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  • 1
    Electronic Resource
    Electronic Resource
    On the symplectic structure of general relativity (1982)
    Springer
    Communications in mathematical physics 86 (1982), S. 55-68 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The relation between the symplectic structures on the canonical and radiative phase spaces of general relativity is exhibited.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205661
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  • 2
    Electronic Resource
    Electronic Resource
    SU(N) Quantum Yang–Mills theory in two dimensions: A complete solution (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5453-5482 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang–Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies R1×R1 and R1×S1. (For the U(1) theory, we also consider the S1×S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder–Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532146
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  • 3
    Electronic Resource
    Electronic Resource
    Quantization of diffeomorphism invariant theories of connections with local degrees of freedom (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 6456-6493 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphism constraint is solved. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions. This provides, in particular, a quantization of the Husain–Kuchar model. The main results also pave the way to quantization of other diffeomorphism invariant theories such as general relativity. In the Riemannian case (i.e., signature ++++), the approach appears to contain all the necessary ingredients already. In the Lorentzian case, it will have to be combined in an appropriate fashion with a coherent state transform to incorporate complex connections. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531252
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  • 4
    Electronic Resource
    Electronic Resource
    Projective techniques and functional integration for gauge theories (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 2170-2191 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used either in the Euclidean path integral approach or the Lorentzian canonical approach. A number of measures discussed are diffeomorphism invariant and therefore of interest to (the connection dynamics version of) quantum general relativity. The account is pedagogical; in particular, prior knowledge of projective techniques is not assumed. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531037
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  • 5
    Electronic Resource
    Electronic Resource
    Recent Developments in Quantum Gravity (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 571 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb50493.x
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  • 6
    Electronic Resource
    Electronic Resource
    A note on helicity and self-duality (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 824-827 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is pointed out that, even if restricted to only self-dual (or anti-self-dual) fields, photon and linearized graviton states of both helicities can be constructed by dropping the restriction to positive-frequency fields. Consequently, contrary to the usual belief, it may not be necessary to work with both self-dual and anti-self-dual fields to obtain the Hilbert space of all quantum states in full quantum gravity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527187
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  • 7
    Electronic Resource
    Electronic Resource
    Geometric quantization and constrained systems (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 1319-1330 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The problem of obtaining the quantum theory of systems with first class constraints is discussed in the context of geometric quantization. The precise structure needed on the constraint surface of the full phase space to obtain a polarization on the reduced phase space is displayed in a form that is particularly convenient for applications. For unconstrained systems, any polarization on the phase space leads to a mathematically consistent quantum description, although not all of these descriptions may be viable from a physical standpoint. It is pointed out that the situation is worse in the presence of constraints: a general polarization on the full phase space need not lead to even a mathematically consistent quantum theory. Examples are given to illustrate the general constructions as well as the subtle difficulties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527138
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  • 8
    Electronic Resource
    Electronic Resource
    An algebraic extension of Dirac quantization: Examples (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6434-6470 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of nonlinear, diffeomorphism invariant theories such as general relativity. Recently, an extension of the required type was proposed using algebraic quantization methods. In this paper, the key conceptual and technical aspects of the algebraic program are illustrated through a number of finite dimensional examples. The choice of examples and some of the analysis is motivated by certain peculiar problems endemic to quantum gravity. However, prior knowledge of general relativity is not assumed in the main discussion. Indeed, the methods introduced and conclusions arrived at are applicable to any system with first class constraints. In particular, they resolve certain technical issues which are present also in the reduced phase space approach to quantization of these systems. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530684
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  • 9
    Electronic Resource
    Electronic Resource
    Penrose's way with relativity (1985)
    [s.l.] : Nature Publishing Group
    Nature 313 (1985), S. 607-608 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] ALTHOUGH spinors were introduced by Elie Cartan about 70 years ago, their use in general relativity became common only rather recently. It is in fact easy to trace the history of this development. The first major event was the lecture by Roger Penrose, entitled "General Relativity in Spinor Form", ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/313607a0
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  • 10
    Electronic Resource
    Electronic Resource
    Framework for twistors (1986)
    [s.l.] : Nature Publishing Group
    Nature 322 (1986), S. 318-319 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] TWISTORS were invented by Roger Pen-rose about 20 years ago. Since then he and his research group have worked on the subject steadily and have built it into a thriving branch of mathematical physics. The goal of the twistor programme is very ambitious - first to recast and then further develop all ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/322318b0
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