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  • 1
    Electronic Resource
    Electronic Resource
    Erratum: "On characteristic equations, trace identities and Casimir operators of simple Lie algebras" [J. Math. Phys. 41, 3192–3225 (2000)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 977-977 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1337797
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  • 2
    Electronic Resource
    Electronic Resource
    Group theoretical foundations of fractional supersymmetry (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 1115-1127 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized Grassmann variable, θ=θ¯,θn=0, for arbitrary integer n=2,3,.... An explicit formula is given in the case of general n for the transformations that leave the theory invariant, and it is shown that these transformations possess interesting group properties. It is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group. Careful attention is paid to some technically important issues, including differentiation, that arise as a result of the peculiar nature of quantities such as θ. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531451
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  • 3
    Electronic Resource
    Electronic Resource
    On integrable models related to the osp(1,2) Gaudin algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3261-3272 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The osp(1,2) Gaudin algebra is defined and integrable models described by it are considered. The models include the osp(1,2) Gaudin magnet and the Dicke model related to it. Detailed discussion of the simplest cases of these models is presented. The effect of the presence of fermions on the separation of variables is indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530465
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  • 4
    Electronic Resource
    Electronic Resource
    On characteristic equations, trace identities and Casimir operators of simple Lie algebras (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 3192-3225 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as to be viable not only for "small" Lie algebras, but also to be suitable for treatment by computer algebra. A very large body of new results emerges in the forms of (a) identities of a tensorial nature, involving structure constants etc. of g, (b) trace identities for powers of matrices of the adjoint and defining representations of g, (c) expressions of nonprimitive Casimir operators of g in terms of primitive ones. The methods are sufficiently tractable to allow not only explicit proof by hand of the nonprimitive nature of the quartic Casimir of g2, f4, e6, but also, e.g., of that of the tenth order Casimir of f4. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533300
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  • 5
    Electronic Resource
    Electronic Resource
    Algebraic structure of parabose Fock space. I. The Green's ansatz revisited (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1054-1065 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green's ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green's ansatz of two (three) terms. Analogs of the form in which the parabose Green's ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530628
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  • 6
    Electronic Resource
    Electronic Resource
    Description of the symmetry groupSU 3/Z 3 of the octet model (1968)
    Springer
    Communications in mathematical physics 11 (1968), S. 91-98 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A study is made of the relationship ofS U 3 and its adjoint groupS U3/Z3 to the subgroup ofR8 which leaves invariant not only the lengtha i a i of a real eight component vectora i but also the cubic invariantd i j k a i a j a k ,d i j k being the totally symmetric isotropicS U3 tensor introduced byGell-Mann. A formula for the rotationR ε R8 corresponding toU ε S U3, and a formula inverse to this, which provides a way of parametrizingU ε S U3, are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01645898
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  • 7
    Electronic Resource
    Electronic Resource
    On Gell-Mann's λ-matrices,d- andf-tensors, octets, and parametrizations ofS U (3) (1968)
    Springer
    Communications in mathematical physics 11 (1968), S. 77-90 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The algebra ofS U (3) is developed on the basis of the matrices λ i ofGell-Mann, and identities involving the tensorsd i j k andf i j k occurring in their multiplication law are derived. Octets and the tensor analysis of the adjoint groupS U (3)/Z(3) ofS U (3) are discussed. Various explicit parametrizations ofS U (3) are presented as generalizations of familiarS U (2) results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01654302
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  • 8
    Electronic Resource
    Electronic Resource
    Dirac matrices and the Dirac matrix description of Lorentz transformations (1966)
    Springer
    Communications in mathematical physics 2 (1966), S. 133-146 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper gives what is believed to be a new discussion of Dirac matrices and of the Dirac matrix description of Lorentz transformations. The five anticommuting quantities γ J (J=1, 2, 3, 0, 5) are treated on an equal footing and recognition of the rule for expressing the three-fold product γ J γ K γ L in terms of one- and two-fold products and of invariant “five-space” tensorsg J K , ε J K I P Q allows all kinds of multiplication and trace laws for Dirac matrices to be derived systematically. The “five-space” formalism for Dirac matrices affords a very convenient vehicle for the Dirac matrix description of de Sitter transformations of a space with quadratic formg K L xHxL. By considering the subset of these which leave the coordinatex 5 invariant, the Dirac matrix description of Lorentz transformations is obtained. Not only does this description give the well-known formula for any Lorentz transformation matrixL in terms of the matrixS, which enters the transformation law of a Dirac spinor ψ(x) underL, it also gives an explicit and apparently new inverse formula expressingS in terms ofL.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01773348
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  • 9
    Electronic Resource
    Electronic Resource
    Tensor formulation of spin-1 and spin-2 fields (1972)
    Springer
    Communications in mathematical physics 24 (1972), S. 211-224 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Spin projection operators which constitute a resolution of the identity in the space of second rank tensor wave functions are constructed. These projectors are then used to establish Lagrangian quantum field theories for free massive particles with spin-1 (two equivalent formulations) and spin-2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01877713
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  • 10
    Electronic Resource
    Electronic Resource
    Point splitting in a curved space-time background: I. Gravitational contribution to the axial anomaly (1979)
    Springer
    General relativity and gravitation 10 (1979), S. 321-334 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A prescription is given for point splitting in a curved space-time background which is a natural generalization of that familiar in quantum electrodynamics and Yang-Mills theory. It is applied (to establish its validity) to the verification of the gravitational anomaly in the divergence of a fermion axial current. Notable features of the prescription are that it defines a point-split current that can be differentiated straightforwardly, and that it involves a natural way of averaging (four-dimensionally) over the directions of point splitting. The method can extend directly from the spin-1/2 fermion case treated to other cases, e.g., to spin-3/2 Rarita-Schwinger fermions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00759490
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