Twistors and fields with sources on worldlines

1985 ◽  
Vol 397 (1812) ◽  
pp. 143-155 ◽  
Keyword(s):  
Minkowski Space ◽  
Twistor Space ◽  
Rest Mass ◽  
Double Cover ◽  
Ruled Surface ◽  
Hausdorff Spaces ◽  
Twistor Spaces ◽  
Non Hausdorff Spaces ◽  
Massless Fields

It is shown that zero-rest-mass fields with sources on an analytic worldline are naturally defined on a double cover of some region of Minkowski space. Twistor spaces are constructed that correspond to such regions and these turn out to be non-Hausdorff spaces, obtained by identifying two copies of regions in ordinary twistor space, except on a ruled surface that corresponds to the worldline. It is shown that cohomology classes on the twistor space corresponds to sourced fields on Minkowski space, thus extending the twistor descrip­tion of massless fields.

On the twistor description of massive fields

1981 ◽  
Vol 374 (1758) ◽  
pp. 431-445 ◽  
Keyword(s):  
Minkowski Space ◽  
Complex Manifold ◽  
Twistor Space ◽  
Spin Operator ◽  
Dirac Equations ◽  
Penrose Transform ◽  
Twistor Description ◽  
Integral Formulae ◽  
Massless Fields ◽  
Massive Fields

This paper forms a part of the twistor programme whereby constructions of physics on Minkowski space are transferred, it is hoped, to simpler constructions on Penrose’s twistor-space . We show how the Penrose transform may be used to describe solutions of the Dirac equations on Minkowski space in terms of certain cohomology classes on a related five-dimensional complex manifold. This is accomplished along the same lines as the corresponding representation of massless fields. It means that Penrose’s integral formulae for massive fields may be interpreted cohomologically. We also give a brief discussion of the spin operator in twistor space.

Massless fields on Minkowski space-time with quantized, Kerr sources

1993 ◽  
Vol 441 (1911) ◽  
pp. 191-200 ◽  
Keyword(s):  
Minkowski Space ◽  
Rest Mass ◽  
Space Time ◽  
Maxwell Field ◽  
Field Equations ◽  
Self Energy ◽  
Minkowski Space Time ◽  
Massless Fields ◽  
Mass Field

Solutions to the zero rest mass field equations generated by spinning Kerr sources are reviewed. It is shown that the act of quantization removes the singularity when the source has spin ½ . For a Maxwell field, the integrated self-energy is also finite.

scholarly journals Generalized almost even-Clifford manifolds and their twistor spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 96-124
Author(s):  
Luis Fernando Hernández-Moguel ◽  
Rafael Herrera
Keyword(s):  
Twistor Space ◽  
Complex Structure ◽  
Twistor Spaces ◽  
Recent Interest ◽  
Generalized Complex Structure ◽  
Generalized Complex ◽  
Space Construction ◽  
Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

scholarly journals Skew compact semigroups

2003 ◽  
Vol 4 (1) ◽  
pp. 133
Author(s):  
Ralph D. Kopperman ◽  
Desmond Robbie
Keyword(s):  
Continuous Semigroup ◽  
Minimal Ideal ◽  
Compact Semigroup ◽  
Closed Ideal ◽  
Hausdorff Spaces ◽  
Compact Spaces ◽  
Compact Semigroups ◽  
Compact Topology ◽  
Hausdorff Group ◽  
Non Hausdorff Spaces

<p>Skew compact spaces are the best behaving generalization of compact Hausdorff spaces to non-Hausdorff spaces. They are those (X ; τ ) such that there is another topology τ* on X for which τ V τ* is compact and (X; τ ; τ*) is pairwise Hausdorff; under these conditions, τ uniquely determines τ *, and (X; τ*) is also skew compact. Much of the theory of compact T<sub>2</sub> semigroups extends to this wider class. We show:</p> <p>A continuous skew compact semigroup is a semigroup with skew compact topology τ, such that the semigroup operation is continuous τ<sup>2</sup>→ τ. Each of these contains a unique minimal ideal which is an upper set with respect to the specialization order.</p> <p>A skew compact semigroup which is a continuous semigroup with respect to both topologies is called a de Groot semigroup. Given one of these, we show:</p> <p>It is a compact Hausdorff group if either the operation is cancellative, or there is a unique idempotent and S<sup>2</sup> = S.</p> <p>Its topology arises from its subinvariant quasimetrics.</p> <p>Each *-closed ideal ≠ S is contained in a proper open ideal.</p>

