dorsal/arxiv
View SchemaCovariant Differential and Integral Calculi for Lattice (l,q)-deformed Fields
| Authors | A. Bugrij, V. Rubtsov, V. Shadura |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9501008 |
| URL | https://arxiv.org/abs/q-alg/9501008 |
| Journal | Hadronic J. 20 (1997) 191-211 |
Abstract
Using the Hecke $\hat R$-matrix, we give a definition of the lattice $(l,q)$-deformed $n$-component boson and Grassmann fields. Here $l$ is a deformation parameter for the commutation relations of "values" of these fields in two arbitrary lattice sites and $q$ is a deformation parameter for $n$-component $q$-boson or $q$-Grassmann variable. In framework of the Wess-Zumino approach to the noncommutative differential calculus the commutation relations between differentials and derivatives of these fields are determined. The $SL_q(n,C)$-invariant generalization of the Berezin integration for the lattice $n$-component $(l,q)$-Grassmann field is suggested. We show that the Gaussian functional integral for this field is expressed through the $(l,q)$-deformed counterpart of the Pfaffian.
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"abstract": "Using the Hecke $\\hat R$-matrix, we give a definition of the lattice\n$(l,q)$-deformed $n$-component boson and Grassmann fields. Here $l$ is a\ndeformation parameter for the commutation relations of \"values\" of these fields\nin two arbitrary lattice sites and $q$ is a deformation parameter for\n$n$-component $q$-boson or $q$-Grassmann variable. In framework of the\nWess-Zumino approach to the noncommutative differential calculus the\ncommutation relations between differentials and derivatives of these fields are\ndetermined. The $SL_q(n,C)$-invariant generalization of the Berezin integration\nfor the lattice $n$-component $(l,q)$-Grassmann field is suggested. We show\nthat the Gaussian functional integral for this field is expressed through the\n$(l,q)$-deformed counterpart of the Pfaffian.",
"arxiv_id": "q-alg/9501008",
"authors": [
"A. Bugrij",
"V. Rubtsov",
"V. Shadura"
],
"categories": [
"q-alg",
"cond-mat",
"hep-th",
"math.QA"
],
"journal_ref": "Hadronic J. 20 (1997) 191-211",
"title": "Covariant Differential and Integral Calculi for Lattice (l,q)-deformed Fields",
"url": "https://arxiv.org/abs/q-alg/9501008"
},
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