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Marcos Sampaio

Publications and source records attributed to Marcos Sampaio.

58 records · Page 4Linked to original sources
arXiv1999

Implicit Regularisation Technique: Calculation of the Two-loop $ϕ^4_4$-theory $β$-function

We propose an implicit regularisation scheme. The main advantage is that since no explicit use of a regulator is made, one can in principle avoid undesirable symmetry violations related to its choice. The divergent amplitudes are split into basic divergent integrals which depend only on the loop momenta and finite integrals. The former can be absorbed by a renormalisation procedure whereas the latter can be evaluated without restrictions. We illustrate with the calculation of the $QED$ and $ϕ^4_4$-theory $β$-function to one and two-loop order, respectively.

hep-th↗
arXiv1998

Yang-Mills beta-function from a large-distance expansion of the Schroedinger functional

For slowly varying fields the Yang-Mills Schroedinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schroedinger functional for arbitrarily varying fields to be reconstructed from this expansion. We also construct the form of the Schroedinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the `standard' perturbative solution of the functional Schroedinger equation which we also describe. In particular the usual result for the beta-function is obtained illustrating how analyticity enables the effects of rapidly varying fields to be computed from the behaviour of slowly varying ones.

hep-th↗
arXiv1997

Short Distance Properties from Large Distance Behaviour

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We also describe an approximate simplification that occurs for the Sine-Gordon and Sinh-Gordon vacuum functionals.

hep-th↗