scholarly journals The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces

2019 ◽  
Vol 69 (1) ◽  
pp. 185-198
Author(s):  
Fadoua Chigr ◽  
Frédéric Mynard
Keyword(s):  
Space Structures ◽  
Theoretic Approach ◽  
Hausdorff Spaces ◽  
Sequential Space ◽  
Countable Space ◽  
The Stability ◽  
First Countable Space ◽  
Algebraic Proofs ◽  
Non Hausdorff Spaces

AbstractThis article fits in the context of the approach to topological problems in terms of the underlying convergence space structures, and serves as yet another illustration of the power of the method. More specifically, we spell out convergence-theoretic characterizations of the notions of weak base, weakly first-countable space, semi-metrizable space, and symmetrizable spaces. With the help of the already established similar characterizations of the notions of Frchet-Ursyohn, sequential, and accessibility spaces, we give a simple algebraic proof of a classical result regarding when a symmetrizable (respectively, weakly first-countable, respectively sequential) space is semi-metrizable (respectively first-countable, respectively Fréchet) that clarifies the situation for non-Hausdorff spaces. Using additionally known results on the commutation of the topologizer with product, we obtain simple algebraic proofs of various results of Y. Tanaka on the stability under product of symmetrizability and weak first-countability, and we obtain the same way a new characterization of spaces whose product with every metrizable topology is weakly first-countable, respectively symmetrizable.

scholarly journals Integrable Complex Structures on Twistor Spaces

2019 ◽  
Vol 70 (3) ◽  
pp. 937-963
Author(s):  
Steven Gindi
Keyword(s):  
Twistor Space ◽  
Complex Structures ◽  
Complex Manifolds ◽  
Twistor Spaces

Abstract We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case, we construct a metric and three compatible complex structures on the twistor space that have equal torsions.

scholarly journals A note on Baire spaces and continuous lattices

1980 ◽  
Vol 21 (2) ◽  
pp. 265-279 ◽  
Author(s):  
Karl H. Hofmann
Keyword(s):  
Spectral Theory ◽  
Baire Category ◽  
Baire Category Theorem ◽  
Hausdorff Spaces ◽  
Theoretical Methods ◽  
Category Theorem ◽  
Continuous Lattices ◽  
Non Hausdorff Spaces

We prove a Baire category theorem for continuous lattices and derive category theorems for non-Hausdorff spaces which imply a category theorem of Isbell's and have applications to the spectral theory of C*-algebras. The same lattice theoretical methods yield a proof of de Groot's category theorem for regular subcompact spaces.

scholarly journals Energy of sections of the Deligne–Hitchin twistor space

2020 ◽  
Author(s):  
Florian Beck ◽  
Sebastian Heller ◽  
Markus Röser
Keyword(s):  
Moduli Space ◽  
Compact Riemann Surface ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Energy Functional ◽  
Conformal Map ◽  
Twistor Spaces ◽  
Holomorphic Sections ◽  
Meromorphic Connection ◽  
Willmore Energy

Abstract We study a natural functional on the space of holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We show that the energy is the residue of the pull-back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. As a byproduct, we show the existence of a hyper-Kähler potentials for new components of real holomorphic sections of twistor spaces of hyper-Kähler manifolds with rotating $$S^1$$ S 1 -action. Additionally, we prove that for a certain class of real holomorphic sections of the Deligne–Hitchin moduli space, the energy functional is basically given by the Willmore energy of corresponding equivariant conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne–Hitchin moduli space from the space of twistor lines.

scholarly journals Complex Multiplication in Twistor Spaces

2020 ◽  
Author(s):  
D Huybrechts
Keyword(s):  
Twistor Space ◽  
Complex Multiplication ◽  
K3 Surface ◽  
Twistor Spaces ◽  
Arithmetic Properties ◽  
Twistor Construction

Abstract Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarised K3 surface with complex multiplication, all algebraic fibres of its twistor space away from the equator have complex multiplication as well.

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