Field Theory

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K S Viswanathan - One of the best experts on this subject based on the ideXlab platform.

Wolfgang Muck - One of the best experts on this subject based on the ideXlab platform.

G Sardanashvily - One of the best experts on this subject based on the ideXlab platform.

  • covariant hamiltonian Field Theory path integral quantization
    International Journal of Theoretical Physics, 2004
    Co-Authors: D Bashkirov, G Sardanashvily
    Abstract:

    The Hamiltonian counterpart of classical Lagrangian Field Theory is covariant Hamiltonian Field Theory where momenta correspond to derivatives of Fields with respect to all world coordinates. In particular, classical Lagrangian and covariant Hamiltonian Field theories are equivalent in the case of a hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is almost-regular. In order to quantize covariant Hamiltonian Field Theory, one usually attempts to construct and quantize a multisymplectic generalization of the Poisson bracket. In the present work, the path integral quantization of covariant Hamiltonian Field Theory is suggested. We use the fact that a covariant Hamiltonian Field system is equivalent to a certain Lagrangian system on a phase space which is quantized in the framework of perturbative quantum Field Theory. We show that, in the case of almost-regular quadratic Lagrangians, path integral quantizations of associated Lagrangian and Hamiltonian Field systems are equivalent.

  • covariant hamiltonian Field Theory path integral quantization
    arXiv: High Energy Physics - Theory, 2004
    Co-Authors: D Bashkirov, G Sardanashvily
    Abstract:

    The Hamiltonian counterpart of classical Lagrangian Field Theory is covariant Hamiltonian Field Theory where momenta correspond to derivatives of Fields with respect to all world coordinates. In particular, classical Lagrangian and covariant Hamiltonian Field theories are equivalent in the case of a hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is almost-regular. In order to quantize covariant Hamiltonian Field Theory, one usually attempts to construct and quantize a multisymplectic generalization of the Poisson bracket. In the present work, the path integral quantization of covariant Hamiltonian Field Theory is suggested. We use the fact that a covariant Hamiltonian Field system is equivalent to a certain Lagrangian system on a phase space which is quantized in the framework of perturbative Field Theory. We show that, in the case of almost-regular quadratic Lagrangians, path integral quantizations of associated Lagrangian and Hamiltonian Field theories are equivalent.

  • connections in classical and quantum Field Theory
    2000
    Co-Authors: Luigi Mangiarotti, G Sardanashvily
    Abstract:

    Elementary gauge Theory geometry of fiber bundles geometric gauge Theory gravitation topological invariants in Field Theory jet bundle formalism Hamiltonian formalism in Field Theory infinite-dimensional bundles.

Ashoke Sen - One of the best experts on this subject based on the ideXlab platform.

Alexander Schmidt - One of the best experts on this subject based on the ideXlab platform.

  • tame class Field Theory for arithmetic schemes
    Inventiones Mathematicae, 2005
    Co-Authors: Alexander Schmidt
    Abstract:

    Takagi's class Field Theory gave a decription of the abelian extensions of a number Field $K$ in terms of ideal groups in $K$. In the 1980s, {\it K. Kato} and {\it S. Saito} [``Global class Field Theory of arithmetic schemes". Applications of algebraic K-Theory to algebraic geometry and number Theory, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Boulder/Colo. 1983, Part I, Contemp. Math. 55, 255--331 (1986; Zbl 0614.14001)] were able to generalize class Field Theory to higher dimensional Fields, and to describe their abelian extensions using a generalized idele class group whose definition is quite involved. In the case of unramified extensions, however, the class Fields can be described geometrically using Chow groups. For Fields of positive characteristic, a similarly geometric description for tamely ramified extensions was obtained by the author and {\it M.~Spiess} [J. Reine Angew. Math. 527, 13--36 (2000; Zbl 0961.14013)]. In this article, an analogous result is proved for the case of mixed characteristic.