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  • 1
    Electronic Resource
    Electronic Resource
    Classification of gauge groups in terms of algebraic structure of first class constraints (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2337-2344 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Properties of gauge transformations for singular Lagrangians are investigated to classify types of gauge groups. A general method of the classification is proposed based on properties of structure functions of the Poisson brackets (or the commutators) of first class constraints. A remarkable result is that the algebraic structure of the gauge group is essentially determined by the first class constraints of the final step of constraint series which are required successively from the stationarity conditions of the constraints. Owing to this consequence, the classification of gauge groups is made simple and transparent. The structure and property of the gauge group can be characterized in terms of the algebraic structure functions among the final step constraints and the number of the steps of the constraints series. The formulation proposed will give a clue to find new types of gauge groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528833
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  • 2
    Electronic Resource
    Electronic Resource
    Derivation of many-body potential among charged particles in the S-matrix method (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2303-2322 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general method of deriving a classical potential from the S-matrix element of particle scattering in the theory of quantized fields is applied to electrodynamics to the post-post-Coulombian approximation. To obtain the many-body potential, a consistent prescription is implemented in subtracting the contributions of the repetition of lower-order potential from the S-matrix elements of the higher-order diagrams. The result shows that the four-body potential between charged particles has a characteristic feature at a large distance and the two-body potential is identical with that given in the reduced Hamiltonian of Wheeler–Feynman electrodynamics. The advantage of the S-matrix method over the canonical formalism is to give the potential directly, without complicated treatment of the interaction with higher derivatives by a method of constrained dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529602
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  • 3
    Electronic Resource
    Electronic Resource
    Addendum to a dynamical formalism of singular Lagrangian system with higher derivatives (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3775-3779 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A formulation for singular Lagrangians with higher derivatives in a previous paper is supplemented and a complete formulation of canonical theory for the systems is presented. It is shown that our previous formulation reproduces all constraints included in the Ostrogradski transformations, by using stationarity conditions of primary constraints. Secondarily, on the effect of adding a total time derivative term to a nonsingular Lagrangian with higher derivatives, the previous paper is revised so as to give a correct formulation for counting the numbers of first and second class constraints. It is concluded that the main part of our previous formulation needs no essential change.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530058
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  • 4
    Electronic Resource
    Electronic Resource
    Canonical formalism of action-at-a-distance electrodynamics and many-particle potential among charged particles (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4655-4667 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The second post-Coulombian Lagrangian of Wheeler–Feynman electrodynamics for a many-particle system is treated according to a canonical formalism of a singular Lagrangian with higher derivatives. The canonical equations are given in terms of a reduced Hamiltonian with Dirac brackets, but they are transformed to be expressed in terms of ordinary Poisson brackets by redefinition of canonical variables. The reduced Hamiltonian includes a characteristic form of three-particle and four-particle potentials. Finally a direct pathway to the reduced Hamiltonian is presented via first-order formalism of the Maxwell theory with charged particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530363
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  • 5
    Electronic Resource
    Electronic Resource
    Kähler surfaces in ℙn given by holomorphic maps from ℙ1 to ℙn−2 (1994)
    Springer
    Archiv der Mathematik 63 (1994), S. 472-476 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01196679
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  • 6
    Electronic Resource
    Electronic Resource
    Geometric BRST quantization, I: Prequantization (1991)
    Springer
    Communications in mathematical physics 136 (1991), S. 209-229 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This is the first part of a two-part paper dedicated to the definition of BRST quantization in the framework of geometric quantization. After recognizing prequantization as a manifestation of the Poisson module structure of the sections of the prequantum line bundle, we define BRST prequantization and show that it is the homological analog of the symplectic reduction of prequantum data. We define a prequantum BRST cohomology theory and interpret it in terms of geometric objects. We then show that all Poisson structures correspond under homological reduction. This allows to prove, in the BRST context, that prequantization and reduction commute.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02100022
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  • 7
    Electronic Resource
    Electronic Resource
    Generalized classical BRST cohomology and reduction of Poisson manifolds (1993)
    Springer
    Communications in mathematical physics 151 (1993), S. 155-182 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a Poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, i.e. the case of reducible “first class” constraints. In particular, our procedure yields a method to deal with “second-class” constraints. We construct the BRST complex and compute its cohomology. BRST cohomology vanishes for negative dimension and is isomorphic as a Poisson algebra to the algebra of smooth functions on the reduced Poisson manifold in zero dimension. We then show that in the general case of reduction of Poisson manifolds, BRST cohomology cannot be identified with the cohomology of vertical differential forms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096751
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