scholarly journals A Note on the Weak Dirac Conjecture

10.37236/6688 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Zeye Han
Keyword(s):  
Dirac Conjecture

We show that every set $\mathcal{P}$ of $n$ non-collinear points in the plane contains a point incident to at least $\lceil\frac{n}{3}\rceil+1$ of the lines determined by $\mathcal{P}$.

scholarly journals Hirzebruch-Type Inequalities Viewed as Tools in Combinatorics

10.37236/8335 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Piotr Pokora
Keyword(s):  
Projective Plane ◽  
Plane Curve ◽  
Combinatorial Problems ◽  
Complex Projective Plane ◽  
Open Problems ◽  
Line Arrangements ◽  
Dirac Conjecture ◽  
Complex Projective

The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to their utility in many combinatorial problems related to point or line arrangements in the plane. We would like to present a summary of the technicalities and also some recent applications, for instance in the context of the Weak Dirac Conjecture. We also advertise some open problems and questions.

Magnetic monopoles: Evidence since the Dirac conjecture

1983 ◽  
Vol 13 (2) ◽  
pp. 195-215 ◽  
Author(s):  
Blas Cabrera ◽  
W. Peter Trower
Keyword(s):  
Magnetic Monopoles ◽  
Dirac Conjecture

A New Approach Treating Constrained Systems Based on the Consistency Condition of Constraints

2003 ◽  
Vol 18 (32) ◽  
pp. 2273-2280
Author(s):  
Zheng-Wen Long ◽  
Bo Liu
Keyword(s):  
Consistency Condition ◽  
Constrained Systems ◽  
New Approach ◽  
Dirac Conjecture ◽  
Dirac Brackets

A new approach treating constrained systems based on the consistency condition of constraints is proposed in this paper. This method is simpler and more rigorous in mathematics. It is not necessary to introduce the concepts of weakly equal, strongly equal, Dirac brackets and Dirac conjecture. The procedure of our method is demonstrated by using Cawley's counterexample to Dirac's conjecture.

scholarly journals A Pseudoline Counterexample to the Strong Dirac Conjecture

10.37236/4015 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Ben Lund ◽  
George B. Purdy ◽  
Justin W. Smith
Keyword(s):  
Infinite Family ◽  
Open Problems ◽  
Dirac Conjecture ◽  
Pseudoline Arrangements

We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of $n$ pseudolines has no member incident to more than $4n/9$ points of intersection. This shows the "Strong Dirac" conjecture to be false for pseudolines.We also raise a number of open problems relating to possible differences between the structure of incidences between points and lines versus the structure of incidences between points and pseudolines.

scholarly journals Gauge identities and the Dirac conjecture

2004 ◽  
Vol 313 (2) ◽  
pp. 479-496 ◽  
Author(s):  
Heinz J. Rothe ◽  
Klaus D. Rothe
Keyword(s):  
Dirac Conjecture

scholarly journals FADDEEV-JACKIW APPROACH TO GAUGE THEORIES AND INEFFECTIVE CONSTRAINTS

1998 ◽  
Vol 13 (21) ◽  
pp. 3691-3710 ◽  
Author(s):  
J. ANTONIO GARCÍA ◽  
JOSEP M. PONS
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Equations Of Motion ◽  
Lagrangian Framework ◽  
Dirac Conjecture ◽  
Dirac Hamiltonian ◽  
General Conditions

The general conditions for the applicability of the Faddeev–Jackiw approach to gauge theories are studied. When the constraints are effective, a new proof in the Lagrangian framework of the equivalence between this method and the Dirac approach is given. We find, however, that the two methods may give different descriptions for the reduced phase space when ineffective constraints are present. In some cases the Faddeev–Jackiw approach may lose some constraints or some equations of motion. We believe that this inequivalence can be related to the failure of the Dirac conjecture (that says that the Dirac Hamiltonian can be enlarged to an Extended Hamiltonian including all first class constraints, without changes in the dynamics) and we suggest that when the Dirac conjecture fails, the Faddeev–Jackiw approach fails to give the correct dynamics. Finally we present some examples that illustrate this inequivalence.

Gauge Symmetries and Dirac Conjecture

2009 ◽  
Vol 48 (7) ◽  
pp. 1894-1904 ◽  
Author(s):  
Yong-Long Wang ◽  
Zi-Ping Li ◽  
Ke Wang
Keyword(s):  
Gauge Symmetries ◽  
Dirac Conjecture

An investigation of the Dirac conjecture on constrained systems

1995 ◽  
Vol 110 (8) ◽  
pp. 893-896
Author(s):  
E. M. Rabei ◽  
Y. Güler
Keyword(s):  
Constrained Systems ◽  
Dirac Conjecture
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