Built on

P.R. Halmos, Measure Theory , Springer, New York, 1974
1974
Earlier work this paper cites.
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces , Pure and Applied Mathematics, vol. 80, Academic Press Inc., New York, 1978
1978
Earlier work this paper cites.
N.J.A. Sloane, Tables of sphere packings and spherical codes , IEEE Trans. Inform. Theory 27
1981
Earlier work this paper cites.
T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups , Graduate Texts in Mathematics, vol. 98, Springer-Verlag, New York, 1985
1985
Earlier work this paper cites.
H.T. Croft, K.J. Falconer, and R.K. Guy, Unsolved Problems in Geometry , Problem Books in Mathematics, Springer-Verlag, New York, 1994, Corrected reprint of the 1991 original
1991
Earlier work this paper cites.
E.B. Saff and A.B.J. Kuijlaars, Distributing many points on a sphere , Math. Intelligencer 19
1997
Earlier work this paper cites.
P.D. Lax, Functional Analysis , Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002
2002
Earlier work this paper cites.
A. Sütő, Crystalline ground states for classical particles , arXiv:math-ph/0508004, Phys. Rev. Lett. 95
Original
2005
Earlier work this paper cites.
by same author, The Principle of the Fermionic Projector , hep-th/0001048, hep-th/0202059, hep-th/0210121, AMS/IP Studies in Advanced Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2006
2006
Earlier work this paper cites.

Similar

by same author, The principle of the fermionic projector: An approach for quantum gravity? , arXiv:gr-qc/0601128, Quantum Gravity (B. Fauser, J. Tolksdorf, and E. Zeidler, eds.), Birkhäuser Verlag, Basel, 2006, pp. 263–281
2006
Cited alongside, same era.
by same author, Fermion systems in discrete space-time—outer symmetries and spontaneous symmetry breaking , arXiv:math-ph/0601039, Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
by same author, A variational principle in discrete space-time: Existence of minimizers , arXiv:math-ph/0503069, Calc. Var. Partial Differential Equations 29
2007
Cited alongside, same era.
A. Diethert, F. Finster, and D. Schiefeneder, Fermion systems in discrete space-time exemplifying the spontaneous generation of a causal structure , arXiv:0710.4420 [math-ph], Int. J. Mod. Phys. A 23
Original
2008
Cited alongside, same era.

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2010

On the Support of Minimizers of Causal Variational Principles

Finster, Felix, Schiefeneder, Daniela

Understand

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically.

It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty.
In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed and explicit analysis of the minimizers.
On the sphere, we get a connection to packing problems and the Tammes distribution.

Built on

P.R. Halmos, Measure Theory , Springer, New York, 1974
1974
Earlier work this paper cites.
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces , Pure and Applied Mathematics, vol. 80, Academic Press Inc., New York, 1978
1978
Earlier work this paper cites.
N.J.A. Sloane, Tables of sphere packings and spherical codes , IEEE Trans. Inform. Theory 27
1981
Earlier work this paper cites.
T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups , Graduate Texts in Mathematics, vol. 98, Springer-Verlag, New York, 1985
1985
Earlier work this paper cites.
H.T. Croft, K.J. Falconer, and R.K. Guy, Unsolved Problems in Geometry , Problem Books in Mathematics, Springer-Verlag, New York, 1994, Corrected reprint of the 1991 original
1991
Earlier work this paper cites.
E.B. Saff and A.B.J. Kuijlaars, Distributing many points on a sphere , Math. Intelligencer 19
1997
Earlier work this paper cites.
P.D. Lax, Functional Analysis , Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002
2002
Earlier work this paper cites.
A. Sütő, Crystalline ground states for classical particles , arXiv:math-ph/0508004, Phys. Rev. Lett. 95
Original
2005
Earlier work this paper cites.
by same author, The Principle of the Fermionic Projector , hep-th/0001048, hep-th/0202059, hep-th/0210121, AMS/IP Studies in Advanced Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2006
2006
Earlier work this paper cites.

Similar

by same author, The principle of the fermionic projector: An approach for quantum gravity? , arXiv:gr-qc/0601128, Quantum Gravity (B. Fauser, J. Tolksdorf, and E. Zeidler, eds.), Birkhäuser Verlag, Basel, 2006, pp. 263–281
2006
Cited alongside, same era.
by same author, Fermion systems in discrete space-time—outer symmetries and spontaneous symmetry breaking , arXiv:math-ph/0601039, Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
by same author, A variational principle in discrete space-time: Existence of minimizers , arXiv:math-ph/0503069, Calc. Var. Partial Differential Equations 29
2007
Cited alongside, same era.
A. Diethert, F. Finster, and D. Schiefeneder, Fermion systems in discrete space-time exemplifying the spontaneous generation of a causal structure , arXiv:0710.4420 [math-ph], Int. J. Mod. Phys. A 23
Original
2008
Cited alongside, same era.

Then

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

S. Capet and G. Friesecke, Minimum energy configurations of classical charges: large N N asymptotics , arXiv:0907.5097 [math.CA], Appl. Math. Res. Express. AMRX (2009), no. 1, 47–73

Original

2009

Cited alongside, same era.

by same author, An action principle for an interacting fermion system and its analysis in the continuum limit , arXiv:0908.1542 [math-ph] (2009)

Original

2009

Cited alongside, same era.

by same author, From discrete space-time to Minkowski space: Basic mechanisms, methods and perspectives , arXiv:0712.0685 [math-ph], Quantum Field Theory (B. Fauser, J. Tolksdorf, and E. Zeidler, eds.), Birkhäuser Verlag, 2009, pp. 235–259

Original

2009

Cited alongside, same era.

by same author, Causal variational principles on measure spaces , arXiv:0811.2666 [math-ph], J. Reine Angew. Math. 646