On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy - INSPIRE

DataBETA

On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy

Carlos Castro
(
- Clark U.
)

Sep, 2010

19 pages

Published in:

Found.Phys. 40 (2010) 1712-1730

DOI:

10.1007/s10701-010-9476-5

View in:

AMS MathSciNet

reference search0 citations

Citations per year

0 Citations

Abstract: (Springer)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of Quantum Gravity.

Noncommutative phase spaces
Nonlinear Quantum Mechanics
Scale fractal calculus
Vacuum energy

References(74)

Figures(0)

Nonlinear quantum mechanics implies polynomial time solution for N P complete and #P problems

Daniel S. Abrams
(
- MIT
)
,
Seth Lloyd
(
- MIT
)

- Phys.Rev.Lett. 81 (1998) 3992-3995
•
e-Print:
- quant-ph/9801041
•
DOI:
- 10.1103/PhysRevLett.81.3992

Path integral formulation of noncommutative quantum mechanics

Ciprian Acatrinei
(
- Crete U. and
- Bucharest, IFIN-HH
)

- JHEP 09 (2001) 007
•
e-Print:
- hep-th/0107078
•
DOI:
- 10.1088/1126-6708/2001/09/007

Emergence of a 4-D world from causal quantum gravity

J. Ambjorn
(
- Bohr Inst. and
- Utrecht U.
)
,
J. Jurkiewicz
(
- Jagiellonian U.
)
,
R. Loll
(
- Utrecht U.
)

- Phys.Rev.Lett. 93 (2004) 131301
•
e-Print:
- hep-th/0404156
•
DOI:
- 10.1103/PhysRevLett.93.131301

Semiclassical universe from first principles

J. Ambjorn
(
- Bohr Inst. and
- Utrecht U.
)
,
J. Jurkiewicz
(
- Jagiellonian U.
)
,
R. Loll
(
- Utrecht U.
)

- Phys.Lett.B 607 (2005) 205-213
•
e-Print:
- hep-th/0411152
•
DOI:
- 10.1016/j.physletb.2004.12.067

Dissipation and noncommutativity in planar quantum mechanics

Rabin Banerjee
(
- Bose Natl. Ctr., Kolkata
)

- Mod.Phys.Lett.A 17 (2002) 631
•
e-Print:
- hep-th/0106280
•
DOI:
- 10.1142/S0217732302006977

Alternatives to Dark Matter: Modified Gravity as an Alternative to dark Matter

Jacob D. Bekenstein
(
- Hebrew U.
)

•
e-Print:
- 1001.3876

Two phases of the noncommutative quantum mechanics

Stefano Bellucci
(
- Frascati
)
,
Armen Nersessian
(
- Frascati and
- Dubna, JINR and
- Yerevan State U.
)
,
Corneliu Sochichiu
(
- Dubna, JINR and
- IAP, Chisinau
)

- Phys.Lett.B 522 (2001) 345-349
•
e-Print:
- hep-th/0106138
•
DOI:
- 10.1016/S0370-2693(01)01304-1

Introduction to PT-Symmetric Quantum Theory

Carl M. Bender
(
- Imperial Coll., London
)

- Contemp.Phys. 46 (2005) 277-292
•
e-Print:
- quant-ph/0501052
•
DOI:
- 10.1080/00107500072632

PT-symmetric quantum electrodynamics

Carl M. Bender
(
- Imperial Coll., London
)
,
Ines Cavero-Pelaez
(
- Oklahoma U.
)
,
Kimball A. Milton
(
- Oklahoma U.
)
,
K.V. Shajesh
(
- Oklahoma U.
)

- Phys.Lett.B 613 (2005) 97-104
•
e-Print:
- hep-th/0501180
•
DOI:
- 10.1016/j.physletb.2005.03.032

The Eight-dimensional quantum Hall effect and the octonions

Bogdan A. Bernevig
(
- Stanford U., Phys. Dept.
)
,
Jiang-ping Hu
(
- UCLA
)
,
Nicolaos Toumbas
(
- Harvard U.
)
,
Shou-Cheng Zhang
(
- Stanford U., Phys. Dept.
)

- Phys.Rev.Lett. 91 (2003) 236803
•
e-Print:
- cond-mat/0306045
•
DOI:
- 10.1103/PhysRevLett.91.236803

Nonlinear Wave Mechanics

Iwo Bialynicki-Birula
(
- Pittsburgh U. and
- Warsaw U.
)
,
Jerzy Mycielski
(
- Warsaw U.
)

- Annals Phys. 100 (1976) 62
•
DOI:
- 10.1016/0003-4916(76)90057-9

Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations

D. Bohm
(
- Sao Paulo U.
)
,
J.P. Vigier
(
- Poincare Inst.
)

- Phys.Rev. 96 (1954) 208-216
•
DOI:
- 10.1103/PhysRev.96.208

A suggestion for unifying quantum theory and relativity

Max Born

- Proc.Roy.Soc.Lond.A 165 (1938) 921, 291-303
•
DOI:
- 10.1098/rspa.1938.0060

Reciprocity Theory of Elementary Particles

Max Born
(
- Edinburgh U.
)

- Rev.Mod.Phys. 21 (1949) 3, 463-473
•
DOI:
- 10.1103/revmodphys.21.463

Black Holes, Qubits and Octonions

L. Borsten
(
- Imperial Coll., London
)
,
D. Dahanayake
(
- Imperial Coll., London
)
,
M.J. Duff
(
- Imperial Coll., London
)
,
H. Ebrahim
(
- Imperial Coll., London and
- IPM, Tehran and
- Brandeis U.
)
,
W. Rubens
(
- Imperial Coll., London
)

- Phys.Rept. 471 (2009) 113-219
•
e-Print:
- 0809.4685
•
DOI:
- 10.1016/j.physrep.2008.11.002

- J.Math.Phys. 31 2633

Nonlinear quantum mechanics as the Weyl geometry of a classical statistical ensemble

Carlos Castro
(
- Texas U.
)

- Found.Phys.Lett. 4 (1991) 81-99
•
DOI:
- 10.1007/BF00666419

- Found.Phys. 22 569

- Found.Phys. 8 1301

Is quantum space-time infinite dimensional <--->?

Carlos Castro
(
- Clark Atlanta U.
)

- Chaos Solitons Fractals 11 (2000) 1663-1670
•
e-Print:
- hep-th/0001134
•
DOI:
- 10.1016/S0960-0779(00)00018-7

How a new scale relativity solves some quantum paradoxes

Carlos Castro
(
- Clark Atlanta U.
)

- Chaos Solitons Fractals 12 (2001) 101-104
•
e-Print:
- hep-th/0007224
•
DOI:
- 10.1016/S0960-0779(00)00196-X

- Prog.Phys. 1 20

The extended relativity theory in Born-Clifford phase spaces with a lower and upper length scales and Clifford group geometric unification

C. Castro
(
- Clark Atlanta U.
)

- Found.Phys. 35 (2005) 971-1041
•
DOI:
- 10.1007/s10701-005-5829-x

- Prog.Phys. 2 86

On the Noncommutative and Nonassociative Geometry of Octonionic Spacetime, Modified Dispersion Relations and Grand Unification

Carlos Castro
(
- Clark Atlanta U.
)

- J.Math.Phys. 48 (2007) 073517
•
DOI:
- 10.1063/1.2752013

1-25 of 74
1
2
3
25 / page