Applications of discrete Clifford calculus in field theories

• Grant number: 13/07590-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): September 01, 2013
• Effective date (End): February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Jayme Vaz Junior
• Grantee: Nelson José Rodrigues Faustino
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project has as its ultimate goal the development of techniques and tools in the context of Clifford algebras that allow us to study from the functional point of view and in higher dimensions, solutions, symmetries and gauge-type invariances associated in the context of quantum field theory on lattices.Besides the possible physical interpretation of the results in terms of fermion doubling and chiral anomalies, much of the work plan will be based on the research of functional integration as Euclidean lattice quantization scheme.

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FAUSTINO, N.. Hypercomplex Fock states for discrete electromagnetic Schrodinger operators: A Bayesian probability perspective. Applied Mathematics and Computation, v. 315, p. 531-548, DEC 15 2017. (13/07590-8)

FAUSTINO, N.. Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle. Applied Mathematics and Computation, v. 247, p. 607-622, NOV 15 2014. (13/07590-8)

FAUSTINO, NELSON. Solutions for the Klein-Gordon and Dirac Equations on the Lattice Based on Chebyshev Polynomials. COMPLEX ANALYSIS AND OPERATOR THEORY, v. 10, n. 2, p. 379-399, FEB 2016. (13/07590-8)

ABREU, LUIS DANIEL; FAUSTINO, NELSON. ON TOEPLITZ OPERATORS AND LOCALIZATION OPERATORS. Proceedings of the American Mathematical Society, v. 143, n. 10, p. 4317-4323, OCT 2015. (13/07590-8)

RODRIGUES FAUSTINO, NELSON JOSE. A conformal group approach to the Dirac-Kahler system on the lattice. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 40, n. 11, p. 4118-4127, JUL 30 2017. (13/07590-8)

FAUSTINO, NELSON. Special Functions of Hypercomplex Variable on the Lattice Based on SU(1,1). Symmetry Integrability and Geometry-Methods and Applications, v. 9, 2013. (13/07590-8)