Quaternionic electron theory: Dirac's equation

De Leo, Stefano; Rodrigues, Waldyr A., Jr.

doi:10.1023/A:1026611718277

Quaternionic electron theory: Dirac's equation

Stefano De Leo
(
- Salento U. and
- INFN, Lecce and
- Campinas State U.
)
,
Waldyr A. Rodrigues, Jr.
(
- Campinas State U.
)

Jun, 1998

14 pages

Published in:

Int.J.Theor.Phys. 37 (1998) 1511-1530

e-Print:

hep-th/9806057 [hep-th]

DOI:

10.1023/A:1026611718277

View in:

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Abstract: (arXiv)

We perform a one-dimensional complexified quaternionic version of the Dirac equation based on

i

-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with

i

-complex geometry is overcome by a nice ``trick'' which allows to avoid the Dirac algebra constraints in formulating our relativistic equation. A brief comparison with other quaternionic formulations is also presented.

Note:

14 pags, Revtex, Int. J. Theor. Phys. (published, May 98)

electron: model
Dirac equation
algebra: quaternion
transformation: CPT

References(38)

Figures(0)

Foundations of quaternion quantum mechanics

David Finkelstein
(
- Yeshiva U.
)
,
Josef M. Jauch
(
- Geneva U. and
- CERN
)
,
David Speiser
(
- Geneva U.
)

- J.Math.Phys. 3 (1962) 207-220
•
DOI:
- 10.1063/1.1703794

Principle of general Q covariance

- J.Math.Phys. 4 (1963) 788-796
•
DOI:
- 10.1063/1.1724320

- J.Math.Phys. 4 136

- Acta Appl.Math. 24 141

- Acta Appl.Math. 24 179

Uniqueness of the scalar product in the tensor product of quaternion Hilbert modules

A. Razon
(
- Tel Aviv U.
)
,
L.P. Horwitz
(
- Tel Aviv U.
)

- J.Math.Phys. 33 (1992) 3098-3104
•
DOI:
- 10.1063/1.529528

Some spectral properties of antiselfadjoint operators on a quaternionic Hilbert space

L.P. Horwitz
(
- Princeton, Inst. Advanced Study
)

- J.Math.Phys. 34 (1993) 3405-3419
•
DOI:
- 10.1063/1.530084

A Soluble model for scattering and decay in quaternionic quantum mechanics. 1. Decay

L.P. Horwitz
(
- Princeton, Inst. Advanced Study
)

- J.Math.Phys. 35 (1994) 2743-2760
•
e-Print:
- hep-th/9312028
•
DOI:
- 10.1063/1.530483

A Soluble model for scattering and decay in quaternionic quantum mechanics. 2. Scattering

L.P. Horwitz
(
- Princeton, Inst. Advanced Study
)

- J.Math.Phys. 35 (1994) 2761-2771
•
e-Print:
- hep-th/9312029
•
DOI:
- 10.1063/1.530484

Special geometry, cubic polynomials and homogeneous quaternionic spaces

B. de Wit
(
- CERN
)
,
Antoine Van Proeyen
(
- Leuven U.
)

- Commun.Math.Phys. 149 (1992) 307-334
•
e-Print:
- hep-th/9112027
•
DOI:
- 10.1007/BF02097627

Hidden symmetries, special geometry and quaternionic manifolds

B. de Wit
(
- Utrecht U.
)
,
Antoine Van Proeyen
(
- Leuven U.
)

- Int.J.Mod.Phys.D 3 (1994) 31-48
•
e-Print:
- hep-th/9310067
•
DOI:
- 10.1142/S0218271894000058

Representations of U(1,q) and constructive quaternion tensor products

S. De Leo
(
- Salento U. and
- INFN, Lecce
)
,
P. Rotelli
(
- Salento U. and
- INFN, Lecce
)

- Nuovo Cim.B 110 (1995) 33-52
•
e-Print:
- hep-th/9308142
•
DOI:
- 10.1007/BF02741288

Quaternion Higgs and the electroweak gauge group

Stefano De Leo
(
- Salento U. and
- INFN, Lecce
)
,
Pietro Rotelli
(
- Salento U. and
- INFN, Lecce
)

- Int.J.Mod.Phys.A 10 (1995) 4359-4370
•
e-Print:
- hep-th/9506179
•
DOI:
- 10.1142/S0217751X95002011

Generalized quantum dynamics

Stephen L. Adler
(
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 415 (1994) 195-242
•
e-Print:
- hep-th/9306009
•
DOI:
- 10.1016/0550-3213(94)90072-8

Composite leptons and quarks constructed as triply occupied quasiparticles in quaternionic quantum mechanics

Stephen L. Adler
(
- Princeton, Inst. Advanced Study
)

- Phys.Lett.B 332 (1994) 358-365
•
e-Print:
- hep-th/9404134
•
DOI:
- 10.1016/0370-2693(94)91265-3

Projective group representations in quaternionic Hilbert space

Stephen L. Adler
(
- Princeton, Inst. Advanced Study
)

- J.Math.Phys. 37 (1996) 2352-2360,
•
e-Print:
- hep-th/9601047
•
DOI:
- 10.1063/1.531514

Duffin-Kemmer-Petiau equation on the quaternion field

Stefano De Leo
(
- INFN, Lecce
)

- Prog.Theor.Phys. 94 (1995) 1109-1120
•
e-Print:
- hep-th/9509058
•
DOI:
- 10.1143/PTP.94.1109

Quaternions and special relativity

Stefano De Leo
(
- Salento U. and
- INFN, Lecce
)

- J.Math.Phys. 37 (1996) 2955-2968
•
e-Print:
- hep-th/9508011
•
DOI:
- 10.1063/1.531548

- J.Phys.A 11 2323

Quaternion Quantum Mechanics: Second Quantization and Gauge Fields

L.P. Horwitz
(
- Tel Aviv U.
)
,
L.C. Biedenharn
(
- Texas U.
)

- Annals Phys. 157 (1984) 432,
- Ann. Phys. ( N.y.) 159 ( 1985) 481. ( Ann. Phys. ( N.y.) 157 ( 1984) 432)
•
DOI:
- 10.1016/0003-4916(84)90068-X

The Dirac Equation on the Quaternion Field

P. Rotelli
(
- Salento U. and
- INFN, Bari
)

- Mod.Phys.Lett.A 4 (1989) 933
•
DOI:
- 10.1142/S0217732389001106

One component Dirac equation

Stefano De Leo
(
- Salento U. and
- INFN, Lecce
)

- Int.J.Mod.Phys.A 11 (1996) 3973-3986
•
e-Print:
- hep-th/9508010
•
DOI:
- 10.1142/S0217751X96001863

The Quaternion scalar field

S. De Leo
(
- Salento U.
)
,
P. Rotelli
(
- Salento U. and
- INFN, Lecce
)

- Phys.Rev.D 45 (1992) 575-579
•
DOI:
- 10.1103/PhysRevD.45.575

- Found.Phys. 20 1213

Nature's natural numbers - relativistic quantum theory over the ring of complex quaternions

J.D. Edmonds
(
- UC, San Diego
)

- Int.J.Theor.Phys. 6 (1972) 205-224
•
DOI:
- 10.1007/BF00672074

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