ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Quaternions and special relativity (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2955-2968 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We reformulate Special Relativity by a quaternionic algebra on reals. Using real linear quaternions, we show that previous difficulties, concerning the appropriate transformations on the 3+1 space–time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531548
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Quaternionic differential operators (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2236-2265 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential equations with constant coefficients. We overcome the problems coming out from the loss of the fundamental theorem of the algebra for quaternions and propose a practical method to solve quaternionic and complex linear second order differential equations with constant coefficients. The resolution of the complex linear Schrödinger equation, in the presence of quaternionic potentials, represents an interesting application of the mathematical material discussed in this paper. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1360195
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Octonionic representations of GL(8,R) and GL(4,C) (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 582-598 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Octonionic algebra being nonassociative is difficult to manipulate. We introduce left/right octonionic barred operators which enable us to reproduce the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an interesting connection between the structure of left/right octonionic barred operators and generic 4×4 complex matrices. As an application we give an octonionic representation of the four-dimensional Clifford algebra. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531879
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Quantum mechanics: From complex to complexified quaternions (1997)
    Springer
    International journal of theoretical physics 36 (1997), S. 2725-2757 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper is an attempt to simplify and clarify the mathematical language used to express quaternionic quantum mechanics (QQM). In our quaternionic approach the choice of “complex” geometries allows an appropriate definition of momentum operator and gives the possibility to obtain consistent formulations of standard theories. Barred operators represent the key to realizing a set of translation rules between quaternionic and complex quantum mechanics (QM). These translations enable us to obtain a rapid quaternionic counterpart of standard quantum mechanical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02435708
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Quaternionic Groups in Physics (1999)
    Springer
    International journal of theoretical physics 38 (1999), S. 2197-2220 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the left and right action ofquaternionic numbers. The standard problems arising inthe definitions of transpose, determinant, and trace forquaternionic matrices are overcome. We investigate the possibility of formulating a new approach toquaternionic group theory. Our aim is to highlight thepossibility of looking at new quaternionic groups by theuse of left and right operators as fundamental step toward a clear and complete discussion ofunification theories in physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026626424174
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Dirac-Hestenes Lagrangian (1999)
    Springer
    International journal of theoretical physics 38 (1999), S. 2349-2369 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford $$\mathbb{R}$$ -algebra $${Cl_{_{1,3} }^ + }$$ . A fundamental ingredient in ourmultivectorial algebraic formulation is a $$\mathbb{D}$$ -complex geometry, $$\mathbb{D} \equiv {span}_\mathbb{D} \left\{ {1,{\gamma }_{{21}} } \right\},{\gamma }_{{21}} \in Cl_{_{1,3} }^ +$$ . We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on $$\mathbb{D}\; \otimes \;\mathcal{F}$$ , where ℱ denotes an $$\mathbb{R}$$ -algebra of functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026627819148
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Toward an Octonionic World (1998)
    Springer
    International journal of theoretical physics 37 (1998), S. 1945-1985 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In order to obtain a consistent formulation ofoctonionic quantum mechanics (OQM), we introduceleft/right-barred operators. Such operators enable us tofind the translation rules between octonionic numbers and 8 × 8 real matrices (a translation isalso given for 4 × 4 complex matrices). The use ofa complex geometry allows us to overcome the hermiticityproblem and define an appropriate momentum operator within OQM. As an application of our results,we develop an octonionic relativistic free waveequation, linear in the derivatives. Even if the wavefunctions are only one-component, we show that fourindependent solutions, corresponding to those of the Diracequation, exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026617314160
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Quaternionic Electron Theory: Dirac's Equation (1998)
    Springer
    International journal of theoretical physics 37 (1998), S. 1511-1529 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We perform a one-dimensional complexifiedquaternionic version of the Dirac equation based oni-complex geometry. The problem of the missing complexparameters in quaternionic quantum mechanics withi-complex geometry is overcome by a nice“trick” which allows us to avoid the Diracalgebra constraints in formulating our relativisticequation. A brief comparison with other quaternionicformulations is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026611718277
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Quaternionic Electron Theory: Geometry, Algebra, and Dirac's Spinors (1998)
    Springer
    International journal of theoretical physics 37 (1998), S. 1707-1720 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The use of complexified quaternions andi-complex geometry in formulating the Dirac equationallows us to give interesting geometric interpretationshidden in the conventional matrix-basedapproach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026692508708
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Complex Geometry and Dirac Equation (1998)
    Springer
    International journal of theoretical physics 37 (1998), S. 2415-2431 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit $$i = \sqrt { - 1} $$ . We discuss two possibilities which appearin the multivector algebra approach: theσ123 and σ21 complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit $$i = \sqrt { - 1} $$ is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026675210893
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...