A Modified Dirac Operator in Parameter–Dependent Clifford Algebra: A Physical Realization

Teodoro, Antonio Di; Franquiz, Ricardo; López, Alexander

doi:10.1007/s00006-014-0510-0

Cited by 6 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These operators are discrete analogues of continuous Dirac operators with non-constant coefficients which have been studied in the literature, e.g., in literature. [23][24][25] A particular important example of such operators is the Beltrami equation. 26 Here, we can clearly see the advantages of the discrete pseudo-differential calculus.…”

Section: Conflict Of Interestmentioning

confidence: 99%

“…Let us now take a look at the Dirac operator with non‐constant coefficients, i.e.,

D_{h}^{+ -} = \sum_{j = 1}^{n} e_{j}^{+} a_{j}^{+} (x) \partial_{h}^{+ j} + e_{j}^{-} a_{j}^{-} (x) \partial_{h}^{- j} .

These operators are discrete analogues of continuous Dirac operators with non‐constant coefficients which have been studied in the literature, e.g., in literature 23–25 . A particular important example of such operators is the Beltrami equation 26 …”

Section: Examples Of Discrete Symbols Of Discrete Operatorsmentioning

confidence: 99%

See 1 more Smart Citation

Discrete pseudo‐differential operators in hypercomplex analysis

Cerejeiras

Kähler

Lucas

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper we discuss discrete pseudo‐differential operators in the context of hypercomplex analysis. We will provide the definitions and establish the necessary calculus which will be used to discuss questions like boundedness and compactness of operators. In the end, we will discuss well‐known examples from hypercomplex analysis as well as give new examples including discrete Dirac operators with non‐constant coefficients.

show abstract

Section: Conflict Of Interestmentioning

confidence: 99%

“…Let us now take a look at the Dirac operator with non‐constant coefficients, i.e.,

D_{h}^{+ -} = \sum_{j = 1}^{n} e_{j}^{+} a_{j}^{+} (x) \partial_{h}^{+ j} + e_{j}^{-} a_{j}^{-} (x) \partial_{h}^{- j} .

Section: Examples Of Discrete Symbols Of Discrete Operatorsmentioning

confidence: 99%

Discrete pseudo‐differential operators in hypercomplex analysis

Cerejeiras

Kähler

Lucas

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Even though, classical Clifford Algebras have been sufficiently developed in the last decade, there is a need to study properties resulting from a more general structure, which allow for a better understanding of natural phenomena. [5,9,12,[18][19][20]22] 1.0. 3…”

Section: Remarkmentioning

confidence: 99%

“…Remark 3 Using more general operators of Cauchy-Riemann type, the Dirichlet problem in the cylinder can also be solved, see [9,11].…”

Section: Example 2 Consider the Cylindrical Domain ω ⊂ R 3 Given In (??)mentioning

confidence: 99%

About the Dirichlet Boundary Value Problem using Clifford Algebras

Ceballos¹

2018

JAM

View full text Add to dashboard Cite

This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.

show abstract

On Weighted Dirac Operators and Their Fundamental Solutions for Anisotropic Media

Vanegas

Vargas

2018

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

A Modified Dirac Operator in Parameter–Dependent Clifford Algebra: A Physical Realization

Cited by 6 publications

References 18 publications

Discrete pseudo‐differential operators in hypercomplex analysis

Discrete pseudo‐differential operators in hypercomplex analysis

About the Dirichlet Boundary Value Problem using Clifford Algebras

On Weighted Dirac Operators and Their Fundamental Solutions for Anisotropic Media

Contact Info

Product

Resources

About