Renormalization without regularization

Smirnov, Vladimir A.

doi:10.1007/bf02557175

Cited by 3 publications

(2 citation statements)

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“…It should be mentioned however, that the application of this method seems more difficult for time or temperature dependent correlators, or, for quantum spin chains, if an external magnetic field is present, namely in situations where the infinite symmetry algebra is not as clearly identified as in the pure case. In these directions, one should cite [36,37], where in particular a finite volume analysis of form factors has been undertaken. The other approach, described essentially in the book [5], is based on the detailed analysis of the structure of Bethe eigenstates and in particular of their scalar products properties.…”

Section: Introductionmentioning

confidence: 99%

Form factors of the XXZ Heisenberg finite chain

Kitanine¹,

Maillet²,

Terras³

1999

Nuclear Physics B

447

907

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Form factors for local spin operators of the XXZ Heisenberg spin-1 2 finite chain are computed. Representation theory of Drinfel'd twists for the quantum affine algebra U q (ŝl 2 ) in finite dimensional modules is used to calculate scalar products of Bethe states (leading to Gaudin formula) and to solve the quantum inverse problem for local spin operators in the finite chain. Hence, we obtain the representation of the n-spin correlation functions in terms of expectation values (in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This leads to the direct calculation of the form factors of the XXZ Heisenberg spin-1 2 finite chain as determinants of usual functions of the parameters of the model. A two-point correlation function for adjacent sites is also derived using similar techniques. * On leave of absence from the St Petersburg branch of the Steklov Mathematical Institute,

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Section: Introductionmentioning

confidence: 99%

Form factors of the XXZ Heisenberg finite chain

Kitanine¹,

Maillet²,

Terras³

1999

Nuclear Physics B

447

907

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“…We should here note that Differential Renormalization (DR) procedure [34,35], which has been vastly investigated in the literature, is done in coordinate space, though the traditional method of renormalization in momentum space (for review see [36,37]). DR is equivalent to traditional renormalization [38][39][40], and is based on the observation that the UV divergence reflects in the fact that the higher order amplitude cannot have a Fourier transform into momentum space due to the short-distance singularity.…”

Section: Introductionmentioning

confidence: 99%

Coordinate space representation for renormalization of quantum electrodynamics

Mojavezi,

Moazzemi,

Zomorrodian

2020

Preprint

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In this paper we present a systematic treatment for fundamental renormalization of quantum electrodynamics in real space. Although the standard renormalization is an old school problem in this case, it has not yet been completely done in position space. The most important difference with well-known differential renormalization is that we do the whole procedure in coordinate space without need to transformation to momentum space. Specially, we directly derive the conterterms in real space. This problem becomes important when the translational symmetry of the system breaks somehow explicitly (for example by nontrivial boundary condition (BC) on the fields). In this case, one is not able to move to momentum space by a simple Fourier transformation. Therefore, in the context of renormalized perturbation theory, by imposing the renormalization conditions, counterterms in coordinate space will depend directly on the fields BCs (or background topology). Trivial BC or trivial background lead to the usual standard conterterms. If the counterterms modify then the quantum corrections of any physical quantity are different from those in free space where we have the translational invariance. We also show that, up to order α, our counterterms are reduced to usual standard terms derived in free space.

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