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Search Results: 1 - 10 of 468032 matches for " P. S. Bisht "
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Generalized Gravi-Electromagnetism
P. S. Bisht,Gaurav Karnatak,O. P. S. Negi
Physics , 2010, DOI: 10.1007/s10773-010-0315-4
Abstract: A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80Hv
Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators
Pushpa,P. S. Bisht,Tianjun Li,O. P. S. Negi
Physics , 2012, DOI: 10.1007/s10773-012-1258-8
Abstract: An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are suitably handled with quaternions and octonions in order to obtain their generators, commutation rules and symmetry properties. Accordingly, Casimir operators for SU(2)and SU(3) flavor symmetries are also constructed for the proper testing of these symmetries in terms of quaternions and octonions.
Quaternion-Octonion SU(3) Flavor Symmetry
Pushpa,P. S. Bisht,Tianjun Li,O. P. S. Negi
Physics , 2011, DOI: 10.1007/s10773-011-1062-x
Abstract: Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interactions
Quaternion Octonion Reformulation of Quantum Chromodynamics
Pushpa,P. S. Bisht,Tianjun Li,O. P. S. Negi
Physics , 2010, DOI: 10.1007/s10773-010-0579-8
Abstract: We have made an attempt to develop the quaternionic formulation of Yang - Mill's field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang- Mill's field while the seven octonion units provide the consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics.
Generalized Octonion Electrodynamics
B. C. Chanyal,P. S. Bisht,O. P. S. Negi
Physics , 2009, DOI: 10.1007/s10773-010-0314-5
Abstract: We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion electrodynamics in manifestly covariant and consistent manner.
Quaternion Octonion Reformulation of Grand Unified Theories
Pushpa,P. S. Bisht,Tianjun Li,O. P. S. Negi
Physics , 2012, DOI: 10.1007/s10773-012-1204-9
Abstract: In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann \lambda matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5)gauge group. We have thus described the SU(5)gauge group and its subgroup SU(3)_{C}\times SU(2)_{L}\times U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.
Octonion and Split Octonion Representation of SO(8) Symmetry
Pushpa,P. S. Bisht,Tianjun Li,O. P. S. Negi
Physics , 2012,
Abstract: The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $\times$ 8 matrices are being used to describe the rotations in SO(8) symmetry. The comparison of 8$\times$8 matrices with octonions has also been shown. The transformations of SO(8) symmetry are represented with the help of Octonions and split Octonions spinors.
Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges
Pushpa,P. S. Bisht,O. P. S. Negi
Physics , 2010, DOI: 10.1007/s10773-011-0707-0
Abstract: Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2)_{e}\times SU(2)_{m}\times U(1)_{e}\times U(1)_{m} in terms of the simultaneous existence of electric and magnetic charges along with their Yang - Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four - gauge symmetry SU(2)_{e}\times SU(2)_{m}\times U(1)_{e}\times U(1)_{m}. Accordingly, we have made an attempt to obtain the abelian and non - Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)\times U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W^{\pm} and Z^{0} bosons fields and the Higgs scalar fields.
Generalized Split-Octonion Electrodynamics
B. C. Chanyal,P. S. Bisht,O. P. S. Negi
Physics , 2010, DOI: 10.1007/s10773-011-0706-1
Abstract: Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell's equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell's equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.
Generalised Split Octonions and their transformation in SO(7) symmetry
K. Pushpa,P. S. Bisht,O. P. S. Negi
Mathematics , 2013, DOI: 10.1007/s10773-014-2022-z
Abstract: Generators of SO(8) group have been described by using direct product of the Gamma matrices and the Pauli Sigma matrices. We have obtained these generators in terms of generalized split octonion also. These generators have been used to describe the rotational transformation of vectors for SO(7) symmetry group.
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