant couplings and present an I.R. consistent technique to study corrections to short distance behavior (Wilson O.P.E. coefficients) due to a relevant perturbation. Our method is the result of a complete reformulation of recent works on the field, and is characterized by a more orthodox treatment of U.V. divergences that allows for simpler formulae and consequently an explicit all order (regularization invariant) I.R. finiteness proof. Underlying hypotheses are discussed in detail and found to be satisfied in conformal theories that constitute a natural field of application of this approach.

Exact consequences of the trace anomaly in four dimensions

The general form of the stress-tensor three-point function in four dimensions is obtained by solving the Ward identities for the diffeomorphism and Weyl symmetries. Several properties of this correlator are discussed, such as the renormalization and scheme independence and the analogies with the anomalous chiral triangle. At the critical point, the coefficients a and c of the four-dimensional trace anomaly are related to two finite, scheme-independent amplitudes of the three-point function. Off-criticality, the imaginary parts of these amplitudes satisfy sum rules which express the total renormalization-group flow of a and c between pairs of critical points. Although these sum rules are similar to that satisfied by the two-dimensional central charge, the monotonicity of the flow, i.e., the four-dimensional analogue of the c-theorem, remains to be proven.

Vacuum expectation values from a variational approach

Abstract In this letter we propose to use an extension of the variational approach known as Truncated Conformal Space to compute numerically the Vacuum Expectation Values of the operators of a conformal field theory perturbed by a relevant operator. As an example we estimate the VEVs of all (UV regular) primary operators of the Ising model and of some of the Tricritical Ising Model when perturbed by any choice of relevant primary operators. We compare our results with some other independent predictions.

Tricritical Ising Model near criticality

The most relevant thermal perturbation of the continuous d=2 minimal conformal theory with c=7/10 (Tricritical Ising Model) is treated here. This model describes the scaling region of the ϕ6 universality class near the tricritical point. The problematic IR divergences of the naive perturbative expansion around conformal theories are dealt within the OPE approach developed at all orders by the authors. The main result is a description of the short distance behavior of correlators that is compared with existing long distance expansion (form factors approach) related to the integrability of the model.

On the short distance behavior of the critical Ising model perturbed by a magnetic field

We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with O.P.E. Wilson coefficients instead of correlators, all order I.R. safe formulas can be obtained for the perturbative expansion with respect to magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, that are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform have been used to compute the I.R. behavior of the regularized integrals. As a corollary of our results, by com- paring the existing numerical data for the lattice model we give an estimate of the Vacuum Expectation Value of the energy operator, left unfixed by usual nonperturbative approaches (Thermodynamic Bethe Ansatz).

Avalanche in the valley (fermions, anomaly and unitarity in high-energy electroweak interactions)

Problems related to fermions, unitarity and chiral anomaly in high energy electroweak interactions, are investigated. Particular attention is paid to the correct functional integration over fermion fields in the background of instanton-anti\-instanton type configurations. This leads to an expansion of correlation functions in terms of a small parameter,

On the fermion level-crossing in the instanton-anti-instanton valley

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FERMIONS IN THE INSTANTON ANTI-INSTANTON VALLEY AND HIGH-ENERGY ELECTROWEAK INTERACTIONS

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Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings

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