Abstract
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the eld of analytic complex functions, the generic role of transformations by reciprocal radii in dimensions higher than two and their linearization in terms of polyspherical coordinates by Darboux, Weyl's attempt to extend General Relativity, the slow rise of nite dimensional conformal transformations in classical eld theories and the problem of their interpretation, then since about 1970 the rapid spread of their acceptance for asymptotic and structural problems in quantum eld theories and beyond, up to the current AdS=CFT conjecture. The occasion for the present article: hundred years ago Bateman and Cunningham discovered the form invariance of Maxwell's equations for electromagnetism with respect to conformal space-time transformations. (orig.)
Kastrup, H A
[1]
- Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
Citation Formats
Kastrup, H A.
On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics.
Germany: N. p.,
2008.
Web.
Kastrup, H A.
On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics.
Germany.
Kastrup, H A.
2008.
"On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics."
Germany.
@misc{etde_21084379,
title = {On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics}
author = {Kastrup, H A}
abstractNote = {The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the eld of analytic complex functions, the generic role of transformations by reciprocal radii in dimensions higher than two and their linearization in terms of polyspherical coordinates by Darboux, Weyl's attempt to extend General Relativity, the slow rise of nite dimensional conformal transformations in classical eld theories and the problem of their interpretation, then since about 1970 the rapid spread of their acceptance for asymptotic and structural problems in quantum eld theories and beyond, up to the current AdS=CFT conjecture. The occasion for the present article: hundred years ago Bateman and Cunningham discovered the form invariance of Maxwell's equations for electromagnetism with respect to conformal space-time transformations. (orig.)}
place = {Germany}
year = {2008}
month = {Aug}
}
title = {On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics}
author = {Kastrup, H A}
abstractNote = {The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the eld of analytic complex functions, the generic role of transformations by reciprocal radii in dimensions higher than two and their linearization in terms of polyspherical coordinates by Darboux, Weyl's attempt to extend General Relativity, the slow rise of nite dimensional conformal transformations in classical eld theories and the problem of their interpretation, then since about 1970 the rapid spread of their acceptance for asymptotic and structural problems in quantum eld theories and beyond, up to the current AdS=CFT conjecture. The occasion for the present article: hundred years ago Bateman and Cunningham discovered the form invariance of Maxwell's equations for electromagnetism with respect to conformal space-time transformations. (orig.)}
place = {Germany}
year = {2008}
month = {Aug}
}