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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

An alternative derivation of the spin-dependent quantum potential

Nicola Cufaro Petroni, Ph. Gueret, A. Kypriakidis, Jean Pierre Vigier

Published Apr 1, 1985• 3 citations
Publisher
DOI
10.1007/bf02747053

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We present a calculation by including the relativistic and off-shell contributions to the interaction potentials between two spin-1/2 fermions mediated by the exchange of light spin-0 particles, in both momentum and coordinate spaces. Our calculation is based on the four-point Green function rather than the scattering amplitude. Among the sixteen potential components, eight that vanish in the non-relativistic limit are shown to acquire nonzero relativistic and off-shell corrections. In addition to providing relativistic and off-shell corrections to the operator basis commonly used in the literature, we introduce an alternative operator basis that facilitates the derivation of interaction potentials in coordinate space. Furthermore, we calculate both the long-range and short-range components of the potentials, which can be useful for future experimental analyses at both macroscopic and atomic scales.
The Polchinski exact renormalization group equation for a scalar field theory in arbitrary dimensions is translated, by means of a covariant Hamiltonian formalism, into a partial differential equation for an effective Hamiltonian density that depends on an infinite tower of momenta fields with higher spin. A natural approximation scheme is then expanding the Hamiltonian in momenta with increasing rank. The first order of this expansion, one next to the local potential approximation, is regulator-independent and already includes infinitely many derivative interactions. Further truncating this down to a quadratic dependence on the momenta leads to an alternative to the first order of the derivative expansion, which is used to compute η=0.03616(1)η=0.03616(1)η=0.03616(1) for the critical exponent of the three dimensional Ising model.