2010Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsOpen access

Quantum field theory without divergences

M. V. Altaĭsky

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Abstract

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to 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 $\ensuremath{\phi}(x)\ensuremath{\rightarrow}{\ensuremath{\phi}}^{(A)}(x)$ and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean ${\ensuremath{\phi}}^{4}$-field theory is taken as an example.

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It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to 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 $\ensuremath{\phi}(x)\ensuremath{\rightarrow}{\ensuremath{\phi}}^{(A)}(x)$ and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean ${\ensuremath{\phi}}^{4}$-field theory is taken as an example.

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Available abstract

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to 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 $\ensuremath{\phi}(x)\ensuremath{\rightarrow}{\ensuremath{\phi}}^{(A)}(x)$ and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean ${\ensuremath{\phi}}^{4}$-field theory is taken as an example.

Key concepts: Quantum field theory, Feynman diagram, Thermal quantum field theory, Euclidean geometry, Field theory (psychology), Mathematical physics, Physics, Field (mathematics)

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