It is shown that loop divergences emerging in the Green functions in quantum
field theory originate from correspondence of the Green functions to {\em
unmeasurable} (and hence unphysical) quantities. This is because no physical
quantity can be measured in a point, but in a region, the size of which is
constrained by the resolution of measuring equipment. The incorporation of the
resolution into the definition of quantum fields $\phi(x)\to\phi^{(A)}(x)$ and
appropriate change of Feynman rules results in finite values of the Green
functions. The Euclidean $\phi^4$-field theory is taken as an example.Comment: 6 pages, LaTeX, revtex, 2 eps figure
We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations which are based on SQUID-based systems operating at temperatures in the mK range.
Abstract. The Euclidean quantum field theory for the fields φ ∆x (x), which depend on both the position x and the resolution ∆x, constructed in SIGMA 2 (2006), 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
